TSTP Solution File: ITP221^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP221^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n026.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 03:21:12 EDT 2023
% Result : Theorem 106.83s 107.21s
% Output : Proof 106.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.50/2.54 % Problem : ITP221^3 : TPTP v8.1.2. Released v8.1.0.
% 2.54/2.54 % Command : do_cvc5 %s %d
% 2.54/2.76 % Computer : n026.cluster.edu
% 2.54/2.76 % Model : x86_64 x86_64
% 2.54/2.76 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.54/2.76 % Memory : 8042.1875MB
% 2.54/2.76 % OS : Linux 3.10.0-693.el7.x86_64
% 2.54/2.76 % CPULimit : 300
% 2.54/2.76 % WCLimit : 300
% 2.54/2.76 % DateTime : Sun Aug 27 16:04:36 EDT 2023
% 2.54/2.76 % CPUTime :
% 5.25/5.42 %----Proving TH0
% 5.25/5.43 %------------------------------------------------------------------------------
% 5.25/5.43 % File : ITP221^3 : TPTP v8.1.2. Released v8.1.0.
% 5.25/5.43 % Domain : Interactive Theorem Proving
% 5.25/5.43 % Problem : Sledgehammer problem VEBT_Definitions 00493_022399
% 5.25/5.43 % Version : [Des22] axioms.
% 5.25/5.43 % English :
% 5.25/5.43
% 5.25/5.43 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.25/5.43 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.25/5.43 % Source : [Des22]
% 5.25/5.43 % Names : 0063_VEBT_Definitions_00493_022399 [Des22]
% 5.25/5.43
% 5.25/5.43 % Status : Theorem
% 5.25/5.43 % Rating : 0.85 v8.1.0
% 5.25/5.43 % Syntax : Number of formulae : 11148 (6201 unt; 899 typ; 0 def)
% 5.25/5.43 % Number of atoms : 25899 (11696 equ; 0 cnn)
% 5.25/5.43 % Maximal formula atoms : 71 ( 2 avg)
% 5.25/5.43 % Number of connectives : 104223 (2335 ~; 517 |;1426 &;91503 @)
% 5.25/5.43 % ( 0 <=>;8442 =>; 0 <=; 0 <~>)
% 5.25/5.43 % Maximal formula depth : 39 ( 5 avg)
% 5.25/5.43 % Number of types : 85 ( 84 usr)
% 5.25/5.43 % Number of type conns : 2723 (2723 >; 0 *; 0 +; 0 <<)
% 5.25/5.43 % Number of symbols : 818 ( 815 usr; 57 con; 0-8 aty)
% 5.25/5.43 % Number of variables : 23152 (1825 ^;20748 !; 579 ?;23152 :)
% 5.25/5.43 % SPC : TH0_THM_EQU_NAR
% 5.25/5.43
% 5.25/5.43 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.25/5.43 % from the van Emde Boas Trees session in the Archive of Formal
% 5.25/5.43 % proofs -
% 5.25/5.43 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.25/5.43 % 2022-02-17 17:39:15.009
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% 5.25/5.43 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
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% 5.25/5.43 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
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% 5.25/5.43 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
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% 5.25/5.43 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
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% 5.25/5.43 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
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% 5.25/5.43 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
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% 5.25/5.43 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
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% 5.25/5.43 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
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% 5.25/5.43 thf(sy_c_Finite__Set_Ocard_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.25/5.43 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
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% 5.25/5.43 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
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% 5.25/5.43 ring_1_of_int_rat: int > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.25/5.43 ring_1_of_int_real: int > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Extended____Nat__Oenat,type,
% 5.25/5.43 inf_in1870772243966228564d_enat: extended_enat > extended_enat > extended_enat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Oinf__class_Oinf_001t__Nat__Onat,type,
% 5.25/5.43 inf_inf_nat: nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.25/5.43 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.25/5.43 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.25/5.43 sup_sup_nat: nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.25/5.43 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.25/5.43 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.25/5.43 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.25/5.43 at_infinity_real: filter_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.25/5.43 append_int: list_int > list_int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.25/5.43 append_nat: list_nat > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oconcat_001_Eo,type,
% 5.25/5.43 concat_o: list_list_o > list_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oconcat_001t__Int__Oint,type,
% 5.25/5.43 concat_int: list_list_int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oconcat_001t__Nat__Onat,type,
% 5.25/5.43 concat_nat: list_list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oconcat_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 concat_VEBT_VEBT: list_list_VEBT_VEBT > list_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 5.25/5.43 distinct_int: list_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 5.25/5.43 distinct_nat: list_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Odrop_001t__Nat__Onat,type,
% 5.25/5.43 drop_nat: nat > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olinorder__class_Osort__key_001t__Int__Oint_001t__Int__Oint,type,
% 5.25/5.43 linord1735203802627413978nt_int: ( int > int ) > list_int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olinorder__class_Osort__key_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.25/5.43 linord738340561235409698at_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.25/5.43 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.25/5.43 cons_int: int > list_int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.25/5.43 cons_nat: nat > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.25/5.43 nil_int: list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.25/5.43 nil_nat: list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Ohd_001t__Nat__Onat,type,
% 5.25/5.43 hd_nat: list_nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.25/5.43 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.25/5.43 set_o2: list_o > set_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.25/5.43 set_complex2: list_complex > set_complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.25/5.43 set_int2: list_int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__List__Olist_I_Eo_J,type,
% 5.25/5.43 set_list_o2: list_list_o > set_list_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Int__Oint_J,type,
% 5.25/5.43 set_list_int2: list_list_int > set_list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.43 set_list_nat2: list_list_nat > set_list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.43 set_list_VEBT_VEBT2: list_list_VEBT_VEBT > set_list_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.25/5.43 set_nat2: list_nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 set_Pr5648618587558075414at_nat: list_P6011104703257516679at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.25/5.43 set_real2: list_real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Olist_Otl_001t__Nat__Onat,type,
% 5.25/5.43 tl_nat: list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001_Eo,type,
% 5.25/5.43 nth_o: list_o > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Code____Numeral__Ointeger,type,
% 5.25/5.43 nth_Code_integer: list_Code_integer > nat > code_integer ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.25/5.43 nth_complex: list_complex > nat > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.25/5.43 nth_int: list_int > nat > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.43 nth_list_nat: list_list_nat > nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.25/5.43 nth_nat: list_nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Num__Onum,type,
% 5.25/5.43 nth_num: list_num > nat > num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.25/5.43 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.25/5.43 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.25/5.43 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.43 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.25/5.43 nth_Pr8522763379788166057eger_o: list_P8526636022914148096eger_o > nat > produc6271795597528267376eger_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 nth_Pr7617993195940197384at_nat: list_P6011104703257516679at_nat > nat > product_prod_nat_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.25/5.43 nth_Pr6456567536196504476um_num: list_P3744719386663036955um_num > nat > product_prod_num_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.25/5.43 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.25/5.43 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.25/5.43 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.43 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.25/5.43 nth_real: list_real > nat > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.25/5.43 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.25/5.43 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.25/5.43 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__Code____Numeral__Ointeger_001_Eo,type,
% 5.25/5.43 produc3607205314601156340eger_o: list_Code_integer > list_o > list_P8526636022914148096eger_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.25/5.43 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__Num__Onum_001t__Num__Onum,type,
% 5.25/5.43 product_num_num: list_num > list_num > list_P3744719386663036955um_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.25/5.43 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.25/5.43 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.25/5.43 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 5.25/5.43 remdups_nat: list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.25/5.43 replicate_o: nat > $o > list_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.25/5.43 replicate_complex: nat > complex > list_complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.25/5.43 replicate_int: nat > int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.25/5.43 replicate_nat: nat > nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 replic4235873036481779905at_nat: nat > product_prod_nat_nat > list_P6011104703257516679at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.25/5.43 replicate_real: nat > real > list_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osorted__wrt_001t__Int__Oint,type,
% 5.25/5.43 sorted_wrt_int: ( int > int > $o ) > list_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osorted__wrt_001t__Nat__Onat,type,
% 5.25/5.43 sorted_wrt_nat: ( nat > nat > $o ) > list_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osubseqs_001_Eo,type,
% 5.25/5.43 subseqs_o: list_o > list_list_o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osubseqs_001t__Int__Oint,type,
% 5.25/5.43 subseqs_int: list_int > list_list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osubseqs_001t__Nat__Onat,type,
% 5.25/5.43 subseqs_nat: list_nat > list_list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Osubseqs_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 subseqs_VEBT_VEBT: list_VEBT_VEBT > list_list_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Otake_001t__Nat__Onat,type,
% 5.25/5.43 take_nat: nat > list_nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oupt,type,
% 5.25/5.43 upt: nat > nat > list_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oupto,type,
% 5.25/5.43 upto: int > int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oupto__aux,type,
% 5.25/5.43 upto_aux: int > int > list_int > list_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_List_Oupto__rel,type,
% 5.25/5.43 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_OSuc,type,
% 5.25/5.43 suc: nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.25/5.43 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.25/5.43 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.25/5.43 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Onat_Opred,type,
% 5.25/5.43 pred: nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.25/5.43 semiri4939895301339042750nteger: nat > code_integer ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.25/5.43 semiri8010041392384452111omplex: nat > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.25/5.43 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.25/5.43 semiri1314217659103216013at_int: nat > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.25/5.43 semiri1316708129612266289at_nat: nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.25/5.43 semiri681578069525770553at_rat: nat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.25/5.43 semiri5074537144036343181t_real: nat > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Complex__Ocomplex,type,
% 5.25/5.43 semiri2816024913162550771omplex: ( complex > complex ) > nat > complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Int__Oint,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Nat__Onat,type,
% 5.25/5.43 semiri8422978514062236437ux_nat: ( nat > nat ) > nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Rat__Orat,type,
% 5.25/5.43 semiri7787848453975740701ux_rat: ( rat > rat ) > nat > rat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osemiring__1__class_Oof__nat__aux_001t__Real__Oreal,type,
% 5.25/5.43 semiri7260567687927622513x_real: ( real > real ) > nat > real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.25/5.43 size_size_list_o: list_o > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Code____Numeral__Ointeger_J,type,
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% 5.25/5.43
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_I_Eo_J_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Int__Oint_J_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__List__Olist_It__Nat__Onat_J_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Num__Onum_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.25/5.43 size_size_list_real: list_real > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.25/5.43 size_size_num: num > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.25/5.43 nat_list_encode: list_nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Oprod__encode,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Oset__decode,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Oset__encode,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.25/5.43 nat_triangle: nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_NthRoot_Oroot,type,
% 5.25/5.43 root: nat > real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_NthRoot_Osqrt,type,
% 5.25/5.43 sqrt: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_OBitM,type,
% 5.25/5.43 bitM: num > num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oinc,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.25/5.43 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.25/5.43 neg_nu7009210354673126013omplex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.25/5.43 neg_numeral_dbl_int: int > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.25/5.43 neg_numeral_dbl_rat: rat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.25/5.43 neg_numeral_dbl_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.25/5.43 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.25/5.43 neg_nu6511756317524482435omplex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.25/5.43 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.25/5.43 neg_nu6075765906172075777c_real: real > real ).
% 5.25/5.43
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.25/5.43 neg_nu8557863876264182079omplex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.25/5.43 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.25/5.43 neg_numeral_sub_int: num > num > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum_OBit0,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum_OBit1,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum_OOne,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum_Osize__num,type,
% 5.25/5.43 size_num: num > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Num_Onum__of__nat,type,
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% 5.25/5.43 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
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% 5.25/5.43
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% 5.25/5.43
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% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
% 5.25/5.43 image_2178119161166701260l_real: ( real > filter2146258269922977983l_real ) > set_real > set_fi7789364187291644575l_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.25/5.43 image_real_real: ( real > real ) > set_real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.25/5.43 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.25/5.43 insert_int: int > set_int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.25/5.43 insert_nat: nat > set_nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Complex__Ocomplex,type,
% 5.25/5.43 set_fo1517530859248394432omplex: ( nat > complex > complex ) > nat > nat > complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Int__Oint,type,
% 5.25/5.43 set_fo2581907887559384638at_int: ( nat > int > int ) > nat > nat > int > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
% 5.25/5.43 set_fo2584398358068434914at_nat: ( nat > nat > nat ) > nat > nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Rat__Orat,type,
% 5.25/5.43 set_fo1949268297981939178at_rat: ( nat > rat > rat ) > nat > nat > rat > rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Real__Oreal,type,
% 5.25/5.43 set_fo3111899725591712190t_real: ( nat > real > real ) > nat > nat > real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
% 5.25/5.43 set_or1266510415728281911st_int: int > int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
% 5.25/5.43 set_or1269000886237332187st_nat: nat > nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
% 5.25/5.43 set_or7049704709247886629st_num: num > num > set_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
% 5.25/5.43 set_or633870826150836451st_rat: rat > rat > set_rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
% 5.25/5.43 set_or1222579329274155063t_real: real > real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.43 set_or370866239135849197et_int: set_int > set_int > set_set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
% 5.25/5.43 set_or4662586982721622107an_int: int > int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
% 5.25/5.43 set_or4665077453230672383an_nat: nat > nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
% 5.25/5.43 set_ord_atLeast_nat: nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
% 5.25/5.43 set_ord_atLeast_real: real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
% 5.25/5.43 set_ord_atMost_int: int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
% 5.25/5.43 set_ord_atMost_nat: nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Num__Onum,type,
% 5.25/5.43 set_ord_atMost_num: num > set_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Rat__Orat,type,
% 5.25/5.43 set_ord_atMost_rat: rat > set_rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Real__Oreal,type,
% 5.25/5.43 set_ord_atMost_real: real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.43 set_or58775011639299419et_int: set_int > set_set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
% 5.25/5.43 set_or6656581121297822940st_int: int > int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
% 5.25/5.43 set_or6659071591806873216st_nat: nat > nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
% 5.25/5.43 set_or5832277885323065728an_int: int > int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
% 5.25/5.43 set_or5834768355832116004an_nat: nat > nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
% 5.25/5.43 set_or1633881224788618240n_real: real > real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
% 5.25/5.43 set_or1210151606488870762an_nat: nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
% 5.25/5.43 set_or5849166863359141190n_real: real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Int__Oint,type,
% 5.25/5.43 set_ord_lessThan_int: int > set_int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
% 5.25/5.43 set_ord_lessThan_nat: nat > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
% 5.25/5.43 set_ord_lessThan_num: num > set_num ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
% 5.25/5.43 set_ord_lessThan_rat: rat > set_rat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
% 5.25/5.43 set_or5984915006950818249n_real: real > set_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_String_Oascii__of,type,
% 5.25/5.43 ascii_of: char > char ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_String_Ochar_OChar,type,
% 5.25/5.43 char2: $o > $o > $o > $o > $o > $o > $o > $o > char ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_String_Ocomm__semiring__1__class_Oof__char_001t__Nat__Onat,type,
% 5.25/5.43 comm_s629917340098488124ar_nat: char > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_String_Ointeger__of__char,type,
% 5.25/5.43 integer_of_char: char > code_integer ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
% 5.25/5.43 unique3096191561947761185of_nat: nat > char ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ocontinuous_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.25/5.43 topolo4422821103128117721l_real: filter_real > ( real > real ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ocontinuous__on_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.25/5.43 topolo5044208981011980120l_real: set_real > ( real > real ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Int__Oint,type,
% 5.25/5.43 topolo4899668324122417113eq_int: ( nat > int ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Nat__Onat,type,
% 5.25/5.43 topolo4902158794631467389eq_nat: ( nat > nat ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Num__Onum,type,
% 5.25/5.43 topolo1459490580787246023eq_num: ( nat > num ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Rat__Orat,type,
% 5.25/5.43 topolo4267028734544971653eq_rat: ( nat > rat ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Real__Oreal,type,
% 5.25/5.43 topolo6980174941875973593q_real: ( nat > real ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Omonoseq_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.43 topolo3100542954746470799et_int: ( nat > set_int ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Otopological__space__class_Oat__within_001t__Real__Oreal,type,
% 5.25/5.43 topolo2177554685111907308n_real: real > set_real > filter_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.25/5.43 topolo2815343760600316023s_real: real > filter_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Complex__Ocomplex,type,
% 5.25/5.43 topolo6517432010174082258omplex: ( nat > complex ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.25/5.43 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.25/5.43 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.25/5.43 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oarccos,type,
% 5.25/5.43 arccos: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.25/5.43 arcosh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oarcsin,type,
% 5.25/5.43 arcsin: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oarctan,type,
% 5.25/5.43 arctan: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.25/5.43 arsinh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.25/5.43 artanh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocos_001t__Complex__Ocomplex,type,
% 5.25/5.43 cos_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.25/5.43 cos_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.25/5.43 cos_coeff: nat > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocosh_001t__Complex__Ocomplex,type,
% 5.25/5.43 cosh_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.25/5.43 cosh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocot_001t__Complex__Ocomplex,type,
% 5.25/5.43 cot_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.25/5.43 cot_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Odiffs_001t__Complex__Ocomplex,type,
% 5.25/5.43 diffs_complex: ( nat > complex ) > nat > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Odiffs_001t__Int__Oint,type,
% 5.25/5.43 diffs_int: ( nat > int ) > nat > int ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Odiffs_001t__Real__Oreal,type,
% 5.25/5.43 diffs_real: ( nat > real ) > nat > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.25/5.43 exp_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.25/5.43 exp_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.25/5.43 ln_ln_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Olog,type,
% 5.25/5.43 log: real > real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Opi,type,
% 5.25/5.43 pi: real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.25/5.43 powr_real: real > real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Osin_001t__Complex__Ocomplex,type,
% 5.25/5.43 sin_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.25/5.43 sin_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.25/5.43 sin_coeff: nat > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Osinh_001t__Complex__Ocomplex,type,
% 5.25/5.43 sinh_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.25/5.43 sinh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Otan_001t__Complex__Ocomplex,type,
% 5.25/5.43 tan_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.25/5.43 tan_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.25/5.43 tanh_complex: complex > complex ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.25/5.43 tanh_real: real > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transitive__Closure_Ortrancl_001t__Nat__Onat,type,
% 5.25/5.43 transi2905341329935302413cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Transitive__Closure_Otrancl_001t__Nat__Onat,type,
% 5.25/5.43 transi6264000038957366511cl_nat: set_Pr1261947904930325089at_nat > set_Pr1261947904930325089at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.25/5.43 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.25/5.43 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.25/5.43 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.25/5.43 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.25/5.43 vEBT_VEBT_high: nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.25/5.43 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.25/5.43 vEBT_VEBT_low: nat > nat > nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.25/5.43 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.25/5.43 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.25/5.43 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.25/5.43 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.25/5.43 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.25/5.43 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.25/5.43 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.25/5.43 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.25/5.43 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.25/5.43 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.43 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.25/5.43 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.25/5.43 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.25/5.43 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.25/5.43 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_Wellfounded_Opred__nat,type,
% 5.25/5.43 pred_nat: set_Pr1261947904930325089at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.25/5.43 fChoice_real: ( real > $o ) > real ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001_Eo,type,
% 5.25/5.43 member_o: $o > set_o > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Code____Numeral__Ointeger,type,
% 5.25/5.43 member_Code_integer: code_integer > set_Code_integer > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.25/5.43 member_complex: complex > set_complex > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Int__Oint,type,
% 5.25/5.43 member_int: int > set_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.25/5.43 member_list_o: list_o > set_list_o > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.25/5.43 member_list_int: list_int > set_list_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.25/5.43 member_list_nat: list_nat > set_list_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.25/5.43 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Nat__Onat,type,
% 5.25/5.43 member_nat: nat > set_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Num__Onum,type,
% 5.25/5.43 member_num: num > set_num > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.25/5.43 member8440522571783428010at_nat: product_prod_nat_nat > set_Pr1261947904930325089at_nat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Rat__Orat,type,
% 5.25/5.43 member_rat: rat > set_rat > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Real__Oreal,type,
% 5.25/5.43 member_real: real > set_real > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.25/5.43 member_set_int: set_int > set_set_int > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.25/5.43 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_deg,type,
% 5.25/5.43 deg: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_info,type,
% 5.25/5.43 info: option4927543243414619207at_nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_m____,type,
% 5.25/5.43 m: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_ma____,type,
% 5.25/5.43 ma: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_mi____,type,
% 5.25/5.43 mi: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_n,type,
% 5.25/5.43 n: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_na____,type,
% 5.25/5.43 na: nat ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_summary,type,
% 5.25/5.43 summary: vEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_treeList,type,
% 5.25/5.43 treeList: list_VEBT_VEBT ).
% 5.25/5.43
% 5.25/5.43 thf(sy_v_x,type,
% 5.25/5.43 x: nat ).
% 5.25/5.43
% 5.25/5.43 % Relevant facts (10210)
% 5.25/5.43 thf(fact_0_both__member__options__def,axiom,
% 5.25/5.43 ( vEBT_V8194947554948674370ptions
% 5.25/5.43 = ( ^ [T: vEBT_VEBT,X: nat] :
% 5.25/5.43 ( ( vEBT_V5719532721284313246member @ T @ X )
% 5.25/5.43 | ( vEBT_VEBT_membermima @ T @ X ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % both_member_options_def
% 5.25/5.43 thf(fact_1__092_060open_0621_A_060_Adeg_092_060close_062,axiom,
% 5.25/5.43 ord_less_nat @ one_one_nat @ deg ).
% 5.25/5.43
% 5.25/5.43 % \<open>1 < deg\<close>
% 5.25/5.43 thf(fact_2_VEBT_Oinject_I1_J,axiom,
% 5.25/5.43 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.25/5.43 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.25/5.43 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.25/5.43 = ( ( X11 = Y11 )
% 5.25/5.43 & ( X12 = Y12 )
% 5.25/5.43 & ( X13 = Y13 )
% 5.25/5.43 & ( X14 = Y14 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % VEBT.inject(1)
% 5.25/5.43 thf(fact_3__C5_Ohyps_C_I3_J,axiom,
% 5.25/5.43 ( ( summary
% 5.25/5.43 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 5.25/5.43 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(3)
% 5.25/5.43 thf(fact_4__C5_Ohyps_C_I2_J,axiom,
% 5.25/5.43 vEBT_invar_vebt @ summary @ m ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(2)
% 5.25/5.43 thf(fact_5_assms_I1_J,axiom,
% 5.25/5.43 vEBT_invar_vebt @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ n ).
% 5.25/5.43
% 5.25/5.43 % assms(1)
% 5.25/5.43 thf(fact_6_assms_I2_J,axiom,
% 5.25/5.43 ord_less_nat @ x @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.25/5.43
% 5.25/5.43 % assms(2)
% 5.25/5.43 thf(fact_7__092_060open_062naive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Anaive__member_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 5.25/5.43 ( ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.43 => ( vEBT_V5719532721284313246member @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 5.25/5.43
% 5.25/5.43 % \<open>naive_member (treeList ! high x (deg div 2)) (low x (deg div 2)) \<Longrightarrow> naive_member (Node info deg treeList summary) x\<close>
% 5.25/5.43 thf(fact_8__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060Longrightarrow_062_Amembermima_A_INode_Ainfo_Adeg_AtreeList_Asummary_J_Ax_092_060close_062,axiom,
% 5.25/5.43 ( ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.43 => ( vEBT_VEBT_membermima @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ).
% 5.25/5.43
% 5.25/5.43 % \<open>membermima (treeList ! high x (deg div 2)) (low x (deg div 2)) \<Longrightarrow> membermima (Node info deg treeList summary) x\<close>
% 5.25/5.43 thf(fact_9__092_060open_062high_Ax_A_Ideg_Adiv_A2_J_A_060_A2_A_094_Am_092_060close_062,axiom,
% 5.25/5.43 ord_less_nat @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ).
% 5.25/5.43
% 5.25/5.43 % \<open>high x (deg div 2) < 2 ^ m\<close>
% 5.25/5.43 thf(fact_10__092_060open_062membermima_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_A_092_060or_062_Anaive__member_A_ItreeList_A_B_Ahigh_Ax_A_Ideg_Adiv_A2_J_J_A_Ilow_Ax_A_Ideg_Adiv_A2_J_J_092_060close_062,axiom,
% 5.25/5.43 ( ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.43 | ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % \<open>membermima (treeList ! high x (deg div 2)) (low x (deg div 2)) \<or> naive_member (treeList ! high x (deg div 2)) (low x (deg div 2))\<close>
% 5.25/5.43 thf(fact_11_assms_I3_J,axiom,
% 5.25/5.43 vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ x @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % assms(3)
% 5.25/5.43 thf(fact_12__C5_Ohyps_C_I1_J,axiom,
% 5.25/5.43 ! [X2: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.25/5.43 => ( ( vEBT_invar_vebt @ X2 @ na )
% 5.25/5.43 & ( ( X2
% 5.25/5.43 = ( vEBT_Node @ info @ deg @ treeList @ summary ) )
% 5.25/5.43 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(1)
% 5.25/5.43 thf(fact_13__C5_Ohyps_C_I7_J,axiom,
% 5.25/5.43 ! [I: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.25/5.43 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ X3 ) )
% 5.25/5.43 = ( vEBT_V8194947554948674370ptions @ summary @ I ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(7)
% 5.25/5.43 thf(fact_14__C5_Ohyps_C_I6_J,axiom,
% 5.25/5.43 ( deg
% 5.25/5.43 = ( plus_plus_nat @ na @ m ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(6)
% 5.25/5.43 thf(fact_15__C5_Ohyps_C_I10_J,axiom,
% 5.25/5.43 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(10)
% 5.25/5.43 thf(fact_16_high__def,axiom,
% 5.25/5.43 ( vEBT_VEBT_high
% 5.25/5.43 = ( ^ [X: nat,N: nat] : ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % high_def
% 5.25/5.43 thf(fact_17_high__bound__aux,axiom,
% 5.25/5.43 ! [Ma: nat,N2: nat,M: nat] :
% 5.25/5.43 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) )
% 5.25/5.43 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % high_bound_aux
% 5.25/5.43 thf(fact_18__C5_Ohyps_C_I8_J,axiom,
% 5.25/5.43 ( ( mi = ma )
% 5.25/5.43 => ! [X2: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.25/5.43 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(8)
% 5.25/5.43 thf(fact_19__C5_Ohyps_C_I5_J,axiom,
% 5.25/5.43 ( m
% 5.25/5.43 = ( suc @ na ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(5)
% 5.25/5.43 thf(fact_20__C5_Ohyps_C_I4_J,axiom,
% 5.25/5.43 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.25/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(4)
% 5.25/5.43 thf(fact_21_in__children__def,axiom,
% 5.25/5.43 ( vEBT_V5917875025757280293ildren
% 5.25/5.43 = ( ^ [N: nat,TreeList: list_VEBT_VEBT,X: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X @ N ) ) @ ( vEBT_VEBT_low @ X @ N ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % in_children_def
% 5.25/5.43 thf(fact_22_add__self__div__2,axiom,
% 5.25/5.43 ! [M: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = M ) ).
% 5.25/5.43
% 5.25/5.43 % add_self_div_2
% 5.25/5.43 thf(fact_23__C5_Ohyps_C_I11_J,axiom,
% 5.25/5.43 ( ( mi != ma )
% 5.25/5.43 => ! [I: nat] :
% 5.25/5.43 ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.25/5.43 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.25/5.43 = I )
% 5.25/5.43 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.25/5.43 & ! [X2: nat] :
% 5.25/5.43 ( ( ( ( vEBT_VEBT_high @ X2 @ na )
% 5.25/5.43 = I )
% 5.25/5.43 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I ) @ ( vEBT_VEBT_low @ X2 @ na ) ) )
% 5.25/5.43 => ( ( ord_less_nat @ mi @ X2 )
% 5.25/5.43 & ( ord_less_eq_nat @ X2 @ ma ) ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(11)
% 5.25/5.43 thf(fact_24_one__add__one,axiom,
% 5.25/5.43 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.25/5.43 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_25_one__add__one,axiom,
% 5.25/5.43 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ one_on7984719198319812577d_enat )
% 5.25/5.43 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_26_one__add__one,axiom,
% 5.25/5.43 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_27_one__add__one,axiom,
% 5.25/5.43 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.25/5.43 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_28_one__add__one,axiom,
% 5.25/5.43 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.25/5.43 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_29_one__add__one,axiom,
% 5.25/5.43 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.25/5.43 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_add_one
% 5.25/5.43 thf(fact_30_power__strict__increasing__iff,axiom,
% 5.25/5.43 ! [B: real,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.43 => ( ( ord_less_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 5.25/5.43 = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_strict_increasing_iff
% 5.25/5.43 thf(fact_31_power__strict__increasing__iff,axiom,
% 5.25/5.43 ! [B: rat,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_rat @ one_one_rat @ B )
% 5.25/5.43 => ( ( ord_less_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 5.25/5.43 = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_strict_increasing_iff
% 5.25/5.43 thf(fact_32_power__strict__increasing__iff,axiom,
% 5.25/5.43 ! [B: nat,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_nat @ one_one_nat @ B )
% 5.25/5.43 => ( ( ord_less_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 5.25/5.43 = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_strict_increasing_iff
% 5.25/5.43 thf(fact_33_power__strict__increasing__iff,axiom,
% 5.25/5.43 ! [B: int,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_int @ one_one_int @ B )
% 5.25/5.43 => ( ( ord_less_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 5.25/5.43 = ( ord_less_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_strict_increasing_iff
% 5.25/5.43 thf(fact_34_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.25/5.43 = ( numeral_numeral_rat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_35_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 5.25/5.43 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_36_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ one_one_complex )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_37_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.25/5.43 = ( numeral_numeral_real @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_38_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.25/5.43 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_39_numeral__plus__one,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.25/5.43 = ( numeral_numeral_int @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_one
% 5.25/5.43 thf(fact_40_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_41_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_42_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_43_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_44_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_45_one__plus__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_plus_numeral
% 5.25/5.43 thf(fact_46_one__less__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ one @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_less_numeral_iff
% 5.25/5.43 thf(fact_47_one__less__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_le72135733267957522d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ one @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_less_numeral_iff
% 5.25/5.43 thf(fact_48_one__less__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ one @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_less_numeral_iff
% 5.25/5.43 thf(fact_49_one__less__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ one @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_less_numeral_iff
% 5.25/5.43 thf(fact_50_one__less__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ one @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_less_numeral_iff
% 5.25/5.43 thf(fact_51_power__inject__exp,axiom,
% 5.25/5.43 ! [A: real,M: nat,N2: nat] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.43 => ( ( ( power_power_real @ A @ M )
% 5.25/5.43 = ( power_power_real @ A @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_inject_exp
% 5.25/5.43 thf(fact_52_power__inject__exp,axiom,
% 5.25/5.43 ! [A: rat,M: nat,N2: nat] :
% 5.25/5.43 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.43 => ( ( ( power_power_rat @ A @ M )
% 5.25/5.43 = ( power_power_rat @ A @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_inject_exp
% 5.25/5.43 thf(fact_53_power__inject__exp,axiom,
% 5.25/5.43 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.43 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.43 => ( ( ( power_power_nat @ A @ M )
% 5.25/5.43 = ( power_power_nat @ A @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_inject_exp
% 5.25/5.43 thf(fact_54_power__inject__exp,axiom,
% 5.25/5.43 ! [A: int,M: nat,N2: nat] :
% 5.25/5.43 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.43 => ( ( ( power_power_int @ A @ M )
% 5.25/5.43 = ( power_power_int @ A @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_inject_exp
% 5.25/5.43 thf(fact_55_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_rat @ N2 )
% 5.25/5.43 = one_one_rat )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_56_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numera1916890842035813515d_enat @ N2 )
% 5.25/5.43 = one_on7984719198319812577d_enat )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_57_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numera6690914467698888265omplex @ N2 )
% 5.25/5.43 = one_one_complex )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_58_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_real @ N2 )
% 5.25/5.43 = one_one_real )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_59_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_nat @ N2 )
% 5.25/5.43 = one_one_nat )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_60_numeral__eq__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_int @ N2 )
% 5.25/5.43 = one_one_int )
% 5.25/5.43 = ( N2 = one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_one_iff
% 5.25/5.43 thf(fact_61_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_one_rat
% 5.25/5.43 = ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_62_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_on7984719198319812577d_enat
% 5.25/5.43 = ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_63_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_one_complex
% 5.25/5.43 = ( numera6690914467698888265omplex @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_64_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_one_real
% 5.25/5.43 = ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_65_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_one_nat
% 5.25/5.43 = ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_66_one__eq__numeral__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( one_one_int
% 5.25/5.43 = ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( one = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % one_eq_numeral_iff
% 5.25/5.43 thf(fact_67_div__exp__eq,axiom,
% 5.25/5.43 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.43 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_eq
% 5.25/5.43 thf(fact_68_div__exp__eq,axiom,
% 5.25/5.43 ! [A: int,M: nat,N2: nat] :
% 5.25/5.43 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.43 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_eq
% 5.25/5.43 thf(fact_69_div__exp__eq,axiom,
% 5.25/5.43 ! [A: code_integer,M: nat,N2: nat] :
% 5.25/5.43 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.43 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div_exp_eq
% 5.25/5.43 thf(fact_70_even__odd__cases,axiom,
% 5.25/5.43 ! [X4: nat] :
% 5.25/5.43 ( ! [N3: nat] :
% 5.25/5.43 ( X4
% 5.25/5.43 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.25/5.43 => ~ ! [N3: nat] :
% 5.25/5.43 ( X4
% 5.25/5.43 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % even_odd_cases
% 5.25/5.43 thf(fact_71__C5_Ohyps_C_I9_J,axiom,
% 5.25/5.43 ord_less_eq_nat @ mi @ ma ).
% 5.25/5.43
% 5.25/5.43 % "5.hyps"(9)
% 5.25/5.43 thf(fact_72_inthall,axiom,
% 5.25/5.43 ! [Xs: list_real,P: real > $o,N2: nat] :
% 5.25/5.43 ( ! [X5: real] :
% 5.25/5.43 ( ( member_real @ X5 @ ( set_real2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_real @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_73_inthall,axiom,
% 5.25/5.43 ! [Xs: list_complex,P: complex > $o,N2: nat] :
% 5.25/5.43 ( ! [X5: complex] :
% 5.25/5.43 ( ( member_complex @ X5 @ ( set_complex2 @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_complex @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_74_inthall,axiom,
% 5.25/5.43 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,N2: nat] :
% 5.25/5.43 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.43 ( ( member8440522571783428010at_nat @ X5 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.43 => ( P @ X5 ) )
% 5.25/5.43 => ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_75_inthall,axiom,
% 5.25/5.43 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N2: nat] :
% 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 => ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_76_inthall,axiom,
% 5.25/5.43 ! [Xs: list_o,P: $o > $o,N2: nat] :
% 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 => ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_77_inthall,axiom,
% 5.25/5.43 ! [Xs: list_nat,P: nat > $o,N2: nat] :
% 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 => ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_78_inthall,axiom,
% 5.25/5.43 ! [Xs: list_int,P: int > $o,N2: nat] :
% 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 => ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.43 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % inthall
% 5.25/5.43 thf(fact_79_numeral__eq__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ( numera1916890842035813515d_enat @ M )
% 5.25/5.43 = ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_iff
% 5.25/5.43 thf(fact_80_numeral__eq__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ( numera6690914467698888265omplex @ M )
% 5.25/5.43 = ( numera6690914467698888265omplex @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_iff
% 5.25/5.43 thf(fact_81_numeral__eq__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_real @ M )
% 5.25/5.43 = ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_iff
% 5.25/5.43 thf(fact_82_numeral__eq__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_nat @ M )
% 5.25/5.43 = ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_iff
% 5.25/5.43 thf(fact_83_numeral__eq__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ( numeral_numeral_int @ M )
% 5.25/5.43 = ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( M = N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_eq_iff
% 5.25/5.43 thf(fact_84_numeral__le__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_iff
% 5.25/5.43 thf(fact_85_numeral__le__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_iff
% 5.25/5.43 thf(fact_86_numeral__le__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_iff
% 5.25/5.43 thf(fact_87_numeral__le__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_iff
% 5.25/5.43 thf(fact_88_numeral__le__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_iff
% 5.25/5.43 thf(fact_89_bits__div__by__1,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % bits_div_by_1
% 5.25/5.43 thf(fact_90_bits__div__by__1,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( divide_divide_int @ A @ one_one_int )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % bits_div_by_1
% 5.25/5.43 thf(fact_91_bits__div__by__1,axiom,
% 5.25/5.43 ! [A: code_integer] :
% 5.25/5.43 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % bits_div_by_1
% 5.25/5.43 thf(fact_92_power__one,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( power_power_rat @ one_one_rat @ N2 )
% 5.25/5.43 = one_one_rat ) ).
% 5.25/5.43
% 5.25/5.43 % power_one
% 5.25/5.43 thf(fact_93_power__one,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( power_power_nat @ one_one_nat @ N2 )
% 5.25/5.43 = one_one_nat ) ).
% 5.25/5.43
% 5.25/5.43 % power_one
% 5.25/5.43 thf(fact_94_power__one,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( power_power_real @ one_one_real @ N2 )
% 5.25/5.43 = one_one_real ) ).
% 5.25/5.43
% 5.25/5.43 % power_one
% 5.25/5.43 thf(fact_95_power__one,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( power_power_int @ one_one_int @ N2 )
% 5.25/5.43 = one_one_int ) ).
% 5.25/5.43
% 5.25/5.43 % power_one
% 5.25/5.43 thf(fact_96_power__one,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( power_power_complex @ one_one_complex @ N2 )
% 5.25/5.43 = one_one_complex ) ).
% 5.25/5.43
% 5.25/5.43 % power_one
% 5.25/5.43 thf(fact_97_power__one__right,axiom,
% 5.25/5.43 ! [A: nat] :
% 5.25/5.43 ( ( power_power_nat @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % power_one_right
% 5.25/5.43 thf(fact_98_power__one__right,axiom,
% 5.25/5.43 ! [A: real] :
% 5.25/5.43 ( ( power_power_real @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % power_one_right
% 5.25/5.43 thf(fact_99_power__one__right,axiom,
% 5.25/5.43 ! [A: int] :
% 5.25/5.43 ( ( power_power_int @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % power_one_right
% 5.25/5.43 thf(fact_100_power__one__right,axiom,
% 5.25/5.43 ! [A: complex] :
% 5.25/5.43 ( ( power_power_complex @ A @ one_one_nat )
% 5.25/5.43 = A ) ).
% 5.25/5.43
% 5.25/5.43 % power_one_right
% 5.25/5.43 thf(fact_101_set__n__deg__not__0,axiom,
% 5.25/5.43 ! [TreeList2: list_VEBT_VEBT,N2: nat,M: nat] :
% 5.25/5.43 ( ! [X5: vEBT_VEBT] :
% 5.25/5.43 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.43 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.25/5.43 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.43 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.43 => ( ord_less_eq_nat @ one_one_nat @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % set_n_deg_not_0
% 5.25/5.43 thf(fact_102_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: rat] :
% 5.25/5.43 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.25/5.43 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_103_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: extended_enat] :
% 5.25/5.43 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 5.25/5.43 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_104_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: complex] :
% 5.25/5.43 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.25/5.43 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_105_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: real] :
% 5.25/5.43 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.25/5.43 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_106_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.25/5.43 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_107_add__numeral__left,axiom,
% 5.25/5.43 ! [V: num,W: num,Z: int] :
% 5.25/5.43 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.25/5.43 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_numeral_left
% 5.25/5.43 thf(fact_108_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: product_prod_nat_nat,P: product_prod_nat_nat > $o] :
% 5.25/5.43 ( ( member8440522571783428010at_nat @ A @ ( collec3392354462482085612at_nat @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_109_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: complex,P: complex > $o] :
% 5.25/5.43 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_110_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: real,P: real > $o] :
% 5.25/5.43 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_111_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: list_nat,P: list_nat > $o] :
% 5.25/5.43 ( ( member_list_nat @ A @ ( collect_list_nat @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_112_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: nat,P: nat > $o] :
% 5.25/5.43 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_113_mem__Collect__eq,axiom,
% 5.25/5.43 ! [A: int,P: int > $o] :
% 5.25/5.43 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.25/5.43 = ( P @ A ) ) ).
% 5.25/5.43
% 5.25/5.43 % mem_Collect_eq
% 5.25/5.43 thf(fact_114_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_Pr1261947904930325089at_nat] :
% 5.25/5.43 ( ( collec3392354462482085612at_nat
% 5.25/5.43 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_115_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_complex] :
% 5.25/5.43 ( ( collect_complex
% 5.25/5.43 @ ^ [X: complex] : ( member_complex @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_116_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_real] :
% 5.25/5.43 ( ( collect_real
% 5.25/5.43 @ ^ [X: real] : ( member_real @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_117_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_list_nat] :
% 5.25/5.43 ( ( collect_list_nat
% 5.25/5.43 @ ^ [X: list_nat] : ( member_list_nat @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_118_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_nat] :
% 5.25/5.43 ( ( collect_nat
% 5.25/5.43 @ ^ [X: nat] : ( member_nat @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_119_Collect__mem__eq,axiom,
% 5.25/5.43 ! [A2: set_int] :
% 5.25/5.43 ( ( collect_int
% 5.25/5.43 @ ^ [X: int] : ( member_int @ X @ A2 ) )
% 5.25/5.43 = A2 ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_mem_eq
% 5.25/5.43 thf(fact_120_Collect__cong,axiom,
% 5.25/5.43 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.43 ( ! [X5: complex] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 = ( Q @ X5 ) )
% 5.25/5.43 => ( ( collect_complex @ P )
% 5.25/5.43 = ( collect_complex @ Q ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_cong
% 5.25/5.43 thf(fact_121_Collect__cong,axiom,
% 5.25/5.43 ! [P: real > $o,Q: real > $o] :
% 5.25/5.43 ( ! [X5: real] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 = ( Q @ X5 ) )
% 5.25/5.43 => ( ( collect_real @ P )
% 5.25/5.43 = ( collect_real @ Q ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_cong
% 5.25/5.43 thf(fact_122_Collect__cong,axiom,
% 5.25/5.43 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.43 ( ! [X5: list_nat] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 = ( Q @ X5 ) )
% 5.25/5.43 => ( ( collect_list_nat @ P )
% 5.25/5.43 = ( collect_list_nat @ Q ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_cong
% 5.25/5.43 thf(fact_123_Collect__cong,axiom,
% 5.25/5.43 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.43 ( ! [X5: nat] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 = ( Q @ X5 ) )
% 5.25/5.43 => ( ( collect_nat @ P )
% 5.25/5.43 = ( collect_nat @ Q ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_cong
% 5.25/5.43 thf(fact_124_Collect__cong,axiom,
% 5.25/5.43 ! [P: int > $o,Q: int > $o] :
% 5.25/5.43 ( ! [X5: int] :
% 5.25/5.43 ( ( P @ X5 )
% 5.25/5.43 = ( Q @ X5 ) )
% 5.25/5.43 => ( ( collect_int @ P )
% 5.25/5.43 = ( collect_int @ Q ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Collect_cong
% 5.25/5.43 thf(fact_125_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_126_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( numera1916890842035813515d_enat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_127_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.25/5.43 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_128_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_129_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_130_numeral__plus__numeral,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_plus_numeral
% 5.25/5.43 thf(fact_131_numeral__less__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_less_iff
% 5.25/5.43 thf(fact_132_numeral__less__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_less_iff
% 5.25/5.43 thf(fact_133_numeral__less__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_less_iff
% 5.25/5.43 thf(fact_134_numeral__less__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_less_iff
% 5.25/5.43 thf(fact_135_numeral__less__iff,axiom,
% 5.25/5.43 ! [M: num,N2: num] :
% 5.25/5.43 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.43 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_less_iff
% 5.25/5.43 thf(fact_136_numeral__le__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat )
% 5.25/5.43 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_one_iff
% 5.25/5.43 thf(fact_137_numeral__le__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ one_one_real )
% 5.25/5.43 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_one_iff
% 5.25/5.43 thf(fact_138_numeral__le__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat )
% 5.25/5.43 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_one_iff
% 5.25/5.43 thf(fact_139_numeral__le__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat )
% 5.25/5.43 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_one_iff
% 5.25/5.43 thf(fact_140_numeral__le__one__iff,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ one_one_int )
% 5.25/5.43 = ( ord_less_eq_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % numeral_le_one_iff
% 5.25/5.43 thf(fact_141_Suc__numeral,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( suc @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.43 = ( numeral_numeral_nat @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_numeral
% 5.25/5.43 thf(fact_142_power__increasing__iff,axiom,
% 5.25/5.43 ! [B: real,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_real @ one_one_real @ B )
% 5.25/5.43 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X4 ) @ ( power_power_real @ B @ Y ) )
% 5.25/5.43 = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_increasing_iff
% 5.25/5.43 thf(fact_143_power__increasing__iff,axiom,
% 5.25/5.43 ! [B: rat,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_rat @ one_one_rat @ B )
% 5.25/5.43 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X4 ) @ ( power_power_rat @ B @ Y ) )
% 5.25/5.43 = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_increasing_iff
% 5.25/5.43 thf(fact_144_power__increasing__iff,axiom,
% 5.25/5.43 ! [B: nat,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_nat @ one_one_nat @ B )
% 5.25/5.43 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X4 ) @ ( power_power_nat @ B @ Y ) )
% 5.25/5.43 = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_increasing_iff
% 5.25/5.43 thf(fact_145_power__increasing__iff,axiom,
% 5.25/5.43 ! [B: int,X4: nat,Y: nat] :
% 5.25/5.43 ( ( ord_less_int @ one_one_int @ B )
% 5.25/5.43 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X4 ) @ ( power_power_int @ B @ Y ) )
% 5.25/5.43 = ( ord_less_eq_nat @ X4 @ Y ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % power_increasing_iff
% 5.25/5.43 thf(fact_146_add__2__eq__Suc_H,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_2_eq_Suc'
% 5.25/5.43 thf(fact_147_add__2__eq__Suc,axiom,
% 5.25/5.43 ! [N2: nat] :
% 5.25/5.43 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.43 = ( suc @ ( suc @ N2 ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_2_eq_Suc
% 5.25/5.43 thf(fact_148_Suc__1,axiom,
% 5.25/5.43 ( ( suc @ one_one_nat )
% 5.25/5.43 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_1
% 5.25/5.43 thf(fact_149_div2__Suc__Suc,axiom,
% 5.25/5.43 ! [M: nat] :
% 5.25/5.43 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.43 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.43
% 5.25/5.43 % div2_Suc_Suc
% 5.25/5.43 thf(fact_150_Suc__div__le__mono,axiom,
% 5.25/5.43 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ ( divide_divide_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.43
% 5.25/5.43 % Suc_div_le_mono
% 5.25/5.43 thf(fact_151_add__One__commute,axiom,
% 5.25/5.43 ! [N2: num] :
% 5.25/5.43 ( ( plus_plus_num @ one @ N2 )
% 5.25/5.43 = ( plus_plus_num @ N2 @ one ) ) ).
% 5.25/5.43
% 5.25/5.43 % add_One_commute
% 5.25/5.43 thf(fact_152_le__numeral__extra_I4_J,axiom,
% 5.25/5.43 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.25/5.43
% 5.25/5.43 % le_numeral_extra(4)
% 5.25/5.43 thf(fact_153_le__numeral__extra_I4_J,axiom,
% 5.25/5.44 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(4)
% 5.25/5.44 thf(fact_154_le__numeral__extra_I4_J,axiom,
% 5.25/5.44 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(4)
% 5.25/5.44 thf(fact_155_le__numeral__extra_I4_J,axiom,
% 5.25/5.44 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.25/5.44
% 5.25/5.44 % le_numeral_extra(4)
% 5.25/5.44 thf(fact_156_div__le__dividend,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ).
% 5.25/5.44
% 5.25/5.44 % div_le_dividend
% 5.25/5.44 thf(fact_157_div__le__mono,axiom,
% 5.25/5.44 ! [M: nat,N2: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N2 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_le_mono
% 5.25/5.44 thf(fact_158_power__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: real] :
% 5.25/5.44 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.44 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_increasing
% 5.25/5.44 thf(fact_159_power__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: rat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_increasing
% 5.25/5.44 thf(fact_160_power__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_increasing
% 5.25/5.44 thf(fact_161_power__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: int] :
% 5.25/5.44 ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.44 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_increasing
% 5.25/5.44 thf(fact_162_power__le__imp__le__exp,axiom,
% 5.25/5.44 ! [A: real,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.44 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_le_imp_le_exp
% 5.25/5.44 thf(fact_163_power__le__imp__le__exp,axiom,
% 5.25/5.44 ! [A: rat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_le_imp_le_exp
% 5.25/5.44 thf(fact_164_power__le__imp__le__exp,axiom,
% 5.25/5.44 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_le_imp_le_exp
% 5.25/5.44 thf(fact_165_power__le__imp__le__exp,axiom,
% 5.25/5.44 ! [A: int,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.44 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_le_imp_le_exp
% 5.25/5.44 thf(fact_166_Suc__nat__number__of__add,axiom,
% 5.25/5.44 ! [V: num,N2: nat] :
% 5.25/5.44 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N2 ) )
% 5.25/5.44 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_nat_number_of_add
% 5.25/5.44 thf(fact_167_one__le__numeral,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_le2932123472753598470d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_numeral
% 5.25/5.44 thf(fact_168_one__le__numeral,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_numeral
% 5.25/5.44 thf(fact_169_one__le__numeral,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_numeral
% 5.25/5.44 thf(fact_170_one__le__numeral,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_numeral
% 5.25/5.44 thf(fact_171_one__le__numeral,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_numeral
% 5.25/5.44 thf(fact_172_one__le__power,axiom,
% 5.25/5.44 ! [A: real,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.44 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_power
% 5.25/5.44 thf(fact_173_one__le__power,axiom,
% 5.25/5.44 ! [A: rat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_power
% 5.25/5.44 thf(fact_174_one__le__power,axiom,
% 5.25/5.44 ! [A: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_power
% 5.25/5.44 thf(fact_175_one__le__power,axiom,
% 5.25/5.44 ! [A: int,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.44 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_le_power
% 5.25/5.44 thf(fact_176_power__gt1,axiom,
% 5.25/5.44 ! [A: real,N2: nat] :
% 5.25/5.44 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.44 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_gt1
% 5.25/5.44 thf(fact_177_power__gt1,axiom,
% 5.25/5.44 ! [A: rat,N2: nat] :
% 5.25/5.44 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_gt1
% 5.25/5.44 thf(fact_178_power__gt1,axiom,
% 5.25/5.44 ! [A: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_gt1
% 5.25/5.44 thf(fact_179_power__gt1,axiom,
% 5.25/5.44 ! [A: int,N2: nat] :
% 5.25/5.44 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.44 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_gt1
% 5.25/5.44 thf(fact_180_power2__nat__le__imp__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_nat_le_imp_le
% 5.25/5.44 thf(fact_181_power2__nat__le__eq__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % power2_nat_le_eq_le
% 5.25/5.44 thf(fact_182_self__le__ge2__pow,axiom,
% 5.25/5.44 ! [K: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % self_le_ge2_pow
% 5.25/5.44 thf(fact_183_is__num__normalize_I1_J,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % is_num_normalize(1)
% 5.25/5.44 thf(fact_184_is__num__normalize_I1_J,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % is_num_normalize(1)
% 5.25/5.44 thf(fact_185_is__num__normalize_I1_J,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % is_num_normalize(1)
% 5.25/5.44 thf(fact_186_ex__power__ivl2,axiom,
% 5.25/5.44 ! [B: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.44 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.25/5.44 => ? [N3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.25/5.44 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ex_power_ivl2
% 5.25/5.44 thf(fact_187_ex__power__ivl1,axiom,
% 5.25/5.44 ! [B: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.25/5.44 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.25/5.44 => ? [N3: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.25/5.44 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ex_power_ivl1
% 5.25/5.44 thf(fact_188_less__numeral__extra_I4_J,axiom,
% 5.25/5.44 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(4)
% 5.25/5.44 thf(fact_189_less__numeral__extra_I4_J,axiom,
% 5.25/5.44 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(4)
% 5.25/5.44 thf(fact_190_less__numeral__extra_I4_J,axiom,
% 5.25/5.44 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(4)
% 5.25/5.44 thf(fact_191_less__numeral__extra_I4_J,axiom,
% 5.25/5.44 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % less_numeral_extra(4)
% 5.25/5.44 thf(fact_192_power__divide,axiom,
% 5.25/5.44 ! [A: real,B: real,N2: nat] :
% 5.25/5.44 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N2 )
% 5.25/5.44 = ( divide_divide_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_divide
% 5.25/5.44 thf(fact_193_power__divide,axiom,
% 5.25/5.44 ! [A: complex,B: complex,N2: nat] :
% 5.25/5.44 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N2 )
% 5.25/5.44 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_divide
% 5.25/5.44 thf(fact_194_not__numeral__less__one,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ one_one_rat ) ).
% 5.25/5.44
% 5.25/5.44 % not_numeral_less_one
% 5.25/5.44 thf(fact_195_not__numeral__less__one,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ).
% 5.25/5.44
% 5.25/5.44 % not_numeral_less_one
% 5.25/5.44 thf(fact_196_not__numeral__less__one,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ one_one_real ) ).
% 5.25/5.44
% 5.25/5.44 % not_numeral_less_one
% 5.25/5.44 thf(fact_197_not__numeral__less__one,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % not_numeral_less_one
% 5.25/5.44 thf(fact_198_not__numeral__less__one,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % not_numeral_less_one
% 5.25/5.44 thf(fact_199_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X4 ) )
% 5.25/5.44 = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_200_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_p3455044024723400733d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X4 ) )
% 5.25/5.44 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_201_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X4 ) )
% 5.25/5.44 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_202_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X4 ) )
% 5.25/5.44 = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_203_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X4 ) )
% 5.25/5.44 = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_204_one__plus__numeral__commute,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X4 ) )
% 5.25/5.44 = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_plus_numeral_commute
% 5.25/5.44 thf(fact_205_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_206_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_207_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_208_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_209_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_210_numeral__Bit0,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0
% 5.25/5.44 thf(fact_211_numeral__One,axiom,
% 5.25/5.44 ( ( numeral_numeral_rat @ one )
% 5.25/5.44 = one_one_rat ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_212_numeral__One,axiom,
% 5.25/5.44 ( ( numera1916890842035813515d_enat @ one )
% 5.25/5.44 = one_on7984719198319812577d_enat ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_213_numeral__One,axiom,
% 5.25/5.44 ( ( numera6690914467698888265omplex @ one )
% 5.25/5.44 = one_one_complex ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_214_numeral__One,axiom,
% 5.25/5.44 ( ( numeral_numeral_real @ one )
% 5.25/5.44 = one_one_real ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_215_numeral__One,axiom,
% 5.25/5.44 ( ( numeral_numeral_nat @ one )
% 5.25/5.44 = one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_216_numeral__One,axiom,
% 5.25/5.44 ( ( numeral_numeral_int @ one )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_One
% 5.25/5.44 thf(fact_217_divide__numeral__1,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % divide_numeral_1
% 5.25/5.44 thf(fact_218_divide__numeral__1,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % divide_numeral_1
% 5.25/5.44 thf(fact_219_power__one__over,axiom,
% 5.25/5.44 ! [A: rat,N2: nat] :
% 5.25/5.44 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N2 )
% 5.25/5.44 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_one_over
% 5.25/5.44 thf(fact_220_power__one__over,axiom,
% 5.25/5.44 ! [A: real,N2: nat] :
% 5.25/5.44 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N2 )
% 5.25/5.44 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_one_over
% 5.25/5.44 thf(fact_221_power__one__over,axiom,
% 5.25/5.44 ! [A: complex,N2: nat] :
% 5.25/5.44 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N2 )
% 5.25/5.44 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_one_over
% 5.25/5.44 thf(fact_222_numerals_I1_J,axiom,
% 5.25/5.44 ( ( numeral_numeral_nat @ one )
% 5.25/5.44 = one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % numerals(1)
% 5.25/5.44 thf(fact_223_numeral__Bit0__div__2,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0_div_2
% 5.25/5.44 thf(fact_224_numeral__Bit0__div__2,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( numeral_numeral_int @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0_div_2
% 5.25/5.44 thf(fact_225_numeral__Bit0__div__2,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % numeral_Bit0_div_2
% 5.25/5.44 thf(fact_226_power__strict__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: real] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.44 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_increasing
% 5.25/5.44 thf(fact_227_power__strict__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: rat] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_increasing
% 5.25/5.44 thf(fact_228_power__strict__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: nat] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_increasing
% 5.25/5.44 thf(fact_229_power__strict__increasing,axiom,
% 5.25/5.44 ! [N2: nat,N4: nat,A: int] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ N4 )
% 5.25/5.44 => ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.44 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_strict_increasing
% 5.25/5.44 thf(fact_230_power__less__imp__less__exp,axiom,
% 5.25/5.44 ! [A: real,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.44 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_less_imp_less_exp
% 5.25/5.44 thf(fact_231_power__less__imp__less__exp,axiom,
% 5.25/5.44 ! [A: rat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.44 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_less_imp_less_exp
% 5.25/5.44 thf(fact_232_power__less__imp__less__exp,axiom,
% 5.25/5.44 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.44 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_less_imp_less_exp
% 5.25/5.44 thf(fact_233_power__less__imp__less__exp,axiom,
% 5.25/5.44 ! [A: int,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.44 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_less_imp_less_exp
% 5.25/5.44 thf(fact_234_one__power2,axiom,
% 5.25/5.44 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_rat ) ).
% 5.25/5.44
% 5.25/5.44 % one_power2
% 5.25/5.44 thf(fact_235_one__power2,axiom,
% 5.25/5.44 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % one_power2
% 5.25/5.44 thf(fact_236_one__power2,axiom,
% 5.25/5.44 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_real ) ).
% 5.25/5.44
% 5.25/5.44 % one_power2
% 5.25/5.44 thf(fact_237_one__power2,axiom,
% 5.25/5.44 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % one_power2
% 5.25/5.44 thf(fact_238_one__power2,axiom,
% 5.25/5.44 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_complex ) ).
% 5.25/5.44
% 5.25/5.44 % one_power2
% 5.25/5.44 thf(fact_239_nat__1__add__1,axiom,
% 5.25/5.44 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.25/5.44 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_1_add_1
% 5.25/5.44 thf(fact_240_less__exp,axiom,
% 5.25/5.44 ! [N2: nat] : ( ord_less_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_exp
% 5.25/5.44 thf(fact_241_semiring__norm_I76_J,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_num @ one @ ( bit0 @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(76)
% 5.25/5.44 thf(fact_242_semiring__norm_I2_J,axiom,
% 5.25/5.44 ( ( plus_plus_num @ one @ one )
% 5.25/5.44 = ( bit0 @ one ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(2)
% 5.25/5.44 thf(fact_243_field__less__half__sum,axiom,
% 5.25/5.44 ! [X4: rat,Y: rat] :
% 5.25/5.44 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.44 => ( ord_less_rat @ X4 @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % field_less_half_sum
% 5.25/5.44 thf(fact_244_field__less__half__sum,axiom,
% 5.25/5.44 ! [X4: real,Y: real] :
% 5.25/5.44 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.44 => ( ord_less_real @ X4 @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % field_less_half_sum
% 5.25/5.44 thf(fact_245_semiring__norm_I75_J,axiom,
% 5.25/5.44 ! [M: num] :
% 5.25/5.44 ~ ( ord_less_num @ M @ one ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(75)
% 5.25/5.44 thf(fact_246_semiring__norm_I78_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( ord_less_num @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(78)
% 5.25/5.44 thf(fact_247_semiring__norm_I6_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( bit0 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(6)
% 5.25/5.44 thf(fact_248_nat__add__left__cancel__le,axiom,
% 5.25/5.44 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.25/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_add_left_cancel_le
% 5.25/5.44 thf(fact_249_nat__add__left__cancel__less,axiom,
% 5.25/5.44 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.25/5.44 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_add_left_cancel_less
% 5.25/5.44 thf(fact_250_add__Suc__right,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_Suc_right
% 5.25/5.44 thf(fact_251_enat__ord__number_I2_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.44 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % enat_ord_number(2)
% 5.25/5.44 thf(fact_252_Suc__le__mono,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( suc @ M ) )
% 5.25/5.44 = ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_le_mono
% 5.25/5.44 thf(fact_253_Suc__less__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.25/5.44 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_less_eq
% 5.25/5.44 thf(fact_254_semiring__norm_I87_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( ( bit0 @ M )
% 5.25/5.44 = ( bit0 @ N2 ) )
% 5.25/5.44 = ( M = N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(87)
% 5.25/5.44 thf(fact_255_nat_Oinject,axiom,
% 5.25/5.44 ! [X22: nat,Y2: nat] :
% 5.25/5.44 ( ( ( suc @ X22 )
% 5.25/5.44 = ( suc @ Y2 ) )
% 5.25/5.44 = ( X22 = Y2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat.inject
% 5.25/5.44 thf(fact_256_old_Onat_Oinject,axiom,
% 5.25/5.44 ! [Nat: nat,Nat2: nat] :
% 5.25/5.44 ( ( ( suc @ Nat )
% 5.25/5.44 = ( suc @ Nat2 ) )
% 5.25/5.44 = ( Nat = Nat2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % old.nat.inject
% 5.25/5.44 thf(fact_257_semiring__norm_I85_J,axiom,
% 5.25/5.44 ! [M: num] :
% 5.25/5.44 ( ( bit0 @ M )
% 5.25/5.44 != one ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(85)
% 5.25/5.44 thf(fact_258_semiring__norm_I83_J,axiom,
% 5.25/5.44 ! [N2: num] :
% 5.25/5.44 ( one
% 5.25/5.44 != ( bit0 @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(83)
% 5.25/5.44 thf(fact_259_lessI,axiom,
% 5.25/5.44 ! [N2: nat] : ( ord_less_nat @ N2 @ ( suc @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % lessI
% 5.25/5.44 thf(fact_260_Suc__mono,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_mono
% 5.25/5.44 thf(fact_261_semiring__norm_I71_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.25/5.44 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(71)
% 5.25/5.44 thf(fact_262_semiring__norm_I68_J,axiom,
% 5.25/5.44 ! [N2: num] : ( ord_less_eq_num @ one @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(68)
% 5.25/5.44 thf(fact_263_semiring__norm_I69_J,axiom,
% 5.25/5.44 ! [M: num] :
% 5.25/5.44 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.25/5.44
% 5.25/5.44 % semiring_norm(69)
% 5.25/5.44 thf(fact_264_enat__ord__number_I1_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.44 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % enat_ord_number(1)
% 5.25/5.44 thf(fact_265_enat__less__induct,axiom,
% 5.25/5.44 ! [P: extended_enat > $o,N2: extended_enat] :
% 5.25/5.44 ( ! [N3: extended_enat] :
% 5.25/5.44 ( ! [M2: extended_enat] :
% 5.25/5.44 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 5.25/5.44 => ( P @ M2 ) )
% 5.25/5.44 => ( P @ N3 ) )
% 5.25/5.44 => ( P @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % enat_less_induct
% 5.25/5.44 thf(fact_266_le__num__One__iff,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( ord_less_eq_num @ X4 @ one )
% 5.25/5.44 = ( X4 = one ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_num_One_iff
% 5.25/5.44 thf(fact_267_two__realpow__ge__one,axiom,
% 5.25/5.44 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % two_realpow_ge_one
% 5.25/5.44 thf(fact_268_Suc__inject,axiom,
% 5.25/5.44 ! [X4: nat,Y: nat] :
% 5.25/5.44 ( ( ( suc @ X4 )
% 5.25/5.44 = ( suc @ Y ) )
% 5.25/5.44 => ( X4 = Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_inject
% 5.25/5.44 thf(fact_269_n__not__Suc__n,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ( N2
% 5.25/5.44 != ( suc @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % n_not_Suc_n
% 5.25/5.44 thf(fact_270_nat__neq__iff,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( M != N2 )
% 5.25/5.44 = ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 | ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_neq_iff
% 5.25/5.44 thf(fact_271_less__not__refl,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % less_not_refl
% 5.25/5.44 thf(fact_272_less__not__refl2,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ M )
% 5.25/5.44 => ( M != N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_not_refl2
% 5.25/5.44 thf(fact_273_less__not__refl3,axiom,
% 5.25/5.44 ! [S: nat,T2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ S @ T2 )
% 5.25/5.44 => ( S != T2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_not_refl3
% 5.25/5.44 thf(fact_274_less__irrefl__nat,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ~ ( ord_less_nat @ N2 @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % less_irrefl_nat
% 5.25/5.44 thf(fact_275_nat__less__induct,axiom,
% 5.25/5.44 ! [P: nat > $o,N2: nat] :
% 5.25/5.44 ( ! [N3: nat] :
% 5.25/5.44 ( ! [M2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M2 @ N3 )
% 5.25/5.44 => ( P @ M2 ) )
% 5.25/5.44 => ( P @ N3 ) )
% 5.25/5.44 => ( P @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_less_induct
% 5.25/5.44 thf(fact_276_infinite__descent,axiom,
% 5.25/5.44 ! [P: nat > $o,N2: nat] :
% 5.25/5.44 ( ! [N3: nat] :
% 5.25/5.44 ( ~ ( P @ N3 )
% 5.25/5.44 => ? [M2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M2 @ N3 )
% 5.25/5.44 & ~ ( P @ M2 ) ) )
% 5.25/5.44 => ( P @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % infinite_descent
% 5.25/5.44 thf(fact_277_linorder__neqE__nat,axiom,
% 5.25/5.44 ! [X4: nat,Y: nat] :
% 5.25/5.44 ( ( X4 != Y )
% 5.25/5.44 => ( ~ ( ord_less_nat @ X4 @ Y )
% 5.25/5.44 => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % linorder_neqE_nat
% 5.25/5.44 thf(fact_278_le__refl,axiom,
% 5.25/5.44 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % le_refl
% 5.25/5.44 thf(fact_279_le__trans,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ( ord_less_eq_nat @ J @ K )
% 5.25/5.44 => ( ord_less_eq_nat @ I2 @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_trans
% 5.25/5.44 thf(fact_280_eq__imp__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( M = N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % eq_imp_le
% 5.25/5.44 thf(fact_281_le__antisym,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.44 => ( M = N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_antisym
% 5.25/5.44 thf(fact_282_nat__le__linear,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 | ( ord_less_eq_nat @ N2 @ M ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_le_linear
% 5.25/5.44 thf(fact_283_Nat_Oex__has__greatest__nat,axiom,
% 5.25/5.44 ! [P: nat > $o,K: nat,B: nat] :
% 5.25/5.44 ( ( P @ K )
% 5.25/5.44 => ( ! [Y3: nat] :
% 5.25/5.44 ( ( P @ Y3 )
% 5.25/5.44 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.25/5.44 => ? [X5: nat] :
% 5.25/5.44 ( ( P @ X5 )
% 5.25/5.44 & ! [Y4: nat] :
% 5.25/5.44 ( ( P @ Y4 )
% 5.25/5.44 => ( ord_less_eq_nat @ Y4 @ X5 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Nat.ex_has_greatest_nat
% 5.25/5.44 thf(fact_284_size__neq__size__imp__neq,axiom,
% 5.25/5.44 ! [X4: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ( size_s6755466524823107622T_VEBT @ X4 )
% 5.25/5.44 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.25/5.44 => ( X4 != Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % size_neq_size_imp_neq
% 5.25/5.44 thf(fact_285_size__neq__size__imp__neq,axiom,
% 5.25/5.44 ! [X4: list_o,Y: list_o] :
% 5.25/5.44 ( ( ( size_size_list_o @ X4 )
% 5.25/5.44 != ( size_size_list_o @ Y ) )
% 5.25/5.44 => ( X4 != Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % size_neq_size_imp_neq
% 5.25/5.44 thf(fact_286_size__neq__size__imp__neq,axiom,
% 5.25/5.44 ! [X4: list_nat,Y: list_nat] :
% 5.25/5.44 ( ( ( size_size_list_nat @ X4 )
% 5.25/5.44 != ( size_size_list_nat @ Y ) )
% 5.25/5.44 => ( X4 != Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % size_neq_size_imp_neq
% 5.25/5.44 thf(fact_287_size__neq__size__imp__neq,axiom,
% 5.25/5.44 ! [X4: list_int,Y: list_int] :
% 5.25/5.44 ( ( ( size_size_list_int @ X4 )
% 5.25/5.44 != ( size_size_list_int @ Y ) )
% 5.25/5.44 => ( X4 != Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % size_neq_size_imp_neq
% 5.25/5.44 thf(fact_288_size__neq__size__imp__neq,axiom,
% 5.25/5.44 ! [X4: num,Y: num] :
% 5.25/5.44 ( ( ( size_size_num @ X4 )
% 5.25/5.44 != ( size_size_num @ Y ) )
% 5.25/5.44 => ( X4 != Y ) ) ).
% 5.25/5.44
% 5.25/5.44 % size_neq_size_imp_neq
% 5.25/5.44 thf(fact_289_Nat_OlessE,axiom,
% 5.25/5.44 ! [I2: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ K )
% 5.25/5.44 => ( ( K
% 5.25/5.44 != ( suc @ I2 ) )
% 5.25/5.44 => ~ ! [J2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.44 => ( K
% 5.25/5.44 != ( suc @ J2 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Nat.lessE
% 5.25/5.44 thf(fact_290_Suc__lessD,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_lessD
% 5.25/5.44 thf(fact_291_Suc__lessE,axiom,
% 5.25/5.44 ! [I2: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( suc @ I2 ) @ K )
% 5.25/5.44 => ~ ! [J2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J2 )
% 5.25/5.44 => ( K
% 5.25/5.44 != ( suc @ J2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_lessE
% 5.25/5.44 thf(fact_292_Suc__lessI,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ( ( suc @ M )
% 5.25/5.44 != N2 )
% 5.25/5.44 => ( ord_less_nat @ ( suc @ M ) @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_lessI
% 5.25/5.44 thf(fact_293_less__SucE,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( M = N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_SucE
% 5.25/5.44 thf(fact_294_less__SucI,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_SucI
% 5.25/5.44 thf(fact_295_Ex__less__Suc,axiom,
% 5.25/5.44 ! [N2: nat,P: nat > $o] :
% 5.25/5.44 ( ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.25/5.44 & ( P @ I3 ) ) )
% 5.25/5.44 = ( ( P @ N2 )
% 5.25/5.44 | ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ N2 )
% 5.25/5.44 & ( P @ I3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Ex_less_Suc
% 5.25/5.44 thf(fact_296_less__Suc__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 = ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 | ( M = N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_Suc_eq
% 5.25/5.44 thf(fact_297_not__less__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ~ ( ord_less_nat @ M @ N2 ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ ( suc @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_less_eq
% 5.25/5.44 thf(fact_298_All__less__Suc,axiom,
% 5.25/5.44 ! [N2: nat,P: nat > $o] :
% 5.25/5.44 ( ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 5.25/5.44 => ( P @ I3 ) ) )
% 5.25/5.44 = ( ( P @ N2 )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ N2 )
% 5.25/5.44 => ( P @ I3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % All_less_Suc
% 5.25/5.44 thf(fact_299_Suc__less__eq2,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.25/5.44 = ( ? [M3: nat] :
% 5.25/5.44 ( ( M
% 5.25/5.44 = ( suc @ M3 ) )
% 5.25/5.44 & ( ord_less_nat @ N2 @ M3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_less_eq2
% 5.25/5.44 thf(fact_300_less__antisym,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] :
% 5.25/5.44 ( ~ ( ord_less_nat @ N2 @ M )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.25/5.44 => ( M = N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_antisym
% 5.25/5.44 thf(fact_301_Suc__less__SucD,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_less_SucD
% 5.25/5.44 thf(fact_302_less__trans__Suc,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ( ord_less_nat @ J @ K )
% 5.25/5.44 => ( ord_less_nat @ ( suc @ I2 ) @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_trans_Suc
% 5.25/5.44 thf(fact_303_less__Suc__induct,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,P: nat > nat > $o] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 5.25/5.44 => ( ! [I4: nat,J2: nat,K2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ J2 )
% 5.25/5.44 => ( ( ord_less_nat @ J2 @ K2 )
% 5.25/5.44 => ( ( P @ I4 @ J2 )
% 5.25/5.44 => ( ( P @ J2 @ K2 )
% 5.25/5.44 => ( P @ I4 @ K2 ) ) ) ) )
% 5.25/5.44 => ( P @ I2 @ J ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_Suc_induct
% 5.25/5.44 thf(fact_304_strict__inc__induct,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,P: nat > $o] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( J
% 5.25/5.44 = ( suc @ I4 ) )
% 5.25/5.44 => ( P @ I4 ) )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ J )
% 5.25/5.44 => ( ( P @ ( suc @ I4 ) )
% 5.25/5.44 => ( P @ I4 ) ) )
% 5.25/5.44 => ( P @ I2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % strict_inc_induct
% 5.25/5.44 thf(fact_305_not__less__less__Suc__eq,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] :
% 5.25/5.44 ( ~ ( ord_less_nat @ N2 @ M )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.25/5.44 = ( N2 = M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_less_less_Suc_eq
% 5.25/5.44 thf(fact_306_Suc__leD,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_leD
% 5.25/5.44 thf(fact_307_le__SucE,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 => ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( M
% 5.25/5.44 = ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_SucE
% 5.25/5.44 thf(fact_308_le__SucI,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_SucI
% 5.25/5.44 thf(fact_309_Suc__le__D,axiom,
% 5.25/5.44 ! [N2: nat,M4: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ M4 )
% 5.25/5.44 => ? [M5: nat] :
% 5.25/5.44 ( M4
% 5.25/5.44 = ( suc @ M5 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_le_D
% 5.25/5.44 thf(fact_310_le__Suc__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 | ( M
% 5.25/5.44 = ( suc @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_Suc_eq
% 5.25/5.44 thf(fact_311_Suc__n__not__le__n,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ~ ( ord_less_eq_nat @ ( suc @ N2 ) @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_n_not_le_n
% 5.25/5.44 thf(fact_312_not__less__eq__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ~ ( ord_less_eq_nat @ M @ N2 ) )
% 5.25/5.44 = ( ord_less_eq_nat @ ( suc @ N2 ) @ M ) ) ).
% 5.25/5.44
% 5.25/5.44 % not_less_eq_eq
% 5.25/5.44 thf(fact_313_full__nat__induct,axiom,
% 5.25/5.44 ! [P: nat > $o,N2: nat] :
% 5.25/5.44 ( ! [N3: nat] :
% 5.25/5.44 ( ! [M2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 5.25/5.44 => ( P @ M2 ) )
% 5.25/5.44 => ( P @ N3 ) )
% 5.25/5.44 => ( P @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % full_nat_induct
% 5.25/5.44 thf(fact_314_nat__induct__at__least,axiom,
% 5.25/5.44 ! [M: nat,N2: nat,P: nat > $o] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ( P @ M )
% 5.25/5.44 => ( ! [N3: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N3 )
% 5.25/5.44 => ( ( P @ N3 )
% 5.25/5.44 => ( P @ ( suc @ N3 ) ) ) )
% 5.25/5.44 => ( P @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_induct_at_least
% 5.25/5.44 thf(fact_315_transitive__stepwise__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat,R: nat > nat > $o] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ! [X5: nat] : ( R @ X5 @ X5 )
% 5.25/5.44 => ( ! [X5: nat,Y3: nat,Z2: nat] :
% 5.25/5.44 ( ( R @ X5 @ Y3 )
% 5.25/5.44 => ( ( R @ Y3 @ Z2 )
% 5.25/5.44 => ( R @ X5 @ Z2 ) ) )
% 5.25/5.44 => ( ! [N3: nat] : ( R @ N3 @ ( suc @ N3 ) )
% 5.25/5.44 => ( R @ M @ N2 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % transitive_stepwise_le
% 5.25/5.44 thf(fact_316_nat__arith_Osuc1,axiom,
% 5.25/5.44 ! [A2: nat,K: nat,A: nat] :
% 5.25/5.44 ( ( A2
% 5.25/5.44 = ( plus_plus_nat @ K @ A ) )
% 5.25/5.44 => ( ( suc @ A2 )
% 5.25/5.44 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_arith.suc1
% 5.25/5.44 thf(fact_317_add__Suc,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 = ( suc @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_Suc
% 5.25/5.44 thf(fact_318_add__Suc__shift,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 = ( plus_plus_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_Suc_shift
% 5.25/5.44 thf(fact_319_nat__less__le,axiom,
% 5.25/5.44 ( ord_less_nat
% 5.25/5.44 = ( ^ [M6: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M6 @ N )
% 5.25/5.44 & ( M6 != N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_less_le
% 5.25/5.44 thf(fact_320_less__imp__le__nat,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_imp_le_nat
% 5.25/5.44 thf(fact_321_le__eq__less__or__eq,axiom,
% 5.25/5.44 ( ord_less_eq_nat
% 5.25/5.44 = ( ^ [M6: nat,N: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M6 @ N )
% 5.25/5.44 | ( M6 = N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_eq_less_or_eq
% 5.25/5.44 thf(fact_322_less__or__eq__imp__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 | ( M = N2 ) )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_or_eq_imp_le
% 5.25/5.44 thf(fact_323_le__neq__implies__less,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ( M != N2 )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_neq_implies_less
% 5.25/5.44 thf(fact_324_less__mono__imp__le__mono,axiom,
% 5.25/5.44 ! [F: nat > nat,I2: nat,J: nat] :
% 5.25/5.44 ( ! [I4: nat,J2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ J2 )
% 5.25/5.44 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_eq_nat @ ( F @ I2 ) @ ( F @ J ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_mono_imp_le_mono
% 5.25/5.44 thf(fact_325_add__lessD1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.25/5.44 => ( ord_less_nat @ I2 @ K ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_lessD1
% 5.25/5.44 thf(fact_326_add__less__mono,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ( ord_less_nat @ K @ L )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_mono
% 5.25/5.44 thf(fact_327_not__add__less1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat] :
% 5.25/5.44 ~ ( ord_less_nat @ ( plus_plus_nat @ I2 @ J ) @ I2 ) ).
% 5.25/5.44
% 5.25/5.44 % not_add_less1
% 5.25/5.44 thf(fact_328_not__add__less2,axiom,
% 5.25/5.44 ! [J: nat,I2: nat] :
% 5.25/5.44 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I2 ) @ I2 ) ).
% 5.25/5.44
% 5.25/5.44 % not_add_less2
% 5.25/5.44 thf(fact_329_add__less__mono1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_mono1
% 5.25/5.44 thf(fact_330_trans__less__add1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % trans_less_add1
% 5.25/5.44 thf(fact_331_trans__less__add2,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % trans_less_add2
% 5.25/5.44 thf(fact_332_less__add__eq__less,axiom,
% 5.25/5.44 ! [K: nat,L: nat,M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ K @ L )
% 5.25/5.44 => ( ( ( plus_plus_nat @ M @ L )
% 5.25/5.44 = ( plus_plus_nat @ K @ N2 ) )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_eq_less
% 5.25/5.44 thf(fact_333_add__leE,axiom,
% 5.25/5.44 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.25/5.44 => ~ ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ~ ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_leE
% 5.25/5.44 thf(fact_334_le__add1,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add1
% 5.25/5.44 thf(fact_335_le__add2,axiom,
% 5.25/5.44 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_add2
% 5.25/5.44 thf(fact_336_add__leD1,axiom,
% 5.25/5.44 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_leD1
% 5.25/5.44 thf(fact_337_add__leD2,axiom,
% 5.25/5.44 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_leD2
% 5.25/5.44 thf(fact_338_le__Suc__ex,axiom,
% 5.25/5.44 ! [K: nat,L: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ K @ L )
% 5.25/5.44 => ? [N3: nat] :
% 5.25/5.44 ( L
% 5.25/5.44 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_Suc_ex
% 5.25/5.44 thf(fact_339_add__le__mono,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ( ord_less_eq_nat @ K @ L )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_mono
% 5.25/5.44 thf(fact_340_add__le__mono1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_mono1
% 5.25/5.44 thf(fact_341_trans__le__add1,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % trans_le_add1
% 5.25/5.44 thf(fact_342_trans__le__add2,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,M: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ord_less_eq_nat @ I2 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % trans_le_add2
% 5.25/5.44 thf(fact_343_nat__le__iff__add,axiom,
% 5.25/5.44 ( ord_less_eq_nat
% 5.25/5.44 = ( ^ [M6: nat,N: nat] :
% 5.25/5.44 ? [K3: nat] :
% 5.25/5.44 ( N
% 5.25/5.44 = ( plus_plus_nat @ M6 @ K3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nat_le_iff_add
% 5.25/5.44 thf(fact_344_lift__Suc__mono__less,axiom,
% 5.25/5.44 ! [F: nat > real,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_real @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less
% 5.25/5.44 thf(fact_345_lift__Suc__mono__less,axiom,
% 5.25/5.44 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less
% 5.25/5.44 thf(fact_346_lift__Suc__mono__less,axiom,
% 5.25/5.44 ! [F: nat > num,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less
% 5.25/5.44 thf(fact_347_lift__Suc__mono__less,axiom,
% 5.25/5.44 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less
% 5.25/5.44 thf(fact_348_lift__Suc__mono__less,axiom,
% 5.25/5.44 ! [F: nat > int,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less
% 5.25/5.44 thf(fact_349_lift__Suc__mono__less__iff,axiom,
% 5.25/5.44 ! [F: nat > real,N2: nat,M: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_real @ ( F @ N2 ) @ ( F @ M ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less_iff
% 5.25/5.44 thf(fact_350_lift__Suc__mono__less__iff,axiom,
% 5.25/5.44 ! [F: nat > rat,N2: nat,M: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_rat @ ( F @ N2 ) @ ( F @ M ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less_iff
% 5.25/5.44 thf(fact_351_lift__Suc__mono__less__iff,axiom,
% 5.25/5.44 ! [F: nat > num,N2: nat,M: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_num @ ( F @ N2 ) @ ( F @ M ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less_iff
% 5.25/5.44 thf(fact_352_lift__Suc__mono__less__iff,axiom,
% 5.25/5.44 ! [F: nat > nat,N2: nat,M: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_nat @ ( F @ N2 ) @ ( F @ M ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less_iff
% 5.25/5.44 thf(fact_353_lift__Suc__mono__less__iff,axiom,
% 5.25/5.44 ! [F: nat > int,N2: nat,M: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_int @ ( F @ N2 ) @ ( F @ M ) )
% 5.25/5.44 = ( ord_less_nat @ N2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_less_iff
% 5.25/5.44 thf(fact_354_lift__Suc__mono__le,axiom,
% 5.25/5.44 ! [F: nat > set_int,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_set_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_le
% 5.25/5.44 thf(fact_355_lift__Suc__mono__le,axiom,
% 5.25/5.44 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_rat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_le
% 5.25/5.44 thf(fact_356_lift__Suc__mono__le,axiom,
% 5.25/5.44 ! [F: nat > num,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_num @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_le
% 5.25/5.44 thf(fact_357_lift__Suc__mono__le,axiom,
% 5.25/5.44 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_nat @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_le
% 5.25/5.44 thf(fact_358_lift__Suc__mono__le,axiom,
% 5.25/5.44 ! [F: nat > int,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_int @ ( F @ N2 ) @ ( F @ N5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_mono_le
% 5.25/5.44 thf(fact_359_lift__Suc__antimono__le,axiom,
% 5.25/5.44 ! [F: nat > set_int,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_antimono_le
% 5.25/5.44 thf(fact_360_lift__Suc__antimono__le,axiom,
% 5.25/5.44 ! [F: nat > rat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_antimono_le
% 5.25/5.44 thf(fact_361_lift__Suc__antimono__le,axiom,
% 5.25/5.44 ! [F: nat > num,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_antimono_le
% 5.25/5.44 thf(fact_362_lift__Suc__antimono__le,axiom,
% 5.25/5.44 ! [F: nat > nat,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_antimono_le
% 5.25/5.44 thf(fact_363_lift__Suc__antimono__le,axiom,
% 5.25/5.44 ! [F: nat > int,N2: nat,N5: nat] :
% 5.25/5.44 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.25/5.44 => ( ( ord_less_eq_nat @ N2 @ N5 )
% 5.25/5.44 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % lift_Suc_antimono_le
% 5.25/5.44 thf(fact_364_le__imp__less__Suc,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_nat @ M @ ( suc @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_imp_less_Suc
% 5.25/5.44 thf(fact_365_less__eq__Suc__le,axiom,
% 5.25/5.44 ( ord_less_nat
% 5.25/5.44 = ( ^ [N: nat] : ( ord_less_eq_nat @ ( suc @ N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_eq_Suc_le
% 5.25/5.44 thf(fact_366_less__Suc__eq__le,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 5.25/5.44 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_Suc_eq_le
% 5.25/5.44 thf(fact_367_le__less__Suc__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.25/5.44 = ( N2 = M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_less_Suc_eq
% 5.25/5.44 thf(fact_368_Suc__le__lessD,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_le_lessD
% 5.25/5.44 thf(fact_369_inc__induct,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,P: nat > $o] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ( P @ J )
% 5.25/5.44 => ( ! [N3: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.25/5.44 => ( ( ord_less_nat @ N3 @ J )
% 5.25/5.44 => ( ( P @ ( suc @ N3 ) )
% 5.25/5.44 => ( P @ N3 ) ) ) )
% 5.25/5.44 => ( P @ I2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % inc_induct
% 5.25/5.44 thf(fact_370_dec__induct,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,P: nat > $o] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 => ( ( P @ I2 )
% 5.25/5.44 => ( ! [N3: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ I2 @ N3 )
% 5.25/5.44 => ( ( ord_less_nat @ N3 @ J )
% 5.25/5.44 => ( ( P @ N3 )
% 5.25/5.44 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.25/5.44 => ( P @ J ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dec_induct
% 5.25/5.44 thf(fact_371_Suc__le__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.25/5.44 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_le_eq
% 5.25/5.44 thf(fact_372_Suc__leI,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ord_less_eq_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_leI
% 5.25/5.44 thf(fact_373_less__natE,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ~ ! [Q2: nat] :
% 5.25/5.44 ( N2
% 5.25/5.44 != ( suc @ ( plus_plus_nat @ M @ Q2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_natE
% 5.25/5.44 thf(fact_374_less__add__Suc1,axiom,
% 5.25/5.44 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ I2 @ M ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_Suc1
% 5.25/5.44 thf(fact_375_less__add__Suc2,axiom,
% 5.25/5.44 ! [I2: nat,M: nat] : ( ord_less_nat @ I2 @ ( suc @ ( plus_plus_nat @ M @ I2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_Suc2
% 5.25/5.44 thf(fact_376_less__iff__Suc__add,axiom,
% 5.25/5.44 ( ord_less_nat
% 5.25/5.44 = ( ^ [M6: nat,N: nat] :
% 5.25/5.44 ? [K3: nat] :
% 5.25/5.44 ( N
% 5.25/5.44 = ( suc @ ( plus_plus_nat @ M6 @ K3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_iff_Suc_add
% 5.25/5.44 thf(fact_377_less__imp__Suc__add,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ? [K2: nat] :
% 5.25/5.44 ( N2
% 5.25/5.44 = ( suc @ ( plus_plus_nat @ M @ K2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_imp_Suc_add
% 5.25/5.44 thf(fact_378_mono__nat__linear__lb,axiom,
% 5.25/5.44 ! [F: nat > nat,M: nat,K: nat] :
% 5.25/5.44 ( ! [M5: nat,N3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M5 @ N3 )
% 5.25/5.44 => ( ord_less_nat @ ( F @ M5 ) @ ( F @ N3 ) ) )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mono_nat_linear_lb
% 5.25/5.44 thf(fact_379_Suc__eq__plus1,axiom,
% 5.25/5.44 ( suc
% 5.25/5.44 = ( ^ [N: nat] : ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_eq_plus1
% 5.25/5.44 thf(fact_380_plus__1__eq__Suc,axiom,
% 5.25/5.44 ( ( plus_plus_nat @ one_one_nat )
% 5.25/5.44 = suc ) ).
% 5.25/5.44
% 5.25/5.44 % plus_1_eq_Suc
% 5.25/5.44 thf(fact_381_Suc__eq__plus1__left,axiom,
% 5.25/5.44 ( suc
% 5.25/5.44 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % Suc_eq_plus1_left
% 5.25/5.44 thf(fact_382_field__sum__of__halves,axiom,
% 5.25/5.44 ! [X4: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = X4 ) ).
% 5.25/5.44
% 5.25/5.44 % field_sum_of_halves
% 5.25/5.44 thf(fact_383_field__sum__of__halves,axiom,
% 5.25/5.44 ! [X4: real] :
% 5.25/5.44 ( ( plus_plus_real @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.25/5.44 = X4 ) ).
% 5.25/5.44
% 5.25/5.44 % field_sum_of_halves
% 5.25/5.44 thf(fact_384_div__by__1,axiom,
% 5.25/5.44 ! [A: rat] :
% 5.25/5.44 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_385_div__by__1,axiom,
% 5.25/5.44 ! [A: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_386_div__by__1,axiom,
% 5.25/5.44 ! [A: int] :
% 5.25/5.44 ( ( divide_divide_int @ A @ one_one_int )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_387_div__by__1,axiom,
% 5.25/5.44 ! [A: real] :
% 5.25/5.44 ( ( divide_divide_real @ A @ one_one_real )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_388_div__by__1,axiom,
% 5.25/5.44 ! [A: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_389_div__by__1,axiom,
% 5.25/5.44 ! [A: code_integer] :
% 5.25/5.44 ( ( divide6298287555418463151nteger @ A @ one_one_Code_integer )
% 5.25/5.44 = A ) ).
% 5.25/5.44
% 5.25/5.44 % div_by_1
% 5.25/5.44 thf(fact_390_add__less__cancel__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.44 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_left
% 5.25/5.44 thf(fact_391_add__less__cancel__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.44 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_left
% 5.25/5.44 thf(fact_392_add__less__cancel__left,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.44 = ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_left
% 5.25/5.44 thf(fact_393_add__less__cancel__left,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.44 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_left
% 5.25/5.44 thf(fact_394_add__less__cancel__right,axiom,
% 5.25/5.44 ! [A: real,C: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.44 = ( ord_less_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_right
% 5.25/5.44 thf(fact_395_add__less__cancel__right,axiom,
% 5.25/5.44 ! [A: rat,C: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.44 = ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_right
% 5.25/5.44 thf(fact_396_add__less__cancel__right,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.44 = ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_right
% 5.25/5.44 thf(fact_397_add__less__cancel__right,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.44 = ( ord_less_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_cancel_right
% 5.25/5.44 thf(fact_398_add__le__cancel__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.44 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_left
% 5.25/5.44 thf(fact_399_add__le__cancel__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_left
% 5.25/5.44 thf(fact_400_add__le__cancel__left,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.44 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_left
% 5.25/5.44 thf(fact_401_add__le__cancel__left,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.44 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_left
% 5.25/5.44 thf(fact_402_add__le__cancel__right,axiom,
% 5.25/5.44 ! [A: real,C: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.44 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_right
% 5.25/5.44 thf(fact_403_add__le__cancel__right,axiom,
% 5.25/5.44 ! [A: rat,C: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.44 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_right
% 5.25/5.44 thf(fact_404_add__le__cancel__right,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.44 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_right
% 5.25/5.44 thf(fact_405_add__le__cancel__right,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.44 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_cancel_right
% 5.25/5.44 thf(fact_406_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_real] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_real @ Xs ) )
% 5.25/5.44 => ( member_real @ ( nth_real @ Xs @ N2 ) @ ( set_real2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_407_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_complex] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.44 => ( member_complex @ ( nth_complex @ Xs @ N2 ) @ ( set_complex2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_408_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.44 => ( member8440522571783428010at_nat @ ( nth_Pr7617993195940197384at_nat @ Xs @ N2 ) @ ( set_Pr5648618587558075414at_nat @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_409_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N2 ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_410_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_o] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 => ( member_o @ ( nth_o @ Xs @ N2 ) @ ( set_o2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_411_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_nat] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 => ( member_nat @ ( nth_nat @ Xs @ N2 ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_412_nth__mem,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_int] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 => ( member_int @ ( nth_int @ Xs @ N2 ) @ ( set_int2 @ Xs ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_mem
% 5.25/5.44 thf(fact_413_list__ball__nth,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.44 => ( P @ X5 ) )
% 5.25/5.44 => ( P @ ( nth_VEBT_VEBT @ Xs @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_ball_nth
% 5.25/5.44 thf(fact_414_list__ball__nth,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_o,P: $o > $o] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 => ( ! [X5: $o] :
% 5.25/5.44 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.25/5.44 => ( P @ X5 ) )
% 5.25/5.44 => ( P @ ( nth_o @ Xs @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_ball_nth
% 5.25/5.44 thf(fact_415_list__ball__nth,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_nat,P: nat > $o] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 => ( ! [X5: nat] :
% 5.25/5.44 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.25/5.44 => ( P @ X5 ) )
% 5.25/5.44 => ( P @ ( nth_nat @ Xs @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_ball_nth
% 5.25/5.44 thf(fact_416_list__ball__nth,axiom,
% 5.25/5.44 ! [N2: nat,Xs: list_int,P: int > $o] :
% 5.25/5.44 ( ( ord_less_nat @ N2 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 => ( ! [X5: int] :
% 5.25/5.44 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.25/5.44 => ( P @ X5 ) )
% 5.25/5.44 => ( P @ ( nth_int @ Xs @ N2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_ball_nth
% 5.25/5.44 thf(fact_417_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: real,Xs: list_real] :
% 5.25/5.44 ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs ) )
% 5.25/5.44 & ( ( nth_real @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_418_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: complex,Xs: list_complex] :
% 5.25/5.44 ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.44 & ( ( nth_complex @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_419_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.44 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.44 & ( ( nth_Pr7617993195940197384at_nat @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_420_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 & ( ( nth_VEBT_VEBT @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_421_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: $o,Xs: list_o] :
% 5.25/5.44 ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 & ( ( nth_o @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_422_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: nat,Xs: list_nat] :
% 5.25/5.44 ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 & ( ( nth_nat @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_423_in__set__conv__nth,axiom,
% 5.25/5.44 ! [X4: int,Xs: list_int] :
% 5.25/5.44 ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.25/5.44 = ( ? [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 & ( ( nth_int @ Xs @ I3 )
% 5.25/5.44 = X4 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % in_set_conv_nth
% 5.25/5.44 thf(fact_424_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_real,P: real > $o,X4: real] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_real @ X4 @ ( set_real2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_425_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_complex,P: complex > $o,X4: complex] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_complex @ X4 @ ( set_complex2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_426_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_P6011104703257516679at_nat,P: product_prod_nat_nat > $o,X4: product_prod_nat_nat] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_s5460976970255530739at_nat @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_Pr7617993195940197384at_nat @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_427_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_428_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_o,P: $o > $o,X4: $o] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_o @ X4 @ ( set_o2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_429_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_nat,P: nat > $o,X4: nat] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_nat @ X4 @ ( set_nat2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_430_all__nth__imp__all__set,axiom,
% 5.25/5.44 ! [Xs: list_int,P: int > $o,X4: int] :
% 5.25/5.44 ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 5.25/5.44 => ( ( member_int @ X4 @ ( set_int2 @ Xs ) )
% 5.25/5.44 => ( P @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_nth_imp_all_set
% 5.25/5.44 thf(fact_431_all__set__conv__all__nth,axiom,
% 5.25/5.44 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.25/5.44 ( ( ! [X: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.44 => ( P @ X ) ) )
% 5.25/5.44 = ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_VEBT_VEBT @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_set_conv_all_nth
% 5.25/5.44 thf(fact_432_all__set__conv__all__nth,axiom,
% 5.25/5.44 ! [Xs: list_o,P: $o > $o] :
% 5.25/5.44 ( ( ! [X: $o] :
% 5.25/5.44 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.25/5.44 => ( P @ X ) ) )
% 5.25/5.44 = ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_o @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_set_conv_all_nth
% 5.25/5.44 thf(fact_433_all__set__conv__all__nth,axiom,
% 5.25/5.44 ! [Xs: list_nat,P: nat > $o] :
% 5.25/5.44 ( ( ! [X: nat] :
% 5.25/5.44 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.25/5.44 => ( P @ X ) ) )
% 5.25/5.44 = ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_nat @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_set_conv_all_nth
% 5.25/5.44 thf(fact_434_all__set__conv__all__nth,axiom,
% 5.25/5.44 ! [Xs: list_int,P: int > $o] :
% 5.25/5.44 ( ( ! [X: int] :
% 5.25/5.44 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.25/5.44 => ( P @ X ) ) )
% 5.25/5.44 = ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 => ( P @ ( nth_int @ Xs @ I3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % all_set_conv_all_nth
% 5.25/5.44 thf(fact_435_gt__half__sum,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % gt_half_sum
% 5.25/5.44 thf(fact_436_gt__half__sum,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % gt_half_sum
% 5.25/5.44 thf(fact_437_less__half__sum,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_half_sum
% 5.25/5.44 thf(fact_438_less__half__sum,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_half_sum
% 5.25/5.44 thf(fact_439_add__right__cancel,axiom,
% 5.25/5.44 ! [B: real,A: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.44 = ( plus_plus_real @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_cancel
% 5.25/5.44 thf(fact_440_add__right__cancel,axiom,
% 5.25/5.44 ! [B: rat,A: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.44 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_cancel
% 5.25/5.44 thf(fact_441_add__right__cancel,axiom,
% 5.25/5.44 ! [B: nat,A: nat,C: nat] :
% 5.25/5.44 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.44 = ( plus_plus_nat @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_cancel
% 5.25/5.44 thf(fact_442_add__right__cancel,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.44 = ( plus_plus_int @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_cancel
% 5.25/5.44 thf(fact_443_add__left__cancel,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.44 = ( plus_plus_real @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_cancel
% 5.25/5.44 thf(fact_444_add__left__cancel,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.44 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_cancel
% 5.25/5.44 thf(fact_445_add__left__cancel,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.44 = ( plus_plus_nat @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_cancel
% 5.25/5.44 thf(fact_446_add__left__cancel,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.44 = ( plus_plus_int @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_cancel
% 5.25/5.44 thf(fact_447_real__arch__pow,axiom,
% 5.25/5.44 ! [X4: real,Y: real] :
% 5.25/5.44 ( ( ord_less_real @ one_one_real @ X4 )
% 5.25/5.44 => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X4 @ N3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % real_arch_pow
% 5.25/5.44 thf(fact_448_less__eq__real__def,axiom,
% 5.25/5.44 ( ord_less_eq_real
% 5.25/5.44 = ( ^ [X: real,Y5: real] :
% 5.25/5.44 ( ( ord_less_real @ X @ Y5 )
% 5.25/5.44 | ( X = Y5 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_eq_real_def
% 5.25/5.44 thf(fact_449_complete__real,axiom,
% 5.25/5.44 ! [S2: set_real] :
% 5.25/5.44 ( ? [X2: real] : ( member_real @ X2 @ S2 )
% 5.25/5.44 => ( ? [Z3: real] :
% 5.25/5.44 ! [X5: real] :
% 5.25/5.44 ( ( member_real @ X5 @ S2 )
% 5.25/5.44 => ( ord_less_eq_real @ X5 @ Z3 ) )
% 5.25/5.44 => ? [Y3: real] :
% 5.25/5.44 ( ! [X2: real] :
% 5.25/5.44 ( ( member_real @ X2 @ S2 )
% 5.25/5.44 => ( ord_less_eq_real @ X2 @ Y3 ) )
% 5.25/5.44 & ! [Z3: real] :
% 5.25/5.44 ( ! [X5: real] :
% 5.25/5.44 ( ( member_real @ X5 @ S2 )
% 5.25/5.44 => ( ord_less_eq_real @ X5 @ Z3 ) )
% 5.25/5.44 => ( ord_less_eq_real @ Y3 @ Z3 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % complete_real
% 5.25/5.44 thf(fact_450_linorder__neqE__linordered__idom,axiom,
% 5.25/5.44 ! [X4: real,Y: real] :
% 5.25/5.44 ( ( X4 != Y )
% 5.25/5.44 => ( ~ ( ord_less_real @ X4 @ Y )
% 5.25/5.44 => ( ord_less_real @ Y @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % linorder_neqE_linordered_idom
% 5.25/5.44 thf(fact_451_linorder__neqE__linordered__idom,axiom,
% 5.25/5.44 ! [X4: rat,Y: rat] :
% 5.25/5.44 ( ( X4 != Y )
% 5.25/5.44 => ( ~ ( ord_less_rat @ X4 @ Y )
% 5.25/5.44 => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % linorder_neqE_linordered_idom
% 5.25/5.44 thf(fact_452_linorder__neqE__linordered__idom,axiom,
% 5.25/5.44 ! [X4: int,Y: int] :
% 5.25/5.44 ( ( X4 != Y )
% 5.25/5.44 => ( ~ ( ord_less_int @ X4 @ Y )
% 5.25/5.44 => ( ord_less_int @ Y @ X4 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % linorder_neqE_linordered_idom
% 5.25/5.44 thf(fact_453_linordered__field__no__ub,axiom,
% 5.25/5.44 ! [X2: real] :
% 5.25/5.44 ? [X_12: real] : ( ord_less_real @ X2 @ X_12 ) ).
% 5.25/5.44
% 5.25/5.44 % linordered_field_no_ub
% 5.25/5.44 thf(fact_454_linordered__field__no__ub,axiom,
% 5.25/5.44 ! [X2: rat] :
% 5.25/5.44 ? [X_12: rat] : ( ord_less_rat @ X2 @ X_12 ) ).
% 5.25/5.44
% 5.25/5.44 % linordered_field_no_ub
% 5.25/5.44 thf(fact_455_linordered__field__no__lb,axiom,
% 5.25/5.44 ! [X2: real] :
% 5.25/5.44 ? [Y3: real] : ( ord_less_real @ Y3 @ X2 ) ).
% 5.25/5.44
% 5.25/5.44 % linordered_field_no_lb
% 5.25/5.44 thf(fact_456_linordered__field__no__lb,axiom,
% 5.25/5.44 ! [X2: rat] :
% 5.25/5.44 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X2 ) ).
% 5.25/5.44
% 5.25/5.44 % linordered_field_no_lb
% 5.25/5.44 thf(fact_457_one__reorient,axiom,
% 5.25/5.44 ! [X4: complex] :
% 5.25/5.44 ( ( one_one_complex = X4 )
% 5.25/5.44 = ( X4 = one_one_complex ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_reorient
% 5.25/5.44 thf(fact_458_one__reorient,axiom,
% 5.25/5.44 ! [X4: real] :
% 5.25/5.44 ( ( one_one_real = X4 )
% 5.25/5.44 = ( X4 = one_one_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_reorient
% 5.25/5.44 thf(fact_459_one__reorient,axiom,
% 5.25/5.44 ! [X4: rat] :
% 5.25/5.44 ( ( one_one_rat = X4 )
% 5.25/5.44 = ( X4 = one_one_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_reorient
% 5.25/5.44 thf(fact_460_one__reorient,axiom,
% 5.25/5.44 ! [X4: nat] :
% 5.25/5.44 ( ( one_one_nat = X4 )
% 5.25/5.44 = ( X4 = one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_reorient
% 5.25/5.44 thf(fact_461_one__reorient,axiom,
% 5.25/5.44 ! [X4: int] :
% 5.25/5.44 ( ( one_one_int = X4 )
% 5.25/5.44 = ( X4 = one_one_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % one_reorient
% 5.25/5.44 thf(fact_462_add__right__imp__eq,axiom,
% 5.25/5.44 ! [B: real,A: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.44 = ( plus_plus_real @ C @ A ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_imp_eq
% 5.25/5.44 thf(fact_463_add__right__imp__eq,axiom,
% 5.25/5.44 ! [B: rat,A: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.44 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_imp_eq
% 5.25/5.44 thf(fact_464_add__right__imp__eq,axiom,
% 5.25/5.44 ! [B: nat,A: nat,C: nat] :
% 5.25/5.44 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.44 = ( plus_plus_nat @ C @ A ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_imp_eq
% 5.25/5.44 thf(fact_465_add__right__imp__eq,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.44 = ( plus_plus_int @ C @ A ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_imp_eq
% 5.25/5.44 thf(fact_466_add__left__imp__eq,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.44 = ( plus_plus_real @ A @ C ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_imp_eq
% 5.25/5.44 thf(fact_467_add__left__imp__eq,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.44 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_imp_eq
% 5.25/5.44 thf(fact_468_add__left__imp__eq,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.44 = ( plus_plus_nat @ A @ C ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_imp_eq
% 5.25/5.44 thf(fact_469_add__left__imp__eq,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.44 = ( plus_plus_int @ A @ C ) )
% 5.25/5.44 => ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_imp_eq
% 5.25/5.44 thf(fact_470_add_Oleft__commute,axiom,
% 5.25/5.44 ! [B: real,A: real,C: real] :
% 5.25/5.44 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.25/5.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_commute
% 5.25/5.44 thf(fact_471_add_Oleft__commute,axiom,
% 5.25/5.44 ! [B: rat,A: rat,C: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.25/5.44 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_commute
% 5.25/5.44 thf(fact_472_add_Oleft__commute,axiom,
% 5.25/5.44 ! [B: nat,A: nat,C: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.25/5.44 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_commute
% 5.25/5.44 thf(fact_473_add_Oleft__commute,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.25/5.44 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_commute
% 5.25/5.44 thf(fact_474_add_Ocommute,axiom,
% 5.25/5.44 ( plus_plus_real
% 5.25/5.44 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.commute
% 5.25/5.44 thf(fact_475_add_Ocommute,axiom,
% 5.25/5.44 ( plus_plus_rat
% 5.25/5.44 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.commute
% 5.25/5.44 thf(fact_476_add_Ocommute,axiom,
% 5.25/5.44 ( plus_plus_nat
% 5.25/5.44 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.commute
% 5.25/5.44 thf(fact_477_add_Ocommute,axiom,
% 5.25/5.44 ( plus_plus_int
% 5.25/5.44 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.commute
% 5.25/5.44 thf(fact_478_add_Oright__cancel,axiom,
% 5.25/5.44 ! [B: real,A: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.44 = ( plus_plus_real @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_cancel
% 5.25/5.44 thf(fact_479_add_Oright__cancel,axiom,
% 5.25/5.44 ! [B: rat,A: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.44 = ( plus_plus_rat @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_cancel
% 5.25/5.44 thf(fact_480_add_Oright__cancel,axiom,
% 5.25/5.44 ! [B: int,A: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.44 = ( plus_plus_int @ C @ A ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.right_cancel
% 5.25/5.44 thf(fact_481_add_Oleft__cancel,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.44 = ( plus_plus_real @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_cancel
% 5.25/5.44 thf(fact_482_add_Oleft__cancel,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.44 = ( plus_plus_rat @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_cancel
% 5.25/5.44 thf(fact_483_add_Oleft__cancel,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.44 = ( plus_plus_int @ A @ C ) )
% 5.25/5.44 = ( B = C ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.left_cancel
% 5.25/5.44 thf(fact_484_add_Oassoc,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.assoc
% 5.25/5.44 thf(fact_485_add_Oassoc,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.assoc
% 5.25/5.44 thf(fact_486_add_Oassoc,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.assoc
% 5.25/5.44 thf(fact_487_add_Oassoc,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add.assoc
% 5.25/5.44 thf(fact_488_group__cancel_Oadd2,axiom,
% 5.25/5.44 ! [B3: real,K: real,B: real,A: real] :
% 5.25/5.44 ( ( B3
% 5.25/5.44 = ( plus_plus_real @ K @ B ) )
% 5.25/5.44 => ( ( plus_plus_real @ A @ B3 )
% 5.25/5.44 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add2
% 5.25/5.44 thf(fact_489_group__cancel_Oadd2,axiom,
% 5.25/5.44 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.25/5.44 ( ( B3
% 5.25/5.44 = ( plus_plus_rat @ K @ B ) )
% 5.25/5.44 => ( ( plus_plus_rat @ A @ B3 )
% 5.25/5.44 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add2
% 5.25/5.44 thf(fact_490_group__cancel_Oadd2,axiom,
% 5.25/5.44 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.25/5.44 ( ( B3
% 5.25/5.44 = ( plus_plus_nat @ K @ B ) )
% 5.25/5.44 => ( ( plus_plus_nat @ A @ B3 )
% 5.25/5.44 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add2
% 5.25/5.44 thf(fact_491_group__cancel_Oadd2,axiom,
% 5.25/5.44 ! [B3: int,K: int,B: int,A: int] :
% 5.25/5.44 ( ( B3
% 5.25/5.44 = ( plus_plus_int @ K @ B ) )
% 5.25/5.44 => ( ( plus_plus_int @ A @ B3 )
% 5.25/5.44 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add2
% 5.25/5.44 thf(fact_492_group__cancel_Oadd1,axiom,
% 5.25/5.44 ! [A2: real,K: real,A: real,B: real] :
% 5.25/5.44 ( ( A2
% 5.25/5.44 = ( plus_plus_real @ K @ A ) )
% 5.25/5.44 => ( ( plus_plus_real @ A2 @ B )
% 5.25/5.44 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add1
% 5.25/5.44 thf(fact_493_group__cancel_Oadd1,axiom,
% 5.25/5.44 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( A2
% 5.25/5.44 = ( plus_plus_rat @ K @ A ) )
% 5.25/5.44 => ( ( plus_plus_rat @ A2 @ B )
% 5.25/5.44 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add1
% 5.25/5.44 thf(fact_494_group__cancel_Oadd1,axiom,
% 5.25/5.44 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( A2
% 5.25/5.44 = ( plus_plus_nat @ K @ A ) )
% 5.25/5.44 => ( ( plus_plus_nat @ A2 @ B )
% 5.25/5.44 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add1
% 5.25/5.44 thf(fact_495_group__cancel_Oadd1,axiom,
% 5.25/5.44 ! [A2: int,K: int,A: int,B: int] :
% 5.25/5.44 ( ( A2
% 5.25/5.44 = ( plus_plus_int @ K @ A ) )
% 5.25/5.44 => ( ( plus_plus_int @ A2 @ B )
% 5.25/5.44 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % group_cancel.add1
% 5.25/5.44 thf(fact_496_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ( plus_plus_real @ I2 @ K )
% 5.25/5.44 = ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(4)
% 5.25/5.44 thf(fact_497_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ( plus_plus_rat @ I2 @ K )
% 5.25/5.44 = ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(4)
% 5.25/5.44 thf(fact_498_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ( plus_plus_nat @ I2 @ K )
% 5.25/5.44 = ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(4)
% 5.25/5.44 thf(fact_499_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ( plus_plus_int @ I2 @ K )
% 5.25/5.44 = ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(4)
% 5.25/5.44 thf(fact_500_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.44 thf(fact_501_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.44 thf(fact_502_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.44 thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % ab_semigroup_add_class.add_ac(1)
% 5.25/5.44 thf(fact_504_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_real,B3: set_real] :
% 5.25/5.44 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: real] :
% 5.25/5.44 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.25/5.44 => ( member_real @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_505_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_complex,B3: set_complex] :
% 5.25/5.44 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: complex] :
% 5.25/5.44 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.25/5.44 => ( member_complex @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_506_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_P6011104703257516679at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.44 ( ( ord_le3146513528884898305at_nat @ ( set_Pr5648618587558075414at_nat @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: product_prod_nat_nat] :
% 5.25/5.44 ( ( member8440522571783428010at_nat @ X @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.25/5.44 => ( member8440522571783428010at_nat @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_507_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.25/5.44 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.25/5.44 => ( member_VEBT_VEBT @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_508_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_nat,B3: set_nat] :
% 5.25/5.44 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: nat] :
% 5.25/5.44 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.25/5.44 => ( member_nat @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_509_subset__code_I1_J,axiom,
% 5.25/5.44 ! [Xs: list_int,B3: set_int] :
% 5.25/5.44 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 5.25/5.44 = ( ! [X: int] :
% 5.25/5.44 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.25/5.44 => ( member_int @ X @ B3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_code(1)
% 5.25/5.44 thf(fact_510_neq__if__length__neq,axiom,
% 5.25/5.44 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.25/5.44 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.25/5.44 => ( Xs != Ys ) ) ).
% 5.25/5.44
% 5.25/5.44 % neq_if_length_neq
% 5.25/5.44 thf(fact_511_neq__if__length__neq,axiom,
% 5.25/5.44 ! [Xs: list_o,Ys: list_o] :
% 5.25/5.44 ( ( ( size_size_list_o @ Xs )
% 5.25/5.44 != ( size_size_list_o @ Ys ) )
% 5.25/5.44 => ( Xs != Ys ) ) ).
% 5.25/5.44
% 5.25/5.44 % neq_if_length_neq
% 5.25/5.44 thf(fact_512_neq__if__length__neq,axiom,
% 5.25/5.44 ! [Xs: list_nat,Ys: list_nat] :
% 5.25/5.44 ( ( ( size_size_list_nat @ Xs )
% 5.25/5.44 != ( size_size_list_nat @ Ys ) )
% 5.25/5.44 => ( Xs != Ys ) ) ).
% 5.25/5.44
% 5.25/5.44 % neq_if_length_neq
% 5.25/5.44 thf(fact_513_neq__if__length__neq,axiom,
% 5.25/5.44 ! [Xs: list_int,Ys: list_int] :
% 5.25/5.44 ( ( ( size_size_list_int @ Xs )
% 5.25/5.44 != ( size_size_list_int @ Ys ) )
% 5.25/5.44 => ( Xs != Ys ) ) ).
% 5.25/5.44
% 5.25/5.44 % neq_if_length_neq
% 5.25/5.44 thf(fact_514_Ex__list__of__length,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ? [Xs2: list_VEBT_VEBT] :
% 5.25/5.44 ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.25/5.44 = N2 ) ).
% 5.25/5.44
% 5.25/5.44 % Ex_list_of_length
% 5.25/5.44 thf(fact_515_Ex__list__of__length,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ? [Xs2: list_o] :
% 5.25/5.44 ( ( size_size_list_o @ Xs2 )
% 5.25/5.44 = N2 ) ).
% 5.25/5.44
% 5.25/5.44 % Ex_list_of_length
% 5.25/5.44 thf(fact_516_Ex__list__of__length,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ? [Xs2: list_nat] :
% 5.25/5.44 ( ( size_size_list_nat @ Xs2 )
% 5.25/5.44 = N2 ) ).
% 5.25/5.44
% 5.25/5.44 % Ex_list_of_length
% 5.25/5.44 thf(fact_517_Ex__list__of__length,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ? [Xs2: list_int] :
% 5.25/5.44 ( ( size_size_list_int @ Xs2 )
% 5.25/5.44 = N2 ) ).
% 5.25/5.44
% 5.25/5.44 % Ex_list_of_length
% 5.25/5.44 thf(fact_518_add__le__imp__le__right,axiom,
% 5.25/5.44 ! [A: real,C: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.44 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_right
% 5.25/5.44 thf(fact_519_add__le__imp__le__right,axiom,
% 5.25/5.44 ! [A: rat,C: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.44 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_right
% 5.25/5.44 thf(fact_520_add__le__imp__le__right,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.44 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_right
% 5.25/5.44 thf(fact_521_add__le__imp__le__right,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.44 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_right
% 5.25/5.44 thf(fact_522_add__le__imp__le__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.44 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_left
% 5.25/5.44 thf(fact_523_add__le__imp__le__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.44 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_left
% 5.25/5.44 thf(fact_524_add__le__imp__le__left,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.44 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_left
% 5.25/5.44 thf(fact_525_add__le__imp__le__left,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.44 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_imp_le_left
% 5.25/5.44 thf(fact_526_le__iff__add,axiom,
% 5.25/5.44 ( ord_less_eq_nat
% 5.25/5.44 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.44 ? [C2: nat] :
% 5.25/5.44 ( B2
% 5.25/5.44 = ( plus_plus_nat @ A3 @ C2 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % le_iff_add
% 5.25/5.44 thf(fact_527_add__right__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_mono
% 5.25/5.44 thf(fact_528_add__right__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_mono
% 5.25/5.44 thf(fact_529_add__right__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_mono
% 5.25/5.44 thf(fact_530_add__right__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_right_mono
% 5.25/5.44 thf(fact_531_less__eqE,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.44 => ~ ! [C3: nat] :
% 5.25/5.44 ( B
% 5.25/5.44 != ( plus_plus_nat @ A @ C3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_eqE
% 5.25/5.44 thf(fact_532_add__left__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_mono
% 5.25/5.44 thf(fact_533_add__left__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_mono
% 5.25/5.44 thf(fact_534_add__left__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_mono
% 5.25/5.44 thf(fact_535_add__left__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_left_mono
% 5.25/5.44 thf(fact_536_add__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono
% 5.25/5.44 thf(fact_537_add__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono
% 5.25/5.44 thf(fact_538_add__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono
% 5.25/5.44 thf(fact_539_add__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono
% 5.25/5.44 thf(fact_540_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(1)
% 5.25/5.44 thf(fact_541_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(1)
% 5.25/5.44 thf(fact_542_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(1)
% 5.25/5.44 thf(fact_543_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(1)
% 5.25/5.44 thf(fact_544_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_eq_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(2)
% 5.25/5.44 thf(fact_545_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_eq_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(2)
% 5.25/5.44 thf(fact_546_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_eq_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(2)
% 5.25/5.44 thf(fact_547_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_eq_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(2)
% 5.25/5.44 thf(fact_548_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(3)
% 5.25/5.44 thf(fact_549_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(3)
% 5.25/5.44 thf(fact_550_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(3)
% 5.25/5.44 thf(fact_551_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_semiring(3)
% 5.25/5.44 thf(fact_552_add__less__imp__less__right,axiom,
% 5.25/5.44 ! [A: real,C: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.44 => ( ord_less_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_right
% 5.25/5.44 thf(fact_553_add__less__imp__less__right,axiom,
% 5.25/5.44 ! [A: rat,C: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.44 => ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_right
% 5.25/5.44 thf(fact_554_add__less__imp__less__right,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.44 => ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_right
% 5.25/5.44 thf(fact_555_add__less__imp__less__right,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.44 => ( ord_less_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_right
% 5.25/5.44 thf(fact_556_add__less__imp__less__left,axiom,
% 5.25/5.44 ! [C: real,A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.25/5.44 => ( ord_less_real @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_left
% 5.25/5.44 thf(fact_557_add__less__imp__less__left,axiom,
% 5.25/5.44 ! [C: rat,A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.25/5.44 => ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_left
% 5.25/5.44 thf(fact_558_add__less__imp__less__left,axiom,
% 5.25/5.44 ! [C: nat,A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.25/5.44 => ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_left
% 5.25/5.44 thf(fact_559_add__less__imp__less__left,axiom,
% 5.25/5.44 ! [C: int,A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.25/5.44 => ( ord_less_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_imp_less_left
% 5.25/5.44 thf(fact_560_add__strict__right__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_right_mono
% 5.25/5.44 thf(fact_561_add__strict__right__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_right_mono
% 5.25/5.44 thf(fact_562_add__strict__right__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ B )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_right_mono
% 5.25/5.44 thf(fact_563_add__strict__right__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ B )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_right_mono
% 5.25/5.44 thf(fact_564_add__strict__left__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_left_mono
% 5.25/5.44 thf(fact_565_add__strict__left__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_left_mono
% 5.25/5.44 thf(fact_566_add__strict__left__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ B )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_left_mono
% 5.25/5.44 thf(fact_567_add__strict__left__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ B )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_left_mono
% 5.25/5.44 thf(fact_568_add__strict__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ( ord_less_real @ C @ D )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_mono
% 5.25/5.44 thf(fact_569_add__strict__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ( ord_less_rat @ C @ D )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_mono
% 5.25/5.44 thf(fact_570_add__strict__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ B )
% 5.25/5.44 => ( ( ord_less_nat @ C @ D )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_mono
% 5.25/5.44 thf(fact_571_add__strict__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ B )
% 5.25/5.44 => ( ( ord_less_int @ C @ D )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_strict_mono
% 5.25/5.44 thf(fact_572_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_real @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(1)
% 5.25/5.44 thf(fact_573_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_rat @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(1)
% 5.25/5.44 thf(fact_574_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(1)
% 5.25/5.44 thf(fact_575_add__mono__thms__linordered__field_I1_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_int @ I2 @ J )
% 5.25/5.44 & ( K = L ) )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(1)
% 5.25/5.44 thf(fact_576_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(2)
% 5.25/5.44 thf(fact_577_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(2)
% 5.25/5.44 thf(fact_578_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(2)
% 5.25/5.44 thf(fact_579_add__mono__thms__linordered__field_I2_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( I2 = J )
% 5.25/5.44 & ( ord_less_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(2)
% 5.25/5.44 thf(fact_580_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_real @ I2 @ J )
% 5.25/5.44 & ( ord_less_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(5)
% 5.25/5.44 thf(fact_581_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_rat @ I2 @ J )
% 5.25/5.44 & ( ord_less_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(5)
% 5.25/5.44 thf(fact_582_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 & ( ord_less_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(5)
% 5.25/5.44 thf(fact_583_add__mono__thms__linordered__field_I5_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_int @ I2 @ J )
% 5.25/5.44 & ( ord_less_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(5)
% 5.25/5.44 thf(fact_584_add__divide__distrib,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat] :
% 5.25/5.44 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_divide_distrib
% 5.25/5.44 thf(fact_585_add__divide__distrib,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real] :
% 5.25/5.44 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_divide_distrib
% 5.25/5.44 thf(fact_586_add__divide__distrib,axiom,
% 5.25/5.44 ! [A: complex,B: complex,C: complex] :
% 5.25/5.44 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.25/5.44 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_divide_distrib
% 5.25/5.44 thf(fact_587_length__induct,axiom,
% 5.25/5.44 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.25/5.44 ( ! [Xs2: list_VEBT_VEBT] :
% 5.25/5.44 ( ! [Ys2: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.25/5.44 => ( P @ Ys2 ) )
% 5.25/5.44 => ( P @ Xs2 ) )
% 5.25/5.44 => ( P @ Xs ) ) ).
% 5.25/5.44
% 5.25/5.44 % length_induct
% 5.25/5.44 thf(fact_588_length__induct,axiom,
% 5.25/5.44 ! [P: list_o > $o,Xs: list_o] :
% 5.25/5.44 ( ! [Xs2: list_o] :
% 5.25/5.44 ( ! [Ys2: list_o] :
% 5.25/5.44 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs2 ) )
% 5.25/5.44 => ( P @ Ys2 ) )
% 5.25/5.44 => ( P @ Xs2 ) )
% 5.25/5.44 => ( P @ Xs ) ) ).
% 5.25/5.44
% 5.25/5.44 % length_induct
% 5.25/5.44 thf(fact_589_length__induct,axiom,
% 5.25/5.44 ! [P: list_nat > $o,Xs: list_nat] :
% 5.25/5.44 ( ! [Xs2: list_nat] :
% 5.25/5.44 ( ! [Ys2: list_nat] :
% 5.25/5.44 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs2 ) )
% 5.25/5.44 => ( P @ Ys2 ) )
% 5.25/5.44 => ( P @ Xs2 ) )
% 5.25/5.44 => ( P @ Xs ) ) ).
% 5.25/5.44
% 5.25/5.44 % length_induct
% 5.25/5.44 thf(fact_590_length__induct,axiom,
% 5.25/5.44 ! [P: list_int > $o,Xs: list_int] :
% 5.25/5.44 ( ! [Xs2: list_int] :
% 5.25/5.44 ( ! [Ys2: list_int] :
% 5.25/5.44 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs2 ) )
% 5.25/5.44 => ( P @ Ys2 ) )
% 5.25/5.44 => ( P @ Xs2 ) )
% 5.25/5.44 => ( P @ Xs ) ) ).
% 5.25/5.44
% 5.25/5.44 % length_induct
% 5.25/5.44 thf(fact_591_add__less__le__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_le_mono
% 5.25/5.44 thf(fact_592_add__less__le__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_le_mono
% 5.25/5.44 thf(fact_593_add__less__le__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_le_mono
% 5.25/5.44 thf(fact_594_add__less__le__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ B )
% 5.25/5.44 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_less_le_mono
% 5.25/5.44 thf(fact_595_add__le__less__mono,axiom,
% 5.25/5.44 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.44 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.44 => ( ( ord_less_real @ C @ D )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_less_mono
% 5.25/5.44 thf(fact_596_add__le__less__mono,axiom,
% 5.25/5.44 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.44 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.44 => ( ( ord_less_rat @ C @ D )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_less_mono
% 5.25/5.44 thf(fact_597_add__le__less__mono,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.44 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.44 => ( ( ord_less_nat @ C @ D )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_less_mono
% 5.25/5.44 thf(fact_598_add__le__less__mono,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.44 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.44 => ( ( ord_less_int @ C @ D )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_le_less_mono
% 5.25/5.44 thf(fact_599_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_real @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(3)
% 5.25/5.44 thf(fact_600_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_rat @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(3)
% 5.25/5.44 thf(fact_601_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_nat @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(3)
% 5.25/5.44 thf(fact_602_add__mono__thms__linordered__field_I3_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_int @ I2 @ J )
% 5.25/5.44 & ( ord_less_eq_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(3)
% 5.25/5.44 thf(fact_603_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.44 ! [I2: real,J: real,K: real,L: real] :
% 5.25/5.44 ( ( ( ord_less_eq_real @ I2 @ J )
% 5.25/5.44 & ( ord_less_real @ K @ L ) )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ I2 @ K ) @ ( plus_plus_real @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(4)
% 5.25/5.44 thf(fact_604_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.44 ! [I2: rat,J: rat,K: rat,L: rat] :
% 5.25/5.44 ( ( ( ord_less_eq_rat @ I2 @ J )
% 5.25/5.44 & ( ord_less_rat @ K @ L ) )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ I2 @ K ) @ ( plus_plus_rat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(4)
% 5.25/5.44 thf(fact_605_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.44 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.44 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.44 & ( ord_less_nat @ K @ L ) )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(4)
% 5.25/5.44 thf(fact_606_add__mono__thms__linordered__field_I4_J,axiom,
% 5.25/5.44 ! [I2: int,J: int,K: int,L: int] :
% 5.25/5.44 ( ( ( ord_less_eq_int @ I2 @ J )
% 5.25/5.44 & ( ord_less_int @ K @ L ) )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ I2 @ K ) @ ( plus_plus_int @ J @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono_thms_linordered_field(4)
% 5.25/5.44 thf(fact_607_add__mono1,axiom,
% 5.25/5.44 ! [A: real,B: real] :
% 5.25/5.44 ( ( ord_less_real @ A @ B )
% 5.25/5.44 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono1
% 5.25/5.44 thf(fact_608_add__mono1,axiom,
% 5.25/5.44 ! [A: rat,B: rat] :
% 5.25/5.44 ( ( ord_less_rat @ A @ B )
% 5.25/5.44 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono1
% 5.25/5.44 thf(fact_609_add__mono1,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( ord_less_nat @ A @ B )
% 5.25/5.44 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono1
% 5.25/5.44 thf(fact_610_add__mono1,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( ord_less_int @ A @ B )
% 5.25/5.44 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % add_mono1
% 5.25/5.44 thf(fact_611_less__add__one,axiom,
% 5.25/5.44 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_one
% 5.25/5.44 thf(fact_612_less__add__one,axiom,
% 5.25/5.44 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_one
% 5.25/5.44 thf(fact_613_less__add__one,axiom,
% 5.25/5.44 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_one
% 5.25/5.44 thf(fact_614_less__add__one,axiom,
% 5.25/5.44 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.25/5.44
% 5.25/5.44 % less_add_one
% 5.25/5.44 thf(fact_615_list__eq__iff__nth__eq,axiom,
% 5.25/5.44 ( ( ^ [Y6: list_VEBT_VEBT,Z4: list_VEBT_VEBT] : ( Y6 = Z4 ) )
% 5.25/5.44 = ( ^ [Xs3: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.25/5.44 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.25/5.44 => ( ( nth_VEBT_VEBT @ Xs3 @ I3 )
% 5.25/5.44 = ( nth_VEBT_VEBT @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_eq_iff_nth_eq
% 5.25/5.44 thf(fact_616_list__eq__iff__nth__eq,axiom,
% 5.25/5.44 ( ( ^ [Y6: list_o,Z4: list_o] : ( Y6 = Z4 ) )
% 5.25/5.44 = ( ^ [Xs3: list_o,Ys3: list_o] :
% 5.25/5.44 ( ( ( size_size_list_o @ Xs3 )
% 5.25/5.44 = ( size_size_list_o @ Ys3 ) )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) )
% 5.25/5.44 => ( ( nth_o @ Xs3 @ I3 )
% 5.25/5.44 = ( nth_o @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_eq_iff_nth_eq
% 5.25/5.44 thf(fact_617_list__eq__iff__nth__eq,axiom,
% 5.25/5.44 ( ( ^ [Y6: list_nat,Z4: list_nat] : ( Y6 = Z4 ) )
% 5.25/5.44 = ( ^ [Xs3: list_nat,Ys3: list_nat] :
% 5.25/5.44 ( ( ( size_size_list_nat @ Xs3 )
% 5.25/5.44 = ( size_size_list_nat @ Ys3 ) )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) )
% 5.25/5.44 => ( ( nth_nat @ Xs3 @ I3 )
% 5.25/5.44 = ( nth_nat @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_eq_iff_nth_eq
% 5.25/5.44 thf(fact_618_list__eq__iff__nth__eq,axiom,
% 5.25/5.44 ( ( ^ [Y6: list_int,Z4: list_int] : ( Y6 = Z4 ) )
% 5.25/5.44 = ( ^ [Xs3: list_int,Ys3: list_int] :
% 5.25/5.44 ( ( ( size_size_list_int @ Xs3 )
% 5.25/5.44 = ( size_size_list_int @ Ys3 ) )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) )
% 5.25/5.44 => ( ( nth_int @ Xs3 @ I3 )
% 5.25/5.44 = ( nth_int @ Ys3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % list_eq_iff_nth_eq
% 5.25/5.44 thf(fact_619_Skolem__list__nth,axiom,
% 5.25/5.44 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.25/5.44 ( ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ? [X3: vEBT_VEBT] : ( P @ I3 @ X3 ) ) )
% 5.25/5.44 = ( ? [Xs3: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.25/5.44 = K )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ( P @ I3 @ ( nth_VEBT_VEBT @ Xs3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Skolem_list_nth
% 5.25/5.44 thf(fact_620_Skolem__list__nth,axiom,
% 5.25/5.44 ! [K: nat,P: nat > $o > $o] :
% 5.25/5.44 ( ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ? [X3: $o] : ( P @ I3 @ X3 ) ) )
% 5.25/5.44 = ( ? [Xs3: list_o] :
% 5.25/5.44 ( ( ( size_size_list_o @ Xs3 )
% 5.25/5.44 = K )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ( P @ I3 @ ( nth_o @ Xs3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Skolem_list_nth
% 5.25/5.44 thf(fact_621_Skolem__list__nth,axiom,
% 5.25/5.44 ! [K: nat,P: nat > nat > $o] :
% 5.25/5.44 ( ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ? [X3: nat] : ( P @ I3 @ X3 ) ) )
% 5.25/5.44 = ( ? [Xs3: list_nat] :
% 5.25/5.44 ( ( ( size_size_list_nat @ Xs3 )
% 5.25/5.44 = K )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ( P @ I3 @ ( nth_nat @ Xs3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Skolem_list_nth
% 5.25/5.44 thf(fact_622_Skolem__list__nth,axiom,
% 5.25/5.44 ! [K: nat,P: nat > int > $o] :
% 5.25/5.44 ( ( ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ? [X3: int] : ( P @ I3 @ X3 ) ) )
% 5.25/5.44 = ( ? [Xs3: list_int] :
% 5.25/5.44 ( ( ( size_size_list_int @ Xs3 )
% 5.25/5.44 = K )
% 5.25/5.44 & ! [I3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I3 @ K )
% 5.25/5.44 => ( P @ I3 @ ( nth_int @ Xs3 @ I3 ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % Skolem_list_nth
% 5.25/5.44 thf(fact_623_nth__equalityI,axiom,
% 5.25/5.44 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.25/5.44 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.25/5.44 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.25/5.44 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.25/5.44 = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 5.25/5.44 => ( Xs = Ys ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_equalityI
% 5.25/5.44 thf(fact_624_nth__equalityI,axiom,
% 5.25/5.44 ! [Xs: list_o,Ys: list_o] :
% 5.25/5.44 ( ( ( size_size_list_o @ Xs )
% 5.25/5.44 = ( size_size_list_o @ Ys ) )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.25/5.44 => ( ( nth_o @ Xs @ I4 )
% 5.25/5.44 = ( nth_o @ Ys @ I4 ) ) )
% 5.25/5.44 => ( Xs = Ys ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_equalityI
% 5.25/5.44 thf(fact_625_nth__equalityI,axiom,
% 5.25/5.44 ! [Xs: list_nat,Ys: list_nat] :
% 5.25/5.44 ( ( ( size_size_list_nat @ Xs )
% 5.25/5.44 = ( size_size_list_nat @ Ys ) )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.25/5.44 => ( ( nth_nat @ Xs @ I4 )
% 5.25/5.44 = ( nth_nat @ Ys @ I4 ) ) )
% 5.25/5.44 => ( Xs = Ys ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_equalityI
% 5.25/5.44 thf(fact_626_nth__equalityI,axiom,
% 5.25/5.44 ! [Xs: list_int,Ys: list_int] :
% 5.25/5.44 ( ( ( size_size_list_int @ Xs )
% 5.25/5.44 = ( size_size_list_int @ Ys ) )
% 5.25/5.44 => ( ! [I4: nat] :
% 5.25/5.44 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.25/5.44 => ( ( nth_int @ Xs @ I4 )
% 5.25/5.44 = ( nth_int @ Ys @ I4 ) ) )
% 5.25/5.44 => ( Xs = Ys ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % nth_equalityI
% 5.25/5.44 thf(fact_627_discrete,axiom,
% 5.25/5.44 ( ord_less_nat
% 5.25/5.44 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % discrete
% 5.25/5.44 thf(fact_628_discrete,axiom,
% 5.25/5.44 ( ord_less_int
% 5.25/5.44 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % discrete
% 5.25/5.44 thf(fact_629_buildup__nothing__in__leaf,axiom,
% 5.25/5.44 ! [N2: nat,X4: nat] :
% 5.25/5.44 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 5.25/5.44
% 5.25/5.44 % buildup_nothing_in_leaf
% 5.25/5.44 thf(fact_630_low__def,axiom,
% 5.25/5.44 ( vEBT_VEBT_low
% 5.25/5.44 = ( ^ [X: nat,N: nat] : ( modulo_modulo_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % low_def
% 5.25/5.44 thf(fact_631_buildup__nothing__in__min__max,axiom,
% 5.25/5.44 ! [N2: nat,X4: nat] :
% 5.25/5.44 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N2 ) @ X4 ) ).
% 5.25/5.44
% 5.25/5.44 % buildup_nothing_in_min_max
% 5.25/5.44 thf(fact_632_invar__vebt_Ointros_I3_J,axiom,
% 5.25/5.44 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.25/5.44 ( ! [X5: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.44 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.25/5.44 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.44 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.44 => ( ( M
% 5.25/5.44 = ( suc @ N2 ) )
% 5.25/5.44 => ( ( Deg
% 5.25/5.44 = ( plus_plus_nat @ N2 @ M ) )
% 5.25/5.44 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.25/5.44 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.44 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.25/5.44 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % invar_vebt.intros(3)
% 5.25/5.44 thf(fact_633_invar__vebt_Ointros_I2_J,axiom,
% 5.25/5.44 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.25/5.44 ( ! [X5: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.44 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.25/5.44 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.44 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.44 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.44 => ( ( M = N2 )
% 5.25/5.44 => ( ( Deg
% 5.25/5.44 = ( plus_plus_nat @ N2 @ M ) )
% 5.25/5.44 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 )
% 5.25/5.44 => ( ! [X5: vEBT_VEBT] :
% 5.25/5.44 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.44 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) )
% 5.25/5.44 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % invar_vebt.intros(2)
% 5.25/5.44 thf(fact_634_dbl__simps_I3_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.25/5.44 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(3)
% 5.25/5.44 thf(fact_635_dbl__simps_I3_J,axiom,
% 5.25/5.44 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.25/5.44 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(3)
% 5.25/5.44 thf(fact_636_dbl__simps_I3_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.25/5.44 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(3)
% 5.25/5.44 thf(fact_637_dbl__simps_I3_J,axiom,
% 5.25/5.44 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.25/5.44 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_simps(3)
% 5.25/5.44 thf(fact_638_power__numeral,axiom,
% 5.25/5.44 ! [K: num,L: num] :
% 5.25/5.44 ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.44 = ( numera1916890842035813515d_enat @ ( pow @ K @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_numeral
% 5.25/5.44 thf(fact_639_power__numeral,axiom,
% 5.25/5.44 ! [K: num,L: num] :
% 5.25/5.44 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.44 = ( numera6690914467698888265omplex @ ( pow @ K @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_numeral
% 5.25/5.44 thf(fact_640_power__numeral,axiom,
% 5.25/5.44 ! [K: num,L: num] :
% 5.25/5.44 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.44 = ( numeral_numeral_real @ ( pow @ K @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_numeral
% 5.25/5.44 thf(fact_641_power__numeral,axiom,
% 5.25/5.44 ! [K: num,L: num] :
% 5.25/5.44 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.44 = ( numeral_numeral_nat @ ( pow @ K @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_numeral
% 5.25/5.44 thf(fact_642_power__numeral,axiom,
% 5.25/5.44 ! [K: num,L: num] :
% 5.25/5.44 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.44 = ( numeral_numeral_int @ ( pow @ K @ L ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_numeral
% 5.25/5.44 thf(fact_643_valid__eq2,axiom,
% 5.25/5.44 ! [T2: vEBT_VEBT,D: nat] :
% 5.25/5.44 ( ( vEBT_VEBT_valid @ T2 @ D )
% 5.25/5.44 => ( vEBT_invar_vebt @ T2 @ D ) ) ).
% 5.25/5.44
% 5.25/5.44 % valid_eq2
% 5.25/5.44 thf(fact_644_valid__eq,axiom,
% 5.25/5.44 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.25/5.44
% 5.25/5.44 % valid_eq
% 5.25/5.44 thf(fact_645_valid__eq1,axiom,
% 5.25/5.44 ! [T2: vEBT_VEBT,D: nat] :
% 5.25/5.44 ( ( vEBT_invar_vebt @ T2 @ D )
% 5.25/5.44 => ( vEBT_VEBT_valid @ T2 @ D ) ) ).
% 5.25/5.44
% 5.25/5.44 % valid_eq1
% 5.25/5.44 thf(fact_646_zdiv__numeral__Bit0,axiom,
% 5.25/5.44 ! [V: num,W: num] :
% 5.25/5.44 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.44 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % zdiv_numeral_Bit0
% 5.25/5.44 thf(fact_647_mod__mod__trivial,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.44 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mod_trivial
% 5.25/5.44 thf(fact_648_mod__mod__trivial,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.44 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mod_trivial
% 5.25/5.44 thf(fact_649_mod__mod__trivial,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_mod_trivial
% 5.25/5.44 thf(fact_650_mod__add__self1,axiom,
% 5.25/5.44 ! [B: nat,A: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.44 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self1
% 5.25/5.44 thf(fact_651_mod__add__self1,axiom,
% 5.25/5.44 ! [B: int,A: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.44 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self1
% 5.25/5.44 thf(fact_652_mod__add__self1,axiom,
% 5.25/5.44 ! [B: code_integer,A: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.25/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self1
% 5.25/5.44 thf(fact_653_mod__add__self2,axiom,
% 5.25/5.44 ! [A: nat,B: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.44 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self2
% 5.25/5.44 thf(fact_654_mod__add__self2,axiom,
% 5.25/5.44 ! [A: int,B: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.44 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self2
% 5.25/5.44 thf(fact_655_mod__add__self2,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.25/5.44 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_self2
% 5.25/5.44 thf(fact_656_mod__less,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.44 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.25/5.44 = M ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_less
% 5.25/5.44 thf(fact_657_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_658_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_659_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_660_bits__one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % bits_one_mod_two_eq_one
% 5.25/5.44 thf(fact_661_bits__one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % bits_one_mod_two_eq_one
% 5.25/5.44 thf(fact_662_bits__one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_Code_integer ) ).
% 5.25/5.44
% 5.25/5.44 % bits_one_mod_two_eq_one
% 5.25/5.44 thf(fact_663_one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_nat ) ).
% 5.25/5.44
% 5.25/5.44 % one_mod_two_eq_one
% 5.25/5.44 thf(fact_664_one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_int ) ).
% 5.25/5.44
% 5.25/5.44 % one_mod_two_eq_one
% 5.25/5.44 thf(fact_665_one__mod__two__eq__one,axiom,
% 5.25/5.44 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.44 = one_one_Code_integer ) ).
% 5.25/5.44
% 5.25/5.44 % one_mod_two_eq_one
% 5.25/5.44 thf(fact_666_mod2__Suc__Suc,axiom,
% 5.25/5.44 ! [M: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.44 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod2_Suc_Suc
% 5.25/5.44 thf(fact_667_mod__add__eq,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_eq
% 5.25/5.44 thf(fact_668_mod__add__eq,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_eq
% 5.25/5.44 thf(fact_669_mod__add__eq,axiom,
% 5.25/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_eq
% 5.25/5.44 thf(fact_670_mod__add__cong,axiom,
% 5.25/5.44 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.25/5.44 ( ( ( modulo_modulo_nat @ A @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.25/5.44 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.25/5.44 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_cong
% 5.25/5.44 thf(fact_671_mod__add__cong,axiom,
% 5.25/5.44 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.25/5.44 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.44 = ( modulo_modulo_int @ A4 @ C ) )
% 5.25/5.44 => ( ( ( modulo_modulo_int @ B @ C )
% 5.25/5.44 = ( modulo_modulo_int @ B4 @ C ) )
% 5.25/5.44 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_cong
% 5.25/5.44 thf(fact_672_mod__add__cong,axiom,
% 5.25/5.44 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.25/5.44 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.25/5.44 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.25/5.44 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_cong
% 5.25/5.44 thf(fact_673_mod__add__left__eq,axiom,
% 5.25/5.44 ! [A: nat,C: nat,B: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_left_eq
% 5.25/5.44 thf(fact_674_mod__add__left__eq,axiom,
% 5.25/5.44 ! [A: int,C: int,B: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.25/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_left_eq
% 5.25/5.44 thf(fact_675_mod__add__left__eq,axiom,
% 5.25/5.44 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_left_eq
% 5.25/5.44 thf(fact_676_mod__add__right__eq,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_right_eq
% 5.25/5.44 thf(fact_677_mod__add__right__eq,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_right_eq
% 5.25/5.44 thf(fact_678_mod__add__right__eq,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_add_right_eq
% 5.25/5.44 thf(fact_679_power__mod,axiom,
% 5.25/5.44 ! [A: nat,B: nat,N2: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N2 ) @ B )
% 5.25/5.44 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N2 ) @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mod
% 5.25/5.44 thf(fact_680_power__mod,axiom,
% 5.25/5.44 ! [A: int,B: int,N2: nat] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N2 ) @ B )
% 5.25/5.44 = ( modulo_modulo_int @ ( power_power_int @ A @ N2 ) @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mod
% 5.25/5.44 thf(fact_681_power__mod,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N2 ) @ B )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ B ) ) ).
% 5.25/5.44
% 5.25/5.44 % power_mod
% 5.25/5.44 thf(fact_682_mod__Suc__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) @ N2 )
% 5.25/5.44 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_Suc_eq
% 5.25/5.44 thf(fact_683_mod__Suc__Suc__eq,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ N2 )
% 5.25/5.44 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_Suc_Suc_eq
% 5.25/5.44 thf(fact_684_mod__less__eq__dividend,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ M ) ).
% 5.25/5.44
% 5.25/5.44 % mod_less_eq_dividend
% 5.25/5.44 thf(fact_685_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num,N2: num] :
% 5.25/5.44 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.25/5.44 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.25/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(9)
% 5.25/5.44 thf(fact_686_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num,N2: num] :
% 5.25/5.44 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.25/5.44 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.25/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(9)
% 5.25/5.44 thf(fact_687_cong__exp__iff__simps_I9_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num,N2: num] :
% 5.25/5.44 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.25/5.44 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(9)
% 5.25/5.44 thf(fact_688_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.25/5.44 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(4)
% 5.25/5.44 thf(fact_689_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.25/5.44 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(4)
% 5.25/5.44 thf(fact_690_cong__exp__iff__simps_I4_J,axiom,
% 5.25/5.44 ! [M: num,N2: num] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.25/5.44 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(4)
% 5.25/5.44 thf(fact_691_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(8)
% 5.25/5.44 thf(fact_692_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(8)
% 5.25/5.44 thf(fact_693_cong__exp__iff__simps_I8_J,axiom,
% 5.25/5.44 ! [M: num,Q3: num] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(8)
% 5.25/5.44 thf(fact_694_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.44 ! [Q3: num,N2: num] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(6)
% 5.25/5.44 thf(fact_695_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.44 ! [Q3: num,N2: num] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(6)
% 5.25/5.44 thf(fact_696_cong__exp__iff__simps_I6_J,axiom,
% 5.25/5.44 ! [Q3: num,N2: num] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.25/5.44 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % cong_exp_iff_simps(6)
% 5.25/5.44 thf(fact_697_div__add1__eq,axiom,
% 5.25/5.44 ! [A: nat,B: nat,C: nat] :
% 5.25/5.44 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.44 = ( 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 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_add1_eq
% 5.25/5.44 thf(fact_698_div__add1__eq,axiom,
% 5.25/5.44 ! [A: int,B: int,C: int] :
% 5.25/5.44 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.44 = ( 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 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_add1_eq
% 5.25/5.44 thf(fact_699_div__add1__eq,axiom,
% 5.25/5.44 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.44 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.25/5.44 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_add1_eq
% 5.25/5.44 thf(fact_700_mod__induct,axiom,
% 5.25/5.44 ! [P: nat > $o,N2: nat,P2: nat,M: nat] :
% 5.25/5.44 ( ( P @ N2 )
% 5.25/5.44 => ( ( ord_less_nat @ N2 @ P2 )
% 5.25/5.44 => ( ( ord_less_nat @ M @ P2 )
% 5.25/5.44 => ( ! [N3: nat] :
% 5.25/5.44 ( ( ord_less_nat @ N3 @ P2 )
% 5.25/5.44 => ( ( P @ N3 )
% 5.25/5.44 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P2 ) ) ) )
% 5.25/5.44 => ( P @ M ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % mod_induct
% 5.25/5.44 thf(fact_701_mod__Suc__le__divisor,axiom,
% 5.25/5.44 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N2 ) ) @ N2 ) ).
% 5.25/5.44
% 5.25/5.44 % mod_Suc_le_divisor
% 5.25/5.44 thf(fact_702_dbl__def,axiom,
% 5.25/5.44 ( neg_numeral_dbl_real
% 5.25/5.44 = ( ^ [X: real] : ( plus_plus_real @ X @ X ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_def
% 5.25/5.44 thf(fact_703_dbl__def,axiom,
% 5.25/5.44 ( neg_numeral_dbl_rat
% 5.25/5.44 = ( ^ [X: rat] : ( plus_plus_rat @ X @ X ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_def
% 5.25/5.44 thf(fact_704_dbl__def,axiom,
% 5.25/5.44 ( neg_numeral_dbl_int
% 5.25/5.44 = ( ^ [X: int] : ( plus_plus_int @ X @ X ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % dbl_def
% 5.25/5.44 thf(fact_705_pow_Osimps_I1_J,axiom,
% 5.25/5.44 ! [X4: num] :
% 5.25/5.44 ( ( pow @ X4 @ one )
% 5.25/5.44 = X4 ) ).
% 5.25/5.44
% 5.25/5.44 % pow.simps(1)
% 5.25/5.44 thf(fact_706_bounded__Max__nat,axiom,
% 5.25/5.44 ! [P: nat > $o,X4: nat,M7: nat] :
% 5.25/5.44 ( ( P @ X4 )
% 5.25/5.44 => ( ! [X5: nat] :
% 5.25/5.44 ( ( P @ X5 )
% 5.25/5.44 => ( ord_less_eq_nat @ X5 @ M7 ) )
% 5.25/5.44 => ~ ! [M5: nat] :
% 5.25/5.44 ( ( P @ M5 )
% 5.25/5.44 => ~ ! [X2: nat] :
% 5.25/5.44 ( ( P @ X2 )
% 5.25/5.44 => ( ord_less_eq_nat @ X2 @ M5 ) ) ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % bounded_Max_nat
% 5.25/5.44 thf(fact_707_div__exp__mod__exp__eq,axiom,
% 5.25/5.44 ! [A: nat,N2: nat,M: nat] :
% 5.25/5.44 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.44 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_exp_mod_exp_eq
% 5.25/5.44 thf(fact_708_div__exp__mod__exp__eq,axiom,
% 5.25/5.44 ! [A: int,N2: nat,M: nat] :
% 5.25/5.44 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.44 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_exp_mod_exp_eq
% 5.25/5.44 thf(fact_709_div__exp__mod__exp__eq,axiom,
% 5.25/5.44 ! [A: code_integer,N2: nat,M: nat] :
% 5.25/5.44 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.44 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % div_exp_mod_exp_eq
% 5.25/5.44 thf(fact_710_buildup__gives__valid,axiom,
% 5.25/5.44 ! [N2: nat] :
% 5.25/5.44 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.44 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N2 ) @ N2 ) ) ).
% 5.25/5.44
% 5.25/5.44 % buildup_gives_valid
% 5.25/5.44 thf(fact_711_psubsetI,axiom,
% 5.25/5.44 ! [A2: set_int,B3: set_int] :
% 5.25/5.44 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.44 => ( ( A2 != B3 )
% 5.25/5.44 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % psubsetI
% 5.25/5.44 thf(fact_712_subset__antisym,axiom,
% 5.25/5.44 ! [A2: set_int,B3: set_int] :
% 5.25/5.44 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.44 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.25/5.44 => ( A2 = B3 ) ) ) ).
% 5.25/5.44
% 5.25/5.44 % subset_antisym
% 5.25/5.44 thf(fact_713_subsetI,axiom,
% 5.25/5.44 ! [A2: set_real,B3: set_real] :
% 5.25/5.44 ( ! [X5: real] :
% 5.25/5.44 ( ( member_real @ X5 @ A2 )
% 5.25/5.44 => ( member_real @ X5 @ B3 ) )
% 5.25/5.44 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.25/5.44
% 5.25/5.44 % subsetI
% 5.25/5.44 thf(fact_714_subsetI,axiom,
% 5.25/5.44 ! [A2: set_nat,B3: set_nat] :
% 5.25/5.44 ( ! [X5: nat] :
% 5.25/5.44 ( ( member_nat @ X5 @ A2 )
% 5.25/5.44 => ( member_nat @ X5 @ B3 ) )
% 5.25/5.44 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.25/5.44
% 5.25/5.44 % subsetI
% 5.25/5.44 thf(fact_715_subsetI,axiom,
% 5.25/5.44 ! [A2: set_complex,B3: set_complex] :
% 5.25/5.44 ( ! [X5: complex] :
% 5.25/5.44 ( ( member_complex @ X5 @ A2 )
% 5.25/5.44 => ( member_complex @ X5 @ B3 ) )
% 5.25/5.44 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 5.25/5.44
% 5.25/5.44 % subsetI
% 5.25/5.44 thf(fact_716_subsetI,axiom,
% 5.25/5.44 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.25/5.44 ( ! [X5: product_prod_nat_nat] :
% 5.25/5.44 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.25/5.44 => ( member8440522571783428010at_nat @ X5 @ B3 ) )
% 5.25/5.44 => ( ord_le3146513528884898305at_nat @ A2 @ B3 ) ) ).
% 5.25/5.44
% 5.25/5.44 % subsetI
% 5.25/5.44 thf(fact_717_subsetI,axiom,
% 5.25/5.44 ! [A2: set_int,B3: set_int] :
% 5.25/5.44 ( ! [X5: int] :
% 5.25/5.44 ( ( member_int @ X5 @ A2 )
% 5.25/5.44 => ( member_int @ X5 @ B3 ) )
% 5.25/5.44 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.44
% 5.25/5.44 % subsetI
% 5.25/5.44 thf(fact_718_verit__eq__simplify_I8_J,axiom,
% 5.25/5.44 ! [X22: num,Y2: num] :
% 5.25/5.44 ( ( ( bit0 @ X22 )
% 5.25/5.45 = ( bit0 @ Y2 ) )
% 5.25/5.45 = ( X22 = Y2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % verit_eq_simplify(8)
% 5.25/5.45 thf(fact_719_order__refl,axiom,
% 5.25/5.45 ! [X4: set_int] : ( ord_less_eq_set_int @ X4 @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % order_refl
% 5.25/5.45 thf(fact_720_order__refl,axiom,
% 5.25/5.45 ! [X4: rat] : ( ord_less_eq_rat @ X4 @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % order_refl
% 5.25/5.45 thf(fact_721_order__refl,axiom,
% 5.25/5.45 ! [X4: num] : ( ord_less_eq_num @ X4 @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % order_refl
% 5.25/5.45 thf(fact_722_order__refl,axiom,
% 5.25/5.45 ! [X4: nat] : ( ord_less_eq_nat @ X4 @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % order_refl
% 5.25/5.45 thf(fact_723_order__refl,axiom,
% 5.25/5.45 ! [X4: int] : ( ord_less_eq_int @ X4 @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % order_refl
% 5.25/5.45 thf(fact_724_dual__order_Orefl,axiom,
% 5.25/5.45 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % dual_order.refl
% 5.25/5.45 thf(fact_725_dual__order_Orefl,axiom,
% 5.25/5.45 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % dual_order.refl
% 5.25/5.45 thf(fact_726_dual__order_Orefl,axiom,
% 5.25/5.45 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % dual_order.refl
% 5.25/5.45 thf(fact_727_dual__order_Orefl,axiom,
% 5.25/5.45 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % dual_order.refl
% 5.25/5.45 thf(fact_728_dual__order_Orefl,axiom,
% 5.25/5.45 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.25/5.45
% 5.25/5.45 % dual_order.refl
% 5.25/5.45 thf(fact_729_mod2__gr__0,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = one_one_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod2_gr_0
% 5.25/5.45 thf(fact_730_length__subseqs,axiom,
% 5.25/5.45 ! [Xs: list_VEBT_VEBT] :
% 5.25/5.45 ( ( size_s8217280938318005548T_VEBT @ ( subseqs_VEBT_VEBT @ Xs ) )
% 5.25/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % length_subseqs
% 5.25/5.45 thf(fact_731_length__subseqs,axiom,
% 5.25/5.45 ! [Xs: list_o] :
% 5.25/5.45 ( ( size_s2710708370519433104list_o @ ( subseqs_o @ Xs ) )
% 5.25/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_o @ Xs ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % length_subseqs
% 5.25/5.45 thf(fact_732_length__subseqs,axiom,
% 5.25/5.45 ! [Xs: list_nat] :
% 5.25/5.45 ( ( size_s3023201423986296836st_nat @ ( subseqs_nat @ Xs ) )
% 5.25/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % length_subseqs
% 5.25/5.45 thf(fact_733_length__subseqs,axiom,
% 5.25/5.45 ! [Xs: list_int] :
% 5.25/5.45 ( ( size_s533118279054570080st_int @ ( subseqs_int @ Xs ) )
% 5.25/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( size_size_list_int @ Xs ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % length_subseqs
% 5.25/5.45 thf(fact_734_invar__vebt_Ointros_I5_J,axiom,
% 5.25/5.45 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.25/5.45 ( ! [X5: vEBT_VEBT] :
% 5.25/5.45 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.45 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.25/5.45 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.45 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.45 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.45 => ( ( M
% 5.25/5.45 = ( suc @ N2 ) )
% 5.25/5.45 => ( ( Deg
% 5.25/5.45 = ( plus_plus_nat @ N2 @ M ) )
% 5.25/5.45 => ( ! [I4: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.45 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 5.25/5.45 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.25/5.45 => ( ( ( Mi = Ma )
% 5.25/5.45 => ! [X5: vEBT_VEBT] :
% 5.25/5.45 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.45 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.25/5.45 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.45 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.45 => ( ( ( Mi != Ma )
% 5.25/5.45 => ! [I4: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.45 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.25/5.45 = I4 )
% 5.25/5.45 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.25/5.45 & ! [X5: nat] :
% 5.25/5.45 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.25/5.45 = I4 )
% 5.25/5.45 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.25/5.45 => ( ( ord_less_nat @ Mi @ X5 )
% 5.25/5.45 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.25/5.45 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % invar_vebt.intros(5)
% 5.25/5.45 thf(fact_735_deg__not__0,axiom,
% 5.25/5.45 ! [T2: vEBT_VEBT,N2: nat] :
% 5.25/5.45 ( ( vEBT_invar_vebt @ T2 @ N2 )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % deg_not_0
% 5.25/5.45 thf(fact_736__C5_Ohyps_C_I12_J,axiom,
% 5.25/5.45 ( ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) )
% 5.25/5.45 = info ) ).
% 5.25/5.45
% 5.25/5.45 % "5.hyps"(12)
% 5.25/5.45 thf(fact_737_le__zero__eq,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_zero_eq
% 5.25/5.45 thf(fact_738_not__gr__zero,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % not_gr_zero
% 5.25/5.45 thf(fact_739_add__0,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add_0
% 5.25/5.45 thf(fact_740_add__0,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add_0
% 5.25/5.45 thf(fact_741_add__0,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add_0
% 5.25/5.45 thf(fact_742_add__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add_0
% 5.25/5.45 thf(fact_743_add__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add_0
% 5.25/5.45 thf(fact_744_zero__eq__add__iff__both__eq__0,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ( zero_zero_nat
% 5.25/5.45 = ( plus_plus_nat @ X4 @ Y ) )
% 5.25/5.45 = ( ( X4 = zero_zero_nat )
% 5.25/5.45 & ( Y = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_add_iff_both_eq_0
% 5.25/5.45 thf(fact_745_add__eq__0__iff__both__eq__0,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ X4 @ Y )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( X4 = zero_zero_nat )
% 5.25/5.45 & ( Y = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_eq_0_iff_both_eq_0
% 5.25/5.45 thf(fact_746_add__cancel__right__right,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_complex @ A @ B ) )
% 5.25/5.45 = ( B = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_right
% 5.25/5.45 thf(fact_747_add__cancel__right__right,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_real @ A @ B ) )
% 5.25/5.45 = ( B = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_right
% 5.25/5.45 thf(fact_748_add__cancel__right__right,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_rat @ A @ B ) )
% 5.25/5.45 = ( B = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_right
% 5.25/5.45 thf(fact_749_add__cancel__right__right,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_nat @ A @ B ) )
% 5.25/5.45 = ( B = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_right
% 5.25/5.45 thf(fact_750_add__cancel__right__right,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_int @ A @ B ) )
% 5.25/5.45 = ( B = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_right
% 5.25/5.45 thf(fact_751_add__cancel__right__left,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_complex @ B @ A ) )
% 5.25/5.45 = ( B = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_left
% 5.25/5.45 thf(fact_752_add__cancel__right__left,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_real @ B @ A ) )
% 5.25/5.45 = ( B = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_left
% 5.25/5.45 thf(fact_753_add__cancel__right__left,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_rat @ B @ A ) )
% 5.25/5.45 = ( B = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_left
% 5.25/5.45 thf(fact_754_add__cancel__right__left,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_nat @ B @ A ) )
% 5.25/5.45 = ( B = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_left
% 5.25/5.45 thf(fact_755_add__cancel__right__left,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( A
% 5.25/5.45 = ( plus_plus_int @ B @ A ) )
% 5.25/5.45 = ( B = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_right_left
% 5.25/5.45 thf(fact_756_add__cancel__left__right,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( ( plus_plus_complex @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_right
% 5.25/5.45 thf(fact_757_add__cancel__left__right,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ( plus_plus_real @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_right
% 5.25/5.45 thf(fact_758_add__cancel__left__right,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ( plus_plus_rat @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_right
% 5.25/5.45 thf(fact_759_add__cancel__left__right,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_right
% 5.25/5.45 thf(fact_760_add__cancel__left__right,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ( plus_plus_int @ A @ B )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_right
% 5.25/5.45 thf(fact_761_add__cancel__left__left,axiom,
% 5.25/5.45 ! [B: complex,A: complex] :
% 5.25/5.45 ( ( ( plus_plus_complex @ B @ A )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_left
% 5.25/5.45 thf(fact_762_add__cancel__left__left,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( ( plus_plus_real @ B @ A )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_left
% 5.25/5.45 thf(fact_763_add__cancel__left__left,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( ( plus_plus_rat @ B @ A )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_left
% 5.25/5.45 thf(fact_764_add__cancel__left__left,axiom,
% 5.25/5.45 ! [B: nat,A: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ B @ A )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_left
% 5.25/5.45 thf(fact_765_add__cancel__left__left,axiom,
% 5.25/5.45 ! [B: int,A: int] :
% 5.25/5.45 ( ( ( plus_plus_int @ B @ A )
% 5.25/5.45 = A )
% 5.25/5.45 = ( B = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_cancel_left_left
% 5.25/5.45 thf(fact_766_double__zero__sym,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( zero_zero_real
% 5.25/5.45 = ( plus_plus_real @ A @ A ) )
% 5.25/5.45 = ( A = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_zero_sym
% 5.25/5.45 thf(fact_767_double__zero__sym,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( zero_zero_rat
% 5.25/5.45 = ( plus_plus_rat @ A @ A ) )
% 5.25/5.45 = ( A = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_zero_sym
% 5.25/5.45 thf(fact_768_double__zero__sym,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( zero_zero_int
% 5.25/5.45 = ( plus_plus_int @ A @ A ) )
% 5.25/5.45 = ( A = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_zero_sym
% 5.25/5.45 thf(fact_769_add_Oright__neutral,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.right_neutral
% 5.25/5.45 thf(fact_770_add_Oright__neutral,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.right_neutral
% 5.25/5.45 thf(fact_771_add_Oright__neutral,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.right_neutral
% 5.25/5.45 thf(fact_772_add_Oright__neutral,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.right_neutral
% 5.25/5.45 thf(fact_773_add_Oright__neutral,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.right_neutral
% 5.25/5.45 thf(fact_774_division__ring__divide__zero,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % division_ring_divide_zero
% 5.25/5.45 thf(fact_775_division__ring__divide__zero,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % division_ring_divide_zero
% 5.25/5.45 thf(fact_776_division__ring__divide__zero,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % division_ring_divide_zero
% 5.25/5.45 thf(fact_777_divide__cancel__right,axiom,
% 5.25/5.45 ! [A: rat,C: rat,B: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ A @ C )
% 5.25/5.45 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.45 = ( ( C = zero_zero_rat )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_right
% 5.25/5.45 thf(fact_778_divide__cancel__right,axiom,
% 5.25/5.45 ! [A: real,C: real,B: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ A @ C )
% 5.25/5.45 = ( divide_divide_real @ B @ C ) )
% 5.25/5.45 = ( ( C = zero_zero_real )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_right
% 5.25/5.45 thf(fact_779_divide__cancel__right,axiom,
% 5.25/5.45 ! [A: complex,C: complex,B: complex] :
% 5.25/5.45 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.25/5.45 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.45 = ( ( C = zero_zero_complex )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_right
% 5.25/5.45 thf(fact_780_divide__cancel__left,axiom,
% 5.25/5.45 ! [C: rat,A: rat,B: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ C @ A )
% 5.25/5.45 = ( divide_divide_rat @ C @ B ) )
% 5.25/5.45 = ( ( C = zero_zero_rat )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_left
% 5.25/5.45 thf(fact_781_divide__cancel__left,axiom,
% 5.25/5.45 ! [C: real,A: real,B: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ C @ A )
% 5.25/5.45 = ( divide_divide_real @ C @ B ) )
% 5.25/5.45 = ( ( C = zero_zero_real )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_left
% 5.25/5.45 thf(fact_782_divide__cancel__left,axiom,
% 5.25/5.45 ! [C: complex,A: complex,B: complex] :
% 5.25/5.45 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.25/5.45 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.25/5.45 = ( ( C = zero_zero_complex )
% 5.25/5.45 | ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_cancel_left
% 5.25/5.45 thf(fact_783_div__by__0,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_784_div__by__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_785_div__by__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_786_div__by__0,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_787_div__by__0,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_788_div__by__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_0
% 5.25/5.45 thf(fact_789_divide__eq__0__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( A = zero_zero_rat )
% 5.25/5.45 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_0_iff
% 5.25/5.45 thf(fact_790_divide__eq__0__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ A @ B )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( A = zero_zero_real )
% 5.25/5.45 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_0_iff
% 5.25/5.45 thf(fact_791_divide__eq__0__iff,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.45 = zero_zero_complex )
% 5.25/5.45 = ( ( A = zero_zero_complex )
% 5.25/5.45 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_0_iff
% 5.25/5.45 thf(fact_792_div__0,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_793_div__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_794_div__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_795_div__0,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_796_div__0,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_797_div__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % div_0
% 5.25/5.45 thf(fact_798_bits__div__by__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_by_0
% 5.25/5.45 thf(fact_799_bits__div__by__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_by_0
% 5.25/5.45 thf(fact_800_bits__div__by__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_by_0
% 5.25/5.45 thf(fact_801_bits__div__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_0
% 5.25/5.45 thf(fact_802_bits__div__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_0
% 5.25/5.45 thf(fact_803_bits__div__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_div_0
% 5.25/5.45 thf(fact_804_bits__mod__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_0
% 5.25/5.45 thf(fact_805_bits__mod__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_0
% 5.25/5.45 thf(fact_806_bits__mod__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_0
% 5.25/5.45 thf(fact_807_mod__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mod_0
% 5.25/5.45 thf(fact_808_mod__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % mod_0
% 5.25/5.45 thf(fact_809_mod__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % mod_0
% 5.25/5.45 thf(fact_810_mod__by__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_0
% 5.25/5.45 thf(fact_811_mod__by__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_0
% 5.25/5.45 thf(fact_812_mod__by__0,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_0
% 5.25/5.45 thf(fact_813_mod__self,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ A @ A )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mod_self
% 5.25/5.45 thf(fact_814_mod__self,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ A @ A )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % mod_self
% 5.25/5.45 thf(fact_815_mod__self,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ A @ A )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % mod_self
% 5.25/5.45 thf(fact_816_less__nat__zero__code,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % less_nat_zero_code
% 5.25/5.45 thf(fact_817_neq0__conv,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( N2 != zero_zero_nat )
% 5.25/5.45 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % neq0_conv
% 5.25/5.45 thf(fact_818_bot__nat__0_Onot__eq__extremum,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( A != zero_zero_nat )
% 5.25/5.45 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % bot_nat_0.not_eq_extremum
% 5.25/5.45 thf(fact_819_le0,axiom,
% 5.25/5.45 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.25/5.45
% 5.25/5.45 % le0
% 5.25/5.45 thf(fact_820_bot__nat__0_Oextremum,axiom,
% 5.25/5.45 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.25/5.45
% 5.25/5.45 % bot_nat_0.extremum
% 5.25/5.45 thf(fact_821_Nat_Oadd__0__right,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.25/5.45 = M ) ).
% 5.25/5.45
% 5.25/5.45 % Nat.add_0_right
% 5.25/5.45 thf(fact_822_add__is__0,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ M @ N2 )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( M = zero_zero_nat )
% 5.25/5.45 & ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_is_0
% 5.25/5.45 thf(fact_823_dbl__simps_I2_J,axiom,
% 5.25/5.45 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_simps(2)
% 5.25/5.45 thf(fact_824_dbl__simps_I2_J,axiom,
% 5.25/5.45 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_simps(2)
% 5.25/5.45 thf(fact_825_dbl__simps_I2_J,axiom,
% 5.25/5.45 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_simps(2)
% 5.25/5.45 thf(fact_826_dbl__simps_I2_J,axiom,
% 5.25/5.45 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % dbl_simps(2)
% 5.25/5.45 thf(fact_827_mi__ma__2__deg,axiom,
% 5.25/5.45 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N2: nat] :
% 5.25/5.45 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N2 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.45 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mi_ma_2_deg
% 5.25/5.45 thf(fact_828_add__le__same__cancel1,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel1
% 5.25/5.45 thf(fact_829_add__le__same__cancel1,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel1
% 5.25/5.45 thf(fact_830_add__le__same__cancel1,axiom,
% 5.25/5.45 ! [B: nat,A: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel1
% 5.25/5.45 thf(fact_831_add__le__same__cancel1,axiom,
% 5.25/5.45 ! [B: int,A: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel1
% 5.25/5.45 thf(fact_832_add__le__same__cancel2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel2
% 5.25/5.45 thf(fact_833_add__le__same__cancel2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel2
% 5.25/5.45 thf(fact_834_add__le__same__cancel2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel2
% 5.25/5.45 thf(fact_835_add__le__same__cancel2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_le_same_cancel2
% 5.25/5.45 thf(fact_836_le__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.45 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel1
% 5.25/5.45 thf(fact_837_le__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel1
% 5.25/5.45 thf(fact_838_le__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.45 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel1
% 5.25/5.45 thf(fact_839_le__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.45 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel1
% 5.25/5.45 thf(fact_840_le__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel2
% 5.25/5.45 thf(fact_841_le__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel2
% 5.25/5.45 thf(fact_842_le__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel2
% 5.25/5.45 thf(fact_843_le__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_add_same_cancel2
% 5.25/5.45 thf(fact_844_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.25/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.45 thf(fact_845_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.45 thf(fact_846_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.25/5.45 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_le_zero_iff_single_add_le_zero
% 5.25/5.45 thf(fact_847_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.25/5.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.45 thf(fact_848_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.25/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.45 thf(fact_849_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.25/5.45 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_double_add_iff_zero_le_single_add
% 5.25/5.45 thf(fact_850_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.25/5.45 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.45 thf(fact_851_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.25/5.45 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.45 thf(fact_852_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.25/5.45 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_double_add_iff_zero_less_single_add
% 5.25/5.45 thf(fact_853_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.25/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.45 thf(fact_854_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.25/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.45 thf(fact_855_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.25/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % double_add_less_zero_iff_single_add_less_zero
% 5.25/5.45 thf(fact_856_less__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel2
% 5.25/5.45 thf(fact_857_less__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel2
% 5.25/5.45 thf(fact_858_less__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.45 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel2
% 5.25/5.45 thf(fact_859_less__add__same__cancel2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.45 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel2
% 5.25/5.45 thf(fact_860_less__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.45 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel1
% 5.25/5.45 thf(fact_861_less__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.45 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel1
% 5.25/5.45 thf(fact_862_less__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.45 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel1
% 5.25/5.45 thf(fact_863_less__add__same__cancel1,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.45 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_add_same_cancel1
% 5.25/5.45 thf(fact_864_add__less__same__cancel2,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel2
% 5.25/5.45 thf(fact_865_add__less__same__cancel2,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel2
% 5.25/5.45 thf(fact_866_add__less__same__cancel2,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel2
% 5.25/5.45 thf(fact_867_add__less__same__cancel2,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.25/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel2
% 5.25/5.45 thf(fact_868_add__less__same__cancel1,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel1
% 5.25/5.45 thf(fact_869_add__less__same__cancel1,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel1
% 5.25/5.45 thf(fact_870_add__less__same__cancel1,axiom,
% 5.25/5.45 ! [B: nat,A: nat] :
% 5.25/5.45 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel1
% 5.25/5.45 thf(fact_871_add__less__same__cancel1,axiom,
% 5.25/5.45 ! [B: int,A: int] :
% 5.25/5.45 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.25/5.45 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_less_same_cancel1
% 5.25/5.45 thf(fact_872_zero__eq__1__divide__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( zero_zero_rat
% 5.25/5.45 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.45 = ( A = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_1_divide_iff
% 5.25/5.45 thf(fact_873_zero__eq__1__divide__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( zero_zero_real
% 5.25/5.45 = ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.45 = ( A = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_1_divide_iff
% 5.25/5.45 thf(fact_874_one__divide__eq__0__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( A = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_divide_eq_0_iff
% 5.25/5.45 thf(fact_875_one__divide__eq__0__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( A = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_divide_eq_0_iff
% 5.25/5.45 thf(fact_876_eq__divide__eq__1,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( one_one_rat
% 5.25/5.45 = ( divide_divide_rat @ B @ A ) )
% 5.25/5.45 = ( ( A != zero_zero_rat )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_eq_1
% 5.25/5.45 thf(fact_877_eq__divide__eq__1,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( one_one_real
% 5.25/5.45 = ( divide_divide_real @ B @ A ) )
% 5.25/5.45 = ( ( A != zero_zero_real )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % eq_divide_eq_1
% 5.25/5.45 thf(fact_878_divide__eq__eq__1,axiom,
% 5.25/5.45 ! [B: rat,A: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ B @ A )
% 5.25/5.45 = one_one_rat )
% 5.25/5.45 = ( ( A != zero_zero_rat )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_eq_1
% 5.25/5.45 thf(fact_879_divide__eq__eq__1,axiom,
% 5.25/5.45 ! [B: real,A: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ B @ A )
% 5.25/5.45 = one_one_real )
% 5.25/5.45 = ( ( A != zero_zero_real )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_eq_1
% 5.25/5.45 thf(fact_880_divide__self__if,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ( A = zero_zero_rat )
% 5.25/5.45 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.45 = zero_zero_rat ) )
% 5.25/5.45 & ( ( A != zero_zero_rat )
% 5.25/5.45 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.45 = one_one_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self_if
% 5.25/5.45 thf(fact_881_divide__self__if,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ( A = zero_zero_real )
% 5.25/5.45 => ( ( divide_divide_real @ A @ A )
% 5.25/5.45 = zero_zero_real ) )
% 5.25/5.45 & ( ( A != zero_zero_real )
% 5.25/5.45 => ( ( divide_divide_real @ A @ A )
% 5.25/5.45 = one_one_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self_if
% 5.25/5.45 thf(fact_882_divide__self__if,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( ( A = zero_zero_complex )
% 5.25/5.45 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.45 = zero_zero_complex ) )
% 5.25/5.45 & ( ( A != zero_zero_complex )
% 5.25/5.45 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.45 = one_one_complex ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self_if
% 5.25/5.45 thf(fact_883_divide__self,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( A != zero_zero_rat )
% 5.25/5.45 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.45 = one_one_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self
% 5.25/5.45 thf(fact_884_divide__self,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( A != zero_zero_real )
% 5.25/5.45 => ( ( divide_divide_real @ A @ A )
% 5.25/5.45 = one_one_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self
% 5.25/5.45 thf(fact_885_divide__self,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( A != zero_zero_complex )
% 5.25/5.45 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.45 = one_one_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_self
% 5.25/5.45 thf(fact_886_one__eq__divide__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( one_one_rat
% 5.25/5.45 = ( divide_divide_rat @ A @ B ) )
% 5.25/5.45 = ( ( B != zero_zero_rat )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_eq_divide_iff
% 5.25/5.45 thf(fact_887_one__eq__divide__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( one_one_real
% 5.25/5.45 = ( divide_divide_real @ A @ B ) )
% 5.25/5.45 = ( ( B != zero_zero_real )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_eq_divide_iff
% 5.25/5.45 thf(fact_888_one__eq__divide__iff,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( one_one_complex
% 5.25/5.45 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.25/5.45 = ( ( B != zero_zero_complex )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % one_eq_divide_iff
% 5.25/5.45 thf(fact_889_div__self,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( A != zero_zero_rat )
% 5.25/5.45 => ( ( divide_divide_rat @ A @ A )
% 5.25/5.45 = one_one_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_890_div__self,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( A != zero_zero_nat )
% 5.25/5.45 => ( ( divide_divide_nat @ A @ A )
% 5.25/5.45 = one_one_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_891_div__self,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( A != zero_zero_int )
% 5.25/5.45 => ( ( divide_divide_int @ A @ A )
% 5.25/5.45 = one_one_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_892_div__self,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( A != zero_zero_real )
% 5.25/5.45 => ( ( divide_divide_real @ A @ A )
% 5.25/5.45 = one_one_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_893_div__self,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( A != zero_zero_complex )
% 5.25/5.45 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.25/5.45 = one_one_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_894_div__self,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.45 => ( ( divide6298287555418463151nteger @ A @ A )
% 5.25/5.45 = one_one_Code_integer ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_self
% 5.25/5.45 thf(fact_895_divide__eq__1__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat] :
% 5.25/5.45 ( ( ( divide_divide_rat @ A @ B )
% 5.25/5.45 = one_one_rat )
% 5.25/5.45 = ( ( B != zero_zero_rat )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_1_iff
% 5.25/5.45 thf(fact_896_divide__eq__1__iff,axiom,
% 5.25/5.45 ! [A: real,B: real] :
% 5.25/5.45 ( ( ( divide_divide_real @ A @ B )
% 5.25/5.45 = one_one_real )
% 5.25/5.45 = ( ( B != zero_zero_real )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_1_iff
% 5.25/5.45 thf(fact_897_divide__eq__1__iff,axiom,
% 5.25/5.45 ! [A: complex,B: complex] :
% 5.25/5.45 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.25/5.45 = one_one_complex )
% 5.25/5.45 = ( ( B != zero_zero_complex )
% 5.25/5.45 & ( A = B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_eq_1_iff
% 5.25/5.45 thf(fact_898_power__0__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N2 ) )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_Suc
% 5.25/5.45 thf(fact_899_power__0__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_Suc
% 5.25/5.45 thf(fact_900_power__0__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_real @ zero_zero_real @ ( suc @ N2 ) )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_Suc
% 5.25/5.45 thf(fact_901_power__0__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_int @ zero_zero_int @ ( suc @ N2 ) )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_Suc
% 5.25/5.45 thf(fact_902_power__0__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N2 ) )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_Suc
% 5.25/5.45 thf(fact_903_power__zero__numeral,axiom,
% 5.25/5.45 ! [K: num] :
% 5.25/5.45 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.45 = zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % power_zero_numeral
% 5.25/5.45 thf(fact_904_power__zero__numeral,axiom,
% 5.25/5.45 ! [K: num] :
% 5.25/5.45 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % power_zero_numeral
% 5.25/5.45 thf(fact_905_power__zero__numeral,axiom,
% 5.25/5.45 ! [K: num] :
% 5.25/5.45 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.25/5.45 = zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % power_zero_numeral
% 5.25/5.45 thf(fact_906_power__zero__numeral,axiom,
% 5.25/5.45 ! [K: num] :
% 5.25/5.45 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % power_zero_numeral
% 5.25/5.45 thf(fact_907_power__zero__numeral,axiom,
% 5.25/5.45 ! [K: num] :
% 5.25/5.45 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.25/5.45 = zero_zero_complex ) ).
% 5.25/5.45
% 5.25/5.45 % power_zero_numeral
% 5.25/5.45 thf(fact_908_mod__by__1,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_1
% 5.25/5.45 thf(fact_909_mod__by__1,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_1
% 5.25/5.45 thf(fact_910_mod__by__1,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_1
% 5.25/5.45 thf(fact_911_bits__mod__by__1,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_by_1
% 5.25/5.45 thf(fact_912_bits__mod__by__1,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_by_1
% 5.25/5.45 thf(fact_913_bits__mod__by__1,axiom,
% 5.25/5.45 ! [A: code_integer] :
% 5.25/5.45 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_by_1
% 5.25/5.45 thf(fact_914_bits__mod__div__trivial,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_div_trivial
% 5.25/5.45 thf(fact_915_bits__mod__div__trivial,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_div_trivial
% 5.25/5.45 thf(fact_916_bits__mod__div__trivial,axiom,
% 5.25/5.45 ! [A: code_integer,B: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_mod_div_trivial
% 5.25/5.45 thf(fact_917_mod__div__trivial,axiom,
% 5.25/5.45 ! [A: nat,B: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mod_div_trivial
% 5.25/5.45 thf(fact_918_mod__div__trivial,axiom,
% 5.25/5.45 ! [A: int,B: int] :
% 5.25/5.45 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % mod_div_trivial
% 5.25/5.45 thf(fact_919_mod__div__trivial,axiom,
% 5.25/5.45 ! [A: code_integer,B: code_integer] :
% 5.25/5.45 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % mod_div_trivial
% 5.25/5.45 thf(fact_920_power__Suc0__right,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % power_Suc0_right
% 5.25/5.45 thf(fact_921_power__Suc0__right,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % power_Suc0_right
% 5.25/5.45 thf(fact_922_power__Suc0__right,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % power_Suc0_right
% 5.25/5.45 thf(fact_923_power__Suc0__right,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % power_Suc0_right
% 5.25/5.45 thf(fact_924_less__Suc0,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_Suc0
% 5.25/5.45 thf(fact_925_zero__less__Suc,axiom,
% 5.25/5.45 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_Suc
% 5.25/5.45 thf(fact_926_add__gr__0,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.45 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.45 | ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_gr_0
% 5.25/5.45 thf(fact_927_less__one,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ N2 @ one_one_nat )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_one
% 5.25/5.45 thf(fact_928_div__by__Suc__0,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = M ) ).
% 5.25/5.45
% 5.25/5.45 % div_by_Suc_0
% 5.25/5.45 thf(fact_929_div__less,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.45 => ( ( divide_divide_nat @ M @ N2 )
% 5.25/5.45 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_less
% 5.25/5.45 thf(fact_930_power__Suc__0,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.25/5.45 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_Suc_0
% 5.25/5.45 thf(fact_931_nat__power__eq__Suc__0__iff,axiom,
% 5.25/5.45 ! [X4: nat,M: nat] :
% 5.25/5.45 ( ( ( power_power_nat @ X4 @ M )
% 5.25/5.45 = ( suc @ zero_zero_nat ) )
% 5.25/5.45 = ( ( M = zero_zero_nat )
% 5.25/5.45 | ( X4
% 5.25/5.45 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_power_eq_Suc_0_iff
% 5.25/5.45 thf(fact_932_nat__zero__less__power__iff,axiom,
% 5.25/5.45 ! [X4: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X4 @ N2 ) )
% 5.25/5.45 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.25/5.45 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_zero_less_power_iff
% 5.25/5.45 thf(fact_933_mod__by__Suc__0,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % mod_by_Suc_0
% 5.25/5.45 thf(fact_934_zero__le__divide__1__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.45 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_divide_1_iff
% 5.25/5.45 thf(fact_935_zero__le__divide__1__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.45 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_divide_1_iff
% 5.25/5.45 thf(fact_936_divide__le__0__1__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.25/5.45 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_0_1_iff
% 5.25/5.45 thf(fact_937_divide__le__0__1__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_0_1_iff
% 5.25/5.45 thf(fact_938_zero__less__divide__1__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.25/5.45 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_divide_1_iff
% 5.25/5.45 thf(fact_939_zero__less__divide__1__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.25/5.45 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_divide_1_iff
% 5.25/5.45 thf(fact_940_less__divide__eq__1__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 @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_divide_eq_1_pos
% 5.25/5.45 thf(fact_941_less__divide__eq__1__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 @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_divide_eq_1_pos
% 5.25/5.45 thf(fact_942_less__divide__eq__1__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 @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_divide_eq_1_neg
% 5.25/5.45 thf(fact_943_less__divide__eq__1__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 @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_divide_eq_1_neg
% 5.25/5.45 thf(fact_944_divide__less__eq__1__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 @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.45 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_eq_1_pos
% 5.25/5.45 thf(fact_945_divide__less__eq__1__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 @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.45 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_eq_1_pos
% 5.25/5.45 thf(fact_946_divide__less__eq__1__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 @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.45 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_eq_1_neg
% 5.25/5.45 thf(fact_947_divide__less__eq__1__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 @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.45 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_eq_1_neg
% 5.25/5.45 thf(fact_948_divide__less__0__1__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.25/5.45 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_0_1_iff
% 5.25/5.45 thf(fact_949_divide__less__0__1__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.25/5.45 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_less_0_1_iff
% 5.25/5.45 thf(fact_950_power__eq__0__iff,axiom,
% 5.25/5.45 ! [A: rat,N2: nat] :
% 5.25/5.45 ( ( ( power_power_rat @ A @ N2 )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( A = zero_zero_rat )
% 5.25/5.45 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_0_iff
% 5.25/5.45 thf(fact_951_power__eq__0__iff,axiom,
% 5.25/5.45 ! [A: nat,N2: nat] :
% 5.25/5.45 ( ( ( power_power_nat @ A @ N2 )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( A = zero_zero_nat )
% 5.25/5.45 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_0_iff
% 5.25/5.45 thf(fact_952_power__eq__0__iff,axiom,
% 5.25/5.45 ! [A: real,N2: nat] :
% 5.25/5.45 ( ( ( power_power_real @ A @ N2 )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( A = zero_zero_real )
% 5.25/5.45 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_0_iff
% 5.25/5.45 thf(fact_953_power__eq__0__iff,axiom,
% 5.25/5.45 ! [A: int,N2: nat] :
% 5.25/5.45 ( ( ( power_power_int @ A @ N2 )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( A = zero_zero_int )
% 5.25/5.45 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_0_iff
% 5.25/5.45 thf(fact_954_power__eq__0__iff,axiom,
% 5.25/5.45 ! [A: complex,N2: nat] :
% 5.25/5.45 ( ( ( power_power_complex @ A @ N2 )
% 5.25/5.45 = zero_zero_complex )
% 5.25/5.45 = ( ( A = zero_zero_complex )
% 5.25/5.45 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_eq_0_iff
% 5.25/5.45 thf(fact_955_le__divide__eq__1__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_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_divide_eq_1_pos
% 5.25/5.45 thf(fact_956_le__divide__eq__1__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_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_divide_eq_1_pos
% 5.25/5.45 thf(fact_957_le__divide__eq__1__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_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_divide_eq_1_neg
% 5.25/5.45 thf(fact_958_le__divide__eq__1__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_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.25/5.45 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_divide_eq_1_neg
% 5.25/5.45 thf(fact_959_divide__le__eq__1__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_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.45 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_eq_1_pos
% 5.25/5.45 thf(fact_960_divide__le__eq__1__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_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.45 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_eq_1_pos
% 5.25/5.45 thf(fact_961_divide__le__eq__1__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_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.25/5.45 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_eq_1_neg
% 5.25/5.45 thf(fact_962_divide__le__eq__1__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_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_le_eq_1_neg
% 5.25/5.45 thf(fact_963_power__strict__decreasing__iff,axiom,
% 5.25/5.45 ! [B: real,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ( ord_less_real @ B @ one_one_real )
% 5.25/5.45 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_decreasing_iff
% 5.25/5.45 thf(fact_964_power__strict__decreasing__iff,axiom,
% 5.25/5.45 ! [B: rat,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.25/5.45 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_decreasing_iff
% 5.25/5.45 thf(fact_965_power__strict__decreasing__iff,axiom,
% 5.25/5.45 ! [B: nat,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.25/5.45 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_decreasing_iff
% 5.25/5.45 thf(fact_966_power__strict__decreasing__iff,axiom,
% 5.25/5.45 ! [B: int,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ( ord_less_int @ B @ one_one_int )
% 5.25/5.45 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_decreasing_iff
% 5.25/5.45 thf(fact_967_power__mono__iff,axiom,
% 5.25/5.45 ! [A: real,B: real,N2: nat] :
% 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 @ N2 )
% 5.25/5.45 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono_iff
% 5.25/5.45 thf(fact_968_power__mono__iff,axiom,
% 5.25/5.45 ! [A: rat,B: rat,N2: nat] :
% 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 @ N2 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono_iff
% 5.25/5.45 thf(fact_969_power__mono__iff,axiom,
% 5.25/5.45 ! [A: nat,B: nat,N2: 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_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono_iff
% 5.25/5.45 thf(fact_970_power__mono__iff,axiom,
% 5.25/5.45 ! [A: int,B: int,N2: nat] :
% 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 @ N2 )
% 5.25/5.45 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono_iff
% 5.25/5.45 thf(fact_971_zero__eq__power2,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( A = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_power2
% 5.25/5.45 thf(fact_972_zero__eq__power2,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( A = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_power2
% 5.25/5.45 thf(fact_973_zero__eq__power2,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( A = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_power2
% 5.25/5.45 thf(fact_974_zero__eq__power2,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( A = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_power2
% 5.25/5.45 thf(fact_975_zero__eq__power2,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_complex )
% 5.25/5.45 = ( A = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_eq_power2
% 5.25/5.45 thf(fact_976_one__div__two__eq__zero,axiom,
% 5.25/5.45 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % one_div_two_eq_zero
% 5.25/5.45 thf(fact_977_one__div__two__eq__zero,axiom,
% 5.25/5.45 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % one_div_two_eq_zero
% 5.25/5.45 thf(fact_978_one__div__two__eq__zero,axiom,
% 5.25/5.45 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % one_div_two_eq_zero
% 5.25/5.45 thf(fact_979_bits__1__div__2,axiom,
% 5.25/5.45 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % bits_1_div_2
% 5.25/5.45 thf(fact_980_bits__1__div__2,axiom,
% 5.25/5.45 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % bits_1_div_2
% 5.25/5.45 thf(fact_981_bits__1__div__2,axiom,
% 5.25/5.45 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_z3403309356797280102nteger ) ).
% 5.25/5.45
% 5.25/5.45 % bits_1_div_2
% 5.25/5.45 thf(fact_982_power__decreasing__iff,axiom,
% 5.25/5.45 ! [B: real,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.45 => ( ( ord_less_real @ B @ one_one_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_decreasing_iff
% 5.25/5.45 thf(fact_983_power__decreasing__iff,axiom,
% 5.25/5.45 ! [B: rat,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.45 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_decreasing_iff
% 5.25/5.45 thf(fact_984_power__decreasing__iff,axiom,
% 5.25/5.45 ! [B: nat,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.45 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_decreasing_iff
% 5.25/5.45 thf(fact_985_power__decreasing__iff,axiom,
% 5.25/5.45 ! [B: int,M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.45 => ( ( ord_less_int @ B @ one_one_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N2 ) )
% 5.25/5.45 = ( ord_less_eq_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_decreasing_iff
% 5.25/5.45 thf(fact_986_power2__eq__iff__nonneg,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( X4 = Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_eq_iff_nonneg
% 5.25/5.45 thf(fact_987_power2__eq__iff__nonneg,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( X4 = Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_eq_iff_nonneg
% 5.25/5.45 thf(fact_988_power2__eq__iff__nonneg,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.45 => ( ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( X4 = Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_eq_iff_nonneg
% 5.25/5.45 thf(fact_989_power2__eq__iff__nonneg,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.45 => ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( X4 = Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_eq_iff_nonneg
% 5.25/5.45 thf(fact_990_power2__less__eq__zero__iff,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.25/5.45 = ( A = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_less_eq_zero_iff
% 5.25/5.45 thf(fact_991_power2__less__eq__zero__iff,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.25/5.45 = ( A = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_less_eq_zero_iff
% 5.25/5.45 thf(fact_992_power2__less__eq__zero__iff,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.25/5.45 = ( A = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % power2_less_eq_zero_iff
% 5.25/5.45 thf(fact_993_zero__less__power2,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( A != zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power2
% 5.25/5.45 thf(fact_994_zero__less__power2,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( A != zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power2
% 5.25/5.45 thf(fact_995_zero__less__power2,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = ( A != zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power2
% 5.25/5.45 thf(fact_996_sum__power2__eq__zero__iff,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( X4 = zero_zero_rat )
% 5.25/5.45 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % sum_power2_eq_zero_iff
% 5.25/5.45 thf(fact_997_sum__power2__eq__zero__iff,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( X4 = zero_zero_real )
% 5.25/5.45 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % sum_power2_eq_zero_iff
% 5.25/5.45 thf(fact_998_sum__power2__eq__zero__iff,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ( ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( X4 = zero_zero_int )
% 5.25/5.45 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % sum_power2_eq_zero_iff
% 5.25/5.45 thf(fact_999_add__self__mod__2,axiom,
% 5.25/5.45 ! [M: nat] :
% 5.25/5.45 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.45 = zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % add_self_mod_2
% 5.25/5.45 thf(fact_1000_psubsetD,axiom,
% 5.25/5.45 ! [A2: set_real,B3: set_real,C: real] :
% 5.25/5.45 ( ( ord_less_set_real @ A2 @ B3 )
% 5.25/5.45 => ( ( member_real @ C @ A2 )
% 5.25/5.45 => ( member_real @ C @ B3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % psubsetD
% 5.25/5.45 thf(fact_1001_psubsetD,axiom,
% 5.25/5.45 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.25/5.45 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.25/5.45 => ( ( member_nat @ C @ A2 )
% 5.25/5.45 => ( member_nat @ C @ B3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % psubsetD
% 5.25/5.45 thf(fact_1002_psubsetD,axiom,
% 5.25/5.45 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.25/5.45 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.25/5.45 => ( ( member_complex @ C @ A2 )
% 5.25/5.45 => ( member_complex @ C @ B3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % psubsetD
% 5.25/5.45 thf(fact_1003_psubsetD,axiom,
% 5.25/5.45 ! [A2: set_int,B3: set_int,C: int] :
% 5.25/5.45 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.45 => ( ( member_int @ C @ A2 )
% 5.25/5.45 => ( member_int @ C @ B3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % psubsetD
% 5.25/5.45 thf(fact_1004_psubsetD,axiom,
% 5.25/5.45 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.25/5.45 ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.25/5.45 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.25/5.45 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % psubsetD
% 5.25/5.45 thf(fact_1005_zero__reorient,axiom,
% 5.25/5.45 ! [X4: complex] :
% 5.25/5.45 ( ( zero_zero_complex = X4 )
% 5.25/5.45 = ( X4 = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_reorient
% 5.25/5.45 thf(fact_1006_zero__reorient,axiom,
% 5.25/5.45 ! [X4: real] :
% 5.25/5.45 ( ( zero_zero_real = X4 )
% 5.25/5.45 = ( X4 = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_reorient
% 5.25/5.45 thf(fact_1007_zero__reorient,axiom,
% 5.25/5.45 ! [X4: rat] :
% 5.25/5.45 ( ( zero_zero_rat = X4 )
% 5.25/5.45 = ( X4 = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_reorient
% 5.25/5.45 thf(fact_1008_zero__reorient,axiom,
% 5.25/5.45 ! [X4: nat] :
% 5.25/5.45 ( ( zero_zero_nat = X4 )
% 5.25/5.45 = ( X4 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_reorient
% 5.25/5.45 thf(fact_1009_zero__reorient,axiom,
% 5.25/5.45 ! [X4: int] :
% 5.25/5.45 ( ( zero_zero_int = X4 )
% 5.25/5.45 = ( X4 = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_reorient
% 5.25/5.45 thf(fact_1010_verit__sum__simplify,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_sum_simplify
% 5.25/5.45 thf(fact_1011_verit__sum__simplify,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_sum_simplify
% 5.25/5.45 thf(fact_1012_verit__sum__simplify,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_sum_simplify
% 5.25/5.45 thf(fact_1013_verit__sum__simplify,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_sum_simplify
% 5.25/5.45 thf(fact_1014_verit__sum__simplify,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % verit_sum_simplify
% 5.25/5.45 thf(fact_1015_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.25/5.45 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X4: nat] :
% 5.25/5.45 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X4 )
% 5.25/5.45 = ( ( X4 = Mi )
% 5.25/5.45 | ( X4 = Ma ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % VEBT_internal.membermima.simps(3)
% 5.25/5.45 thf(fact_1016_power__0__left,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ( N2 = zero_zero_nat )
% 5.25/5.45 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.25/5.45 = one_one_rat ) )
% 5.25/5.45 & ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.25/5.45 = zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_left
% 5.25/5.45 thf(fact_1017_power__0__left,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ( N2 = zero_zero_nat )
% 5.25/5.45 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = one_one_nat ) )
% 5.25/5.45 & ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_left
% 5.25/5.45 thf(fact_1018_power__0__left,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ( N2 = zero_zero_nat )
% 5.25/5.45 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.25/5.45 = one_one_real ) )
% 5.25/5.45 & ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.25/5.45 = zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_left
% 5.25/5.45 thf(fact_1019_power__0__left,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ( N2 = zero_zero_nat )
% 5.25/5.45 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.25/5.45 = one_one_int ) )
% 5.25/5.45 & ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.25/5.45 = zero_zero_int ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_left
% 5.25/5.45 thf(fact_1020_power__0__left,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ( N2 = zero_zero_nat )
% 5.25/5.45 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.25/5.45 = one_one_complex ) )
% 5.25/5.45 & ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.25/5.45 = zero_zero_complex ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_0_left
% 5.25/5.45 thf(fact_1021_zero__power,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( power_power_rat @ zero_zero_rat @ N2 )
% 5.25/5.45 = zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_power
% 5.25/5.45 thf(fact_1022_zero__power,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( power_power_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_power
% 5.25/5.45 thf(fact_1023_zero__power,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( power_power_real @ zero_zero_real @ N2 )
% 5.25/5.45 = zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_power
% 5.25/5.45 thf(fact_1024_zero__power,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( power_power_int @ zero_zero_int @ N2 )
% 5.25/5.45 = zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_power
% 5.25/5.45 thf(fact_1025_zero__power,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( power_power_complex @ zero_zero_complex @ N2 )
% 5.25/5.45 = zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_power
% 5.25/5.45 thf(fact_1026_zero__le,axiom,
% 5.25/5.45 ! [X4: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X4 ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le
% 5.25/5.45 thf(fact_1027_le__numeral__extra_I3_J,axiom,
% 5.25/5.45 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.25/5.45
% 5.25/5.45 % le_numeral_extra(3)
% 5.25/5.45 thf(fact_1028_le__numeral__extra_I3_J,axiom,
% 5.25/5.45 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.25/5.45
% 5.25/5.45 % le_numeral_extra(3)
% 5.25/5.45 thf(fact_1029_le__numeral__extra_I3_J,axiom,
% 5.25/5.45 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.25/5.45
% 5.25/5.45 % le_numeral_extra(3)
% 5.25/5.45 thf(fact_1030_le__numeral__extra_I3_J,axiom,
% 5.25/5.45 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.25/5.45
% 5.25/5.45 % le_numeral_extra(3)
% 5.25/5.45 thf(fact_1031_zero__less__iff__neq__zero,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = ( N2 != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_iff_neq_zero
% 5.25/5.45 thf(fact_1032_gr__implies__not__zero,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.45 => ( N2 != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr_implies_not_zero
% 5.25/5.45 thf(fact_1033_not__less__zero,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_less_zero
% 5.25/5.45 thf(fact_1034_gr__zeroI,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr_zeroI
% 5.25/5.45 thf(fact_1035_less__numeral__extra_I3_J,axiom,
% 5.25/5.45 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(3)
% 5.25/5.45 thf(fact_1036_less__numeral__extra_I3_J,axiom,
% 5.25/5.45 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(3)
% 5.25/5.45 thf(fact_1037_less__numeral__extra_I3_J,axiom,
% 5.25/5.45 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(3)
% 5.25/5.45 thf(fact_1038_less__numeral__extra_I3_J,axiom,
% 5.25/5.45 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % less_numeral_extra(3)
% 5.25/5.45 thf(fact_1039_field__lbound__gt__zero,axiom,
% 5.25/5.45 ! [D1: real,D2: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ D2 )
% 5.25/5.45 => ? [E: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.45 & ( ord_less_real @ E @ D1 )
% 5.25/5.45 & ( ord_less_real @ E @ D2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % field_lbound_gt_zero
% 5.25/5.45 thf(fact_1040_field__lbound__gt__zero,axiom,
% 5.25/5.45 ! [D1: rat,D2: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ D2 )
% 5.25/5.45 => ? [E: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.25/5.45 & ( ord_less_rat @ E @ D1 )
% 5.25/5.45 & ( ord_less_rat @ E @ D2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % field_lbound_gt_zero
% 5.25/5.45 thf(fact_1041_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_zero_rat
% 5.25/5.45 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1042_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_z5237406670263579293d_enat
% 5.25/5.45 != ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1043_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_zero_complex
% 5.25/5.45 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1044_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_zero_real
% 5.25/5.45 != ( numeral_numeral_real @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1045_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_zero_nat
% 5.25/5.45 != ( numeral_numeral_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1046_zero__neq__numeral,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ( zero_zero_int
% 5.25/5.45 != ( numeral_numeral_int @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_numeral
% 5.25/5.45 thf(fact_1047_zero__neq__one,axiom,
% 5.25/5.45 zero_zero_complex != one_one_complex ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_one
% 5.25/5.45 thf(fact_1048_zero__neq__one,axiom,
% 5.25/5.45 zero_zero_real != one_one_real ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_one
% 5.25/5.45 thf(fact_1049_zero__neq__one,axiom,
% 5.25/5.45 zero_zero_rat != one_one_rat ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_one
% 5.25/5.45 thf(fact_1050_zero__neq__one,axiom,
% 5.25/5.45 zero_zero_nat != one_one_nat ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_one
% 5.25/5.45 thf(fact_1051_zero__neq__one,axiom,
% 5.25/5.45 zero_zero_int != one_one_int ).
% 5.25/5.45
% 5.25/5.45 % zero_neq_one
% 5.25/5.45 thf(fact_1052_add_Ogroup__left__neutral,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.group_left_neutral
% 5.25/5.45 thf(fact_1053_add_Ogroup__left__neutral,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.group_left_neutral
% 5.25/5.45 thf(fact_1054_add_Ogroup__left__neutral,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.group_left_neutral
% 5.25/5.45 thf(fact_1055_add_Ogroup__left__neutral,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.group_left_neutral
% 5.25/5.45 thf(fact_1056_add_Ocomm__neutral,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.comm_neutral
% 5.25/5.45 thf(fact_1057_add_Ocomm__neutral,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.comm_neutral
% 5.25/5.45 thf(fact_1058_add_Ocomm__neutral,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.comm_neutral
% 5.25/5.45 thf(fact_1059_add_Ocomm__neutral,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.comm_neutral
% 5.25/5.45 thf(fact_1060_add_Ocomm__neutral,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.25/5.45 = A ) ).
% 5.25/5.45
% 5.25/5.45 % add.comm_neutral
% 5.25/5.45 thf(fact_1061_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.45 ! [A: complex] :
% 5.25/5.45 ( ( plus_plus_complex @ zero_zero_complex @ 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_1062_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.45 ! [A: real] :
% 5.25/5.45 ( ( plus_plus_real @ zero_zero_real @ 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_1063_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.45 ! [A: rat] :
% 5.25/5.45 ( ( plus_plus_rat @ zero_zero_rat @ 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_1064_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.45 ! [A: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ zero_zero_nat @ 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_1065_comm__monoid__add__class_Oadd__0,axiom,
% 5.25/5.45 ! [A: int] :
% 5.25/5.45 ( ( 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_1066_power__not__zero,axiom,
% 5.25/5.45 ! [A: rat,N2: nat] :
% 5.25/5.45 ( ( A != zero_zero_rat )
% 5.25/5.45 => ( ( power_power_rat @ A @ N2 )
% 5.25/5.45 != zero_zero_rat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1067_power__not__zero,axiom,
% 5.25/5.45 ! [A: nat,N2: nat] :
% 5.25/5.45 ( ( A != zero_zero_nat )
% 5.25/5.45 => ( ( power_power_nat @ A @ N2 )
% 5.25/5.45 != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1068_power__not__zero,axiom,
% 5.25/5.45 ! [A: real,N2: nat] :
% 5.25/5.45 ( ( A != zero_zero_real )
% 5.25/5.45 => ( ( power_power_real @ A @ N2 )
% 5.25/5.45 != zero_zero_real ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1069_power__not__zero,axiom,
% 5.25/5.45 ! [A: int,N2: nat] :
% 5.25/5.45 ( ( A != zero_zero_int )
% 5.25/5.45 => ( ( power_power_int @ A @ N2 )
% 5.25/5.45 != zero_zero_int ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1070_power__not__zero,axiom,
% 5.25/5.45 ! [A: complex,N2: nat] :
% 5.25/5.45 ( ( A != zero_zero_complex )
% 5.25/5.45 => ( ( power_power_complex @ A @ N2 )
% 5.25/5.45 != zero_zero_complex ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_not_zero
% 5.25/5.45 thf(fact_1071_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_1072_vebt__buildup_Ocases,axiom,
% 5.25/5.45 ! [X4: nat] :
% 5.25/5.45 ( ( X4 != zero_zero_nat )
% 5.25/5.45 => ( ( X4
% 5.25/5.45 != ( suc @ zero_zero_nat ) )
% 5.25/5.45 => ~ ! [Va2: nat] :
% 5.25/5.45 ( X4
% 5.25/5.45 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % vebt_buildup.cases
% 5.25/5.45 thf(fact_1073_not0__implies__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ? [M5: nat] :
% 5.25/5.45 ( N2
% 5.25/5.45 = ( suc @ M5 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % not0_implies_Suc
% 5.25/5.45 thf(fact_1074_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_1075_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_1076_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_1077_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_1078_diff__induct,axiom,
% 5.25/5.45 ! [P: nat > nat > $o,M: nat,N2: 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 @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % diff_induct
% 5.25/5.45 thf(fact_1079_nat__induct,axiom,
% 5.25/5.45 ! [P: nat > $o,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_induct
% 5.25/5.45 thf(fact_1080_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_1081_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_1082_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_1083_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_1084_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_1085_infinite__descent0,axiom,
% 5.25/5.45 ! [P: nat > $o,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % infinite_descent0
% 5.25/5.45 thf(fact_1086_gr__implies__not0,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ N2 )
% 5.25/5.45 => ( N2 != zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr_implies_not0
% 5.25/5.45 thf(fact_1087_less__zeroE,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % less_zeroE
% 5.25/5.45 thf(fact_1088_not__less0,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ~ ( ord_less_nat @ N2 @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_less0
% 5.25/5.45 thf(fact_1089_not__gr0,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N2 ) )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % not_gr0
% 5.25/5.45 thf(fact_1090_gr0I,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( N2 != zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0I
% 5.25/5.45 thf(fact_1091_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_1092_le__0__eq,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ N2 @ zero_zero_nat )
% 5.25/5.45 = ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % le_0_eq
% 5.25/5.45 thf(fact_1093_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_1094_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_1095_less__eq__nat_Osimps_I1_J,axiom,
% 5.25/5.45 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N2 ) ).
% 5.25/5.45
% 5.25/5.45 % less_eq_nat.simps(1)
% 5.25/5.45 thf(fact_1096_add__eq__self__zero,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ M @ N2 )
% 5.25/5.45 = M )
% 5.25/5.45 => ( N2 = zero_zero_nat ) ) ).
% 5.25/5.45
% 5.25/5.45 % add_eq_self_zero
% 5.25/5.45 thf(fact_1097_plus__nat_Oadd__0,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( plus_plus_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = N2 ) ).
% 5.25/5.45
% 5.25/5.45 % plus_nat.add_0
% 5.25/5.45 thf(fact_1098_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: real,N2: nat,B: real] :
% 5.25/5.45 ( ( ( power_power_real @ A @ N2 )
% 5.25/5.45 = ( power_power_real @ B @ N2 ) )
% 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 @ N2 )
% 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_1099_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: rat,N2: nat,B: rat] :
% 5.25/5.45 ( ( ( power_power_rat @ A @ N2 )
% 5.25/5.45 = ( power_power_rat @ B @ N2 ) )
% 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 @ N2 )
% 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_1100_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: nat,N2: nat,B: nat] :
% 5.25/5.45 ( ( ( power_power_nat @ A @ N2 )
% 5.25/5.45 = ( power_power_nat @ B @ N2 ) )
% 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 @ N2 )
% 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_1101_power__eq__imp__eq__base,axiom,
% 5.25/5.45 ! [A: int,N2: nat,B: int] :
% 5.25/5.45 ( ( ( power_power_int @ A @ N2 )
% 5.25/5.45 = ( power_power_int @ B @ N2 ) )
% 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 @ N2 )
% 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_1102_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N2: nat,A: real,B: real] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 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 @ N2 )
% 5.25/5.45 = ( power_power_real @ B @ N2 ) )
% 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_1103_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N2: nat,A: rat,B: rat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 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 @ N2 )
% 5.25/5.45 = ( power_power_rat @ B @ N2 ) )
% 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_1104_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N2: nat,A: nat,B: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 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 @ N2 )
% 5.25/5.45 = ( power_power_nat @ B @ N2 ) )
% 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_1105_power__eq__iff__eq__base,axiom,
% 5.25/5.45 ! [N2: nat,A: int,B: int] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 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 @ N2 )
% 5.25/5.45 = ( power_power_int @ B @ N2 ) )
% 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_1106_power__strict__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,N2: 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 @ N2 )
% 5.25/5.45 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1107_power__strict__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,N2: 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 @ N2 )
% 5.25/5.45 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1108_power__strict__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,N2: 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 @ N2 )
% 5.25/5.45 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1109_power__strict__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,N2: 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 @ N2 )
% 5.25/5.45 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_strict_mono
% 5.25/5.45 thf(fact_1110_zero__le__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1111_zero__le__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1112_zero__le__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1113_zero__le__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1114_zero__le__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_numeral
% 5.25/5.45 thf(fact_1115_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1116_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1117_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1118_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1119_not__numeral__le__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_le_zero
% 5.25/5.45 thf(fact_1120_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ zero_zero_rat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1121_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ zero_z5237406670263579293d_enat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1122_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ zero_zero_real ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1123_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N2 ) @ zero_zero_nat ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1124_not__numeral__less__zero,axiom,
% 5.25/5.45 ! [N2: num] :
% 5.25/5.45 ~ ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ zero_zero_int ) ).
% 5.25/5.45
% 5.25/5.45 % not_numeral_less_zero
% 5.25/5.45 thf(fact_1125_zero__less__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1126_zero__less__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1127_zero__less__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1128_zero__less__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1129_zero__less__numeral,axiom,
% 5.25/5.45 ! [N2: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_numeral
% 5.25/5.45 thf(fact_1130_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_1131_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_1132_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_1133_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_1134_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_1135_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_1136_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_1137_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_1138_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_1139_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_1140_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_1141_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_1142_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_1143_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_1144_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_1145_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_1146_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_1147_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_1148_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_1149_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_1150_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_1151_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_1152_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_1153_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_1154_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_1155_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_1156_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_1157_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_1158_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_1159_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_1160_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_1161_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_1162_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_1163_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_1164_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_1165_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_1166_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ( ( plus_plus_real @ X4 @ Y )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( X4 = 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_1167_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ( ( plus_plus_rat @ X4 @ Y )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( X4 = 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_1168_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.45 => ( ( ( plus_plus_nat @ X4 @ Y )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( X4 = 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_1169_add__nonneg__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.45 => ( ( ( plus_plus_int @ X4 @ Y )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( X4 = 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_1170_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ( ( plus_plus_real @ X4 @ Y )
% 5.25/5.45 = zero_zero_real )
% 5.25/5.45 = ( ( X4 = 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_1171_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ( ( plus_plus_rat @ X4 @ Y )
% 5.25/5.45 = zero_zero_rat )
% 5.25/5.45 = ( ( X4 = 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_1172_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ X4 @ zero_zero_nat )
% 5.25/5.45 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.25/5.45 => ( ( ( plus_plus_nat @ X4 @ Y )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( X4 = 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_1173_add__nonpos__eq__0__iff,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.25/5.45 => ( ( ( plus_plus_int @ X4 @ Y )
% 5.25/5.45 = zero_zero_int )
% 5.25/5.45 = ( ( X4 = 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_1174_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_1175_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_1176_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_1177_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_1178_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_1179_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_1180_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_1181_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_1182_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_1183_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_1184_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_1185_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_1186_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_1187_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_1188_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_1189_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_1190_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_1191_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_1192_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_1193_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_1194_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_1195_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_1196_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_1197_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_1198_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_1199_add__less__zeroD,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ X4 @ 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_1200_add__less__zeroD,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ ( plus_plus_rat @ X4 @ Y ) @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ X4 @ 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_1201_add__less__zeroD,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ( ord_less_int @ ( plus_plus_int @ X4 @ Y ) @ zero_zero_int )
% 5.25/5.45 => ( ( ord_less_int @ X4 @ 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_1202_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_1203_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_1204_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_1205_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_1206_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_1207_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_1208_divide__nonneg__nonneg,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonneg
% 5.25/5.45 thf(fact_1209_divide__nonneg__nonneg,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonneg
% 5.25/5.45 thf(fact_1210_divide__nonneg__nonpos,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonpos
% 5.25/5.45 thf(fact_1211_divide__nonneg__nonpos,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonneg_nonpos
% 5.25/5.45 thf(fact_1212_divide__nonpos__nonneg,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X4 @ 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 @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonneg
% 5.25/5.45 thf(fact_1213_divide__nonpos__nonneg,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X4 @ 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 @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonneg
% 5.25/5.45 thf(fact_1214_divide__nonpos__nonpos,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_eq_real @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonpos
% 5.25/5.45 thf(fact_1215_divide__nonpos__nonpos,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_nonpos_nonpos
% 5.25/5.45 thf(fact_1216_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_1217_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_1218_power__mono,axiom,
% 5.25/5.45 ! [A: real,B: real,N2: 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 @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1219_power__mono,axiom,
% 5.25/5.45 ! [A: rat,B: rat,N2: 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 @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1220_power__mono,axiom,
% 5.25/5.45 ! [A: nat,B: nat,N2: 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 @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1221_power__mono,axiom,
% 5.25/5.45 ! [A: int,B: int,N2: 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 @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % power_mono
% 5.25/5.45 thf(fact_1222_zero__le__power,axiom,
% 5.25/5.45 ! [A: real,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1223_zero__le__power,axiom,
% 5.25/5.45 ! [A: rat,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1224_zero__le__power,axiom,
% 5.25/5.45 ! [A: nat,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1225_zero__le__power,axiom,
% 5.25/5.45 ! [A: int,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_le_power
% 5.25/5.45 thf(fact_1226_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_1227_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_1228_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_1229_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_1230_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_1231_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_1232_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_1233_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_1234_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_1235_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_1236_divide__pos__pos,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_pos
% 5.25/5.45 thf(fact_1237_divide__pos__pos,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_pos
% 5.25/5.45 thf(fact_1238_divide__pos__neg,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.25/5.45 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_neg
% 5.25/5.45 thf(fact_1239_divide__pos__neg,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.25/5.45 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_pos_neg
% 5.25/5.45 thf(fact_1240_divide__neg__pos,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ X4 @ zero_zero_rat )
% 5.25/5.45 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.45 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_pos
% 5.25/5.45 thf(fact_1241_divide__neg__pos,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.25/5.45 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.45 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_pos
% 5.25/5.45 thf(fact_1242_divide__neg__neg,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ( ord_less_rat @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_neg
% 5.25/5.45 thf(fact_1243_divide__neg__neg,axiom,
% 5.25/5.45 ! [X4: real,Y: real] :
% 5.25/5.45 ( ( ord_less_real @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % divide_neg_neg
% 5.25/5.45 thf(fact_1244_zero__less__power,axiom,
% 5.25/5.45 ! [A: real,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1245_zero__less__power,axiom,
% 5.25/5.45 ! [A: rat,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1246_zero__less__power,axiom,
% 5.25/5.45 ! [A: nat,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1247_zero__less__power,axiom,
% 5.25/5.45 ! [A: int,N2: 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 @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % zero_less_power
% 5.25/5.45 thf(fact_1248_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_1249_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_1250_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_1251_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_1252_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_1253_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_1254_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_1255_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_1256_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_1257_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_1258_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_1259_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_1260_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_1261_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_1262_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_1263_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_1264_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_1265_Ex__less__Suc2,axiom,
% 5.25/5.45 ! [N2: nat,P: nat > $o] :
% 5.25/5.45 ( ( ? [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 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 @ N2 )
% 5.25/5.45 & ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % Ex_less_Suc2
% 5.25/5.45 thf(fact_1266_gr0__conv__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 = ( ? [M6: nat] :
% 5.25/5.45 ( N2
% 5.25/5.45 = ( suc @ M6 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0_conv_Suc
% 5.25/5.45 thf(fact_1267_All__less__Suc2,axiom,
% 5.25/5.45 ! [N2: nat,P: nat > $o] :
% 5.25/5.45 ( ( ! [I3: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I3 @ ( suc @ N2 ) )
% 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 @ N2 )
% 5.25/5.45 => ( P @ ( suc @ I3 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % All_less_Suc2
% 5.25/5.45 thf(fact_1268_gr0__implies__Suc,axiom,
% 5.25/5.45 ! [N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ? [M5: nat] :
% 5.25/5.45 ( N2
% 5.25/5.45 = ( suc @ M5 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % gr0_implies_Suc
% 5.25/5.45 thf(fact_1269_less__Suc__eq__0__disj,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ M @ ( suc @ N2 ) )
% 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 @ N2 ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_Suc_eq_0_disj
% 5.25/5.45 thf(fact_1270_add__is__1,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( plus_plus_nat @ M @ N2 )
% 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 & ( N2 = zero_zero_nat ) )
% 5.25/5.45 | ( ( M = zero_zero_nat )
% 5.25/5.45 & ( N2
% 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_1271_one__is__add,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( suc @ zero_zero_nat )
% 5.25/5.45 = ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.45 = ( ( ( M
% 5.25/5.45 = ( suc @ zero_zero_nat ) )
% 5.25/5.45 & ( N2 = zero_zero_nat ) )
% 5.25/5.45 | ( ( M = zero_zero_nat )
% 5.25/5.45 & ( N2
% 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_1272_ex__least__nat__le,axiom,
% 5.25/5.45 ! [P: nat > $o,N2: nat] :
% 5.25/5.45 ( ( P @ N2 )
% 5.25/5.45 => ( ~ ( P @ zero_zero_nat )
% 5.25/5.45 => ? [K2: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ K2 @ N2 )
% 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_1273_less__imp__add__positive,axiom,
% 5.25/5.45 ! [I2: nat,J: nat] :
% 5.25/5.45 ( ( ord_less_nat @ I2 @ J )
% 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 = J ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % less_imp_add_positive
% 5.25/5.45 thf(fact_1274_div__less__mono,axiom,
% 5.25/5.45 ! [A2: nat,B3: nat,N2: nat] :
% 5.25/5.45 ( ( ord_less_nat @ A2 @ B3 )
% 5.25/5.45 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ( ( modulo_modulo_nat @ A2 @ N2 )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 => ( ( ( modulo_modulo_nat @ B3 @ N2 )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N2 ) @ ( divide_divide_nat @ B3 @ N2 ) ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % div_less_mono
% 5.25/5.45 thf(fact_1275_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_1276_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( divide_divide_nat @ M @ N2 )
% 5.25/5.45 = zero_zero_nat )
% 5.25/5.45 = ( ( ord_less_nat @ M @ N2 )
% 5.25/5.45 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % Euclidean_Division.div_eq_0_iff
% 5.25/5.45 thf(fact_1277_nat__power__less__imp__less,axiom,
% 5.25/5.45 ! [I2: nat,M: nat,N2: 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 @ N2 ) )
% 5.25/5.45 => ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % nat_power_less_imp_less
% 5.25/5.45 thf(fact_1278_mod__Suc,axiom,
% 5.25/5.45 ! [M: nat,N2: nat] :
% 5.25/5.45 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.25/5.45 = N2 )
% 5.25/5.45 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.25/5.45 = zero_zero_nat ) )
% 5.25/5.45 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.25/5.45 != N2 )
% 5.25/5.45 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N2 )
% 5.25/5.45 = ( suc @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_Suc
% 5.25/5.45 thf(fact_1279_mod__less__divisor,axiom,
% 5.25/5.45 ! [N2: nat,M: nat] :
% 5.25/5.45 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.45 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.25/5.45
% 5.25/5.45 % mod_less_divisor
% 5.25/5.45 thf(fact_1280_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.25/5.45 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.25/5.45 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.25/5.45
% 5.25/5.45 % VEBT_internal.naive_member.simps(2)
% 5.25/5.45 thf(fact_1281_order__antisym__conv,axiom,
% 5.25/5.45 ! [Y: set_int,X4: set_int] :
% 5.25/5.45 ( ( ord_less_eq_set_int @ Y @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.45 = ( X4 = Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % order_antisym_conv
% 5.25/5.45 thf(fact_1282_order__antisym__conv,axiom,
% 5.25/5.45 ! [Y: rat,X4: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ Y @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.45 = ( X4 = Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % order_antisym_conv
% 5.25/5.45 thf(fact_1283_order__antisym__conv,axiom,
% 5.25/5.45 ! [Y: num,X4: num] :
% 5.25/5.45 ( ( ord_less_eq_num @ Y @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.45 = ( X4 = Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % order_antisym_conv
% 5.25/5.45 thf(fact_1284_order__antisym__conv,axiom,
% 5.25/5.45 ! [Y: nat,X4: nat] :
% 5.25/5.45 ( ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.45 = ( X4 = Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % order_antisym_conv
% 5.25/5.45 thf(fact_1285_order__antisym__conv,axiom,
% 5.25/5.45 ! [Y: int,X4: int] :
% 5.25/5.45 ( ( ord_less_eq_int @ Y @ X4 )
% 5.25/5.45 => ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.45 = ( X4 = Y ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % order_antisym_conv
% 5.25/5.45 thf(fact_1286_linorder__le__cases,axiom,
% 5.25/5.45 ! [X4: rat,Y: rat] :
% 5.25/5.45 ( ~ ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.45 => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 5.25/5.45
% 5.25/5.45 % linorder_le_cases
% 5.25/5.45 thf(fact_1287_linorder__le__cases,axiom,
% 5.25/5.45 ! [X4: num,Y: num] :
% 5.25/5.45 ( ~ ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.45 => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 5.25/5.45
% 5.25/5.45 % linorder_le_cases
% 5.25/5.45 thf(fact_1288_linorder__le__cases,axiom,
% 5.25/5.45 ! [X4: nat,Y: nat] :
% 5.25/5.45 ( ~ ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.45 => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 5.25/5.45
% 5.25/5.45 % linorder_le_cases
% 5.25/5.45 thf(fact_1289_linorder__le__cases,axiom,
% 5.25/5.45 ! [X4: int,Y: int] :
% 5.25/5.45 ( ~ ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.45 => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 5.25/5.45
% 5.25/5.45 % linorder_le_cases
% 5.25/5.45 thf(fact_1290_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.45 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.45 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ord_le_eq_subst
% 5.25/5.45 thf(fact_1291_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.45 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.45 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ord_le_eq_subst
% 5.25/5.45 thf(fact_1292_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.45 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.45 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ord_le_eq_subst
% 5.25/5.45 thf(fact_1293_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.45 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.45 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.45 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.45 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ord_le_eq_subst
% 5.25/5.45 thf(fact_1294_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.45 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: num,Y3: num] :
% 5.25/5.45 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.45 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.45 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.45
% 5.25/5.45 % ord_le_eq_subst
% 5.25/5.45 thf(fact_1295_ord__le__eq__subst,axiom,
% 5.25/5.45 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.45 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.45 => ( ( ( F @ B )
% 5.25/5.45 = C )
% 5.25/5.45 => ( ! [X5: num,Y3: num] :
% 5.25/5.45 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_subst
% 5.25/5.46 thf(fact_1296_ord__le__eq__subst,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_subst
% 5.25/5.46 thf(fact_1297_ord__le__eq__subst,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_subst
% 5.25/5.46 thf(fact_1298_ord__le__eq__subst,axiom,
% 5.25/5.46 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_subst
% 5.25/5.46 thf(fact_1299_ord__le__eq__subst,axiom,
% 5.25/5.46 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_subst
% 5.25/5.46 thf(fact_1300_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1301_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1302_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1303_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1304_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1305_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1306_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1307_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: int,F: num > int,B: num,C: num] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1308_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1309_ord__eq__le__subst,axiom,
% 5.25/5.46 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_subst
% 5.25/5.46 thf(fact_1310_linorder__linear,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.46 | ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_linear
% 5.25/5.46 thf(fact_1311_linorder__linear,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.46 | ( ord_less_eq_num @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_linear
% 5.25/5.46 thf(fact_1312_linorder__linear,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.46 | ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_linear
% 5.25/5.46 thf(fact_1313_linorder__linear,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.46 | ( ord_less_eq_int @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_linear
% 5.25/5.46 thf(fact_1314_verit__la__disequality,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 | ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_la_disequality
% 5.25/5.46 thf(fact_1315_verit__la__disequality,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 | ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.46 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_la_disequality
% 5.25/5.46 thf(fact_1316_verit__la__disequality,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 | ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_la_disequality
% 5.25/5.46 thf(fact_1317_verit__la__disequality,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 | ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.46 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_la_disequality
% 5.25/5.46 thf(fact_1318_order__eq__refl,axiom,
% 5.25/5.46 ! [X4: set_int,Y: set_int] :
% 5.25/5.46 ( ( X4 = Y )
% 5.25/5.46 => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_eq_refl
% 5.25/5.46 thf(fact_1319_order__eq__refl,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( X4 = Y )
% 5.25/5.46 => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_eq_refl
% 5.25/5.46 thf(fact_1320_order__eq__refl,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( X4 = Y )
% 5.25/5.46 => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_eq_refl
% 5.25/5.46 thf(fact_1321_order__eq__refl,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( X4 = Y )
% 5.25/5.46 => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_eq_refl
% 5.25/5.46 thf(fact_1322_order__eq__refl,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( X4 = Y )
% 5.25/5.46 => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_eq_refl
% 5.25/5.46 thf(fact_1323_order__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1324_order__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1325_order__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1326_order__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1327_order__subst2,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1328_order__subst2,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1329_order__subst2,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1330_order__subst2,axiom,
% 5.25/5.46 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1331_order__subst2,axiom,
% 5.25/5.46 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1332_order__subst2,axiom,
% 5.25/5.46 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst2
% 5.25/5.46 thf(fact_1333_order__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1334_order__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1335_order__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1336_order__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.46 => ( ! [X5: int,Y3: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1337_order__subst1,axiom,
% 5.25/5.46 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1338_order__subst1,axiom,
% 5.25/5.46 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1339_order__subst1,axiom,
% 5.25/5.46 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1340_order__subst1,axiom,
% 5.25/5.46 ! [A: num,F: int > num,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.46 => ( ! [X5: int,Y3: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1341_order__subst1,axiom,
% 5.25/5.46 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1342_order__subst1,axiom,
% 5.25/5.46 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_subst1
% 5.25/5.46 thf(fact_1343_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.46 & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Orderings.order_eq_iff
% 5.25/5.46 thf(fact_1344_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.46 & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Orderings.order_eq_iff
% 5.25/5.46 thf(fact_1345_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: num,B2: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.46 & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Orderings.order_eq_iff
% 5.25/5.46 thf(fact_1346_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.46 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Orderings.order_eq_iff
% 5.25/5.46 thf(fact_1347_Orderings_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: int,B2: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.46 & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Orderings.order_eq_iff
% 5.25/5.46 thf(fact_1348_antisym,axiom,
% 5.25/5.46 ! [A: set_int,B: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym
% 5.25/5.46 thf(fact_1349_antisym,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym
% 5.25/5.46 thf(fact_1350_antisym,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ A )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym
% 5.25/5.46 thf(fact_1351_antisym,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym
% 5.25/5.46 thf(fact_1352_antisym,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ A )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym
% 5.25/5.46 thf(fact_1353_dual__order_Otrans,axiom,
% 5.25/5.46 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ C @ B )
% 5.25/5.46 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.trans
% 5.25/5.46 thf(fact_1354_dual__order_Otrans,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 @ C @ B )
% 5.25/5.46 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.trans
% 5.25/5.46 thf(fact_1355_dual__order_Otrans,axiom,
% 5.25/5.46 ! [B: num,A: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_num @ C @ B )
% 5.25/5.46 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.trans
% 5.25/5.46 thf(fact_1356_dual__order_Otrans,axiom,
% 5.25/5.46 ! [B: nat,A: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.46 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.trans
% 5.25/5.46 thf(fact_1357_dual__order_Otrans,axiom,
% 5.25/5.46 ! [B: int,A: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ C @ B )
% 5.25/5.46 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.trans
% 5.25/5.46 thf(fact_1358_dual__order_Oantisym,axiom,
% 5.25/5.46 ! [B: set_int,A: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.antisym
% 5.25/5.46 thf(fact_1359_dual__order_Oantisym,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.antisym
% 5.25/5.46 thf(fact_1360_dual__order_Oantisym,axiom,
% 5.25/5.46 ! [B: num,A: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.antisym
% 5.25/5.46 thf(fact_1361_dual__order_Oantisym,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.antisym
% 5.25/5.46 thf(fact_1362_dual__order_Oantisym,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.46 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.46 => ( A = B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.antisym
% 5.25/5.46 thf(fact_1363_dual__order_Oeq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.46 & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.eq_iff
% 5.25/5.46 thf(fact_1364_dual__order_Oeq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.46 & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.eq_iff
% 5.25/5.46 thf(fact_1365_dual__order_Oeq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: num,B2: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.46 & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.eq_iff
% 5.25/5.46 thf(fact_1366_dual__order_Oeq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.46 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.eq_iff
% 5.25/5.46 thf(fact_1367_dual__order_Oeq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A3: int,B2: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.46 & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.eq_iff
% 5.25/5.46 thf(fact_1368_linorder__wlog,axiom,
% 5.25/5.46 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.25/5.46 ( ! [A5: rat,B5: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: rat,B5: rat] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_wlog
% 5.25/5.46 thf(fact_1369_linorder__wlog,axiom,
% 5.25/5.46 ! [P: num > num > $o,A: num,B: num] :
% 5.25/5.46 ( ! [A5: num,B5: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: num,B5: num] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_wlog
% 5.25/5.46 thf(fact_1370_linorder__wlog,axiom,
% 5.25/5.46 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.25/5.46 ( ! [A5: nat,B5: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: nat,B5: nat] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_wlog
% 5.25/5.46 thf(fact_1371_linorder__wlog,axiom,
% 5.25/5.46 ! [P: int > int > $o,A: int,B: int] :
% 5.25/5.46 ( ! [A5: int,B5: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: int,B5: int] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_wlog
% 5.25/5.46 thf(fact_1372_order__trans,axiom,
% 5.25/5.46 ! [X4: set_int,Y: set_int,Z: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.25/5.46 => ( ord_less_eq_set_int @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_trans
% 5.25/5.46 thf(fact_1373_order__trans,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.46 => ( ord_less_eq_rat @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_trans
% 5.25/5.46 thf(fact_1374_order__trans,axiom,
% 5.25/5.46 ! [X4: num,Y: num,Z: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.46 => ( ord_less_eq_num @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_trans
% 5.25/5.46 thf(fact_1375_order__trans,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat,Z: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.46 => ( ord_less_eq_nat @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_trans
% 5.25/5.46 thf(fact_1376_order__trans,axiom,
% 5.25/5.46 ! [X4: int,Y: int,Z: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.46 => ( ord_less_eq_int @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_trans
% 5.25/5.46 thf(fact_1377_order_Otrans,axiom,
% 5.25/5.46 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.46 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.trans
% 5.25/5.46 thf(fact_1378_order_Otrans,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 @ B @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.trans
% 5.25/5.46 thf(fact_1379_order_Otrans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.trans
% 5.25/5.46 thf(fact_1380_order_Otrans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.trans
% 5.25/5.46 thf(fact_1381_order_Otrans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.trans
% 5.25/5.46 thf(fact_1382_order__antisym,axiom,
% 5.25/5.46 ! [X4: set_int,Y: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ Y @ X4 )
% 5.25/5.46 => ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_antisym
% 5.25/5.46 thf(fact_1383_order__antisym,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_rat @ Y @ X4 )
% 5.25/5.46 => ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_antisym
% 5.25/5.46 thf(fact_1384_order__antisym,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_num @ Y @ X4 )
% 5.25/5.46 => ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_antisym
% 5.25/5.46 thf(fact_1385_order__antisym,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.46 => ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_antisym
% 5.25/5.46 thf(fact_1386_order__antisym,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_eq_int @ Y @ X4 )
% 5.25/5.46 => ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_antisym
% 5.25/5.46 thf(fact_1387_ord__le__eq__trans,axiom,
% 5.25/5.46 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_trans
% 5.25/5.46 thf(fact_1388_ord__le__eq__trans,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 => ( ( B = C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_trans
% 5.25/5.46 thf(fact_1389_ord__le__eq__trans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_trans
% 5.25/5.46 thf(fact_1390_ord__le__eq__trans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_trans
% 5.25/5.46 thf(fact_1391_ord__le__eq__trans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_le_eq_trans
% 5.25/5.46 thf(fact_1392_ord__eq__le__trans,axiom,
% 5.25/5.46 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.46 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_trans
% 5.25/5.46 thf(fact_1393_ord__eq__le__trans,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_trans
% 5.25/5.46 thf(fact_1394_ord__eq__le__trans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.46 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_trans
% 5.25/5.46 thf(fact_1395_ord__eq__le__trans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_trans
% 5.25/5.46 thf(fact_1396_ord__eq__le__trans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.46 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_le_trans
% 5.25/5.46 thf(fact_1397_order__class_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [X: set_int,Y5: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ X @ Y5 )
% 5.25/5.46 & ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_class.order_eq_iff
% 5.25/5.46 thf(fact_1398_order__class_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [X: rat,Y5: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X @ Y5 )
% 5.25/5.46 & ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_class.order_eq_iff
% 5.25/5.46 thf(fact_1399_order__class_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: num,Z4: num] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [X: num,Y5: num] :
% 5.25/5.46 ( ( ord_less_eq_num @ X @ Y5 )
% 5.25/5.46 & ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_class.order_eq_iff
% 5.25/5.46 thf(fact_1400_order__class_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [X: nat,Y5: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ X @ Y5 )
% 5.25/5.46 & ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_class.order_eq_iff
% 5.25/5.46 thf(fact_1401_order__class_Oorder__eq__iff,axiom,
% 5.25/5.46 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [X: int,Y5: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ X @ Y5 )
% 5.25/5.46 & ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_class.order_eq_iff
% 5.25/5.46 thf(fact_1402_le__cases3,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.46 ( ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_rat @ Y @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ X4 @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_rat @ X4 @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.25/5.46 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ Y @ X4 ) )
% 5.25/5.46 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ Z @ X4 ) )
% 5.25/5.46 => ~ ( ( ord_less_eq_rat @ Z @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_rat @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_cases3
% 5.25/5.46 thf(fact_1403_le__cases3,axiom,
% 5.25/5.46 ! [X4: num,Y: num,Z: num] :
% 5.25/5.46 ( ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_num @ Y @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_num @ X4 @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_num @ X4 @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.25/5.46 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_num @ Y @ X4 ) )
% 5.25/5.46 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_num @ Z @ X4 ) )
% 5.25/5.46 => ~ ( ( ord_less_eq_num @ Z @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_num @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_cases3
% 5.25/5.46 thf(fact_1404_le__cases3,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat,Z: nat] :
% 5.25/5.46 ( ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ X4 @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_nat @ X4 @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.25/5.46 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ Y @ X4 ) )
% 5.25/5.46 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ Z @ X4 ) )
% 5.25/5.46 => ~ ( ( ord_less_eq_nat @ Z @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_cases3
% 5.25/5.46 thf(fact_1405_le__cases3,axiom,
% 5.25/5.46 ! [X4: int,Y: int,Z: int] :
% 5.25/5.46 ( ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_int @ Y @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_int @ X4 @ Z ) )
% 5.25/5.46 => ( ( ( ord_less_eq_int @ X4 @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.25/5.46 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.25/5.46 => ~ ( ord_less_eq_int @ Y @ X4 ) )
% 5.25/5.46 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.46 => ~ ( ord_less_eq_int @ Z @ X4 ) )
% 5.25/5.46 => ~ ( ( ord_less_eq_int @ Z @ X4 )
% 5.25/5.46 => ~ ( ord_less_eq_int @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % le_cases3
% 5.25/5.46 thf(fact_1406_nle__le,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.46 = ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.46 & ( B != A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nle_le
% 5.25/5.46 thf(fact_1407_nle__le,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.25/5.46 = ( ( ord_less_eq_num @ B @ A )
% 5.25/5.46 & ( B != A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nle_le
% 5.25/5.46 thf(fact_1408_nle__le,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.25/5.46 = ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.46 & ( B != A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nle_le
% 5.25/5.46 thf(fact_1409_nle__le,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.25/5.46 = ( ( ord_less_eq_int @ B @ A )
% 5.25/5.46 & ( B != A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nle_le
% 5.25/5.46 thf(fact_1410_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.46 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(2)
% 5.25/5.46 thf(fact_1411_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.46 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(2)
% 5.25/5.46 thf(fact_1412_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.46 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(2)
% 5.25/5.46 thf(fact_1413_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.46 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(2)
% 5.25/5.46 thf(fact_1414_verit__comp__simplify1_I2_J,axiom,
% 5.25/5.46 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(2)
% 5.25/5.46 thf(fact_1415_order__less__imp__not__less,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_less
% 5.25/5.46 thf(fact_1416_order__less__imp__not__less,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_less
% 5.25/5.46 thf(fact_1417_order__less__imp__not__less,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_less
% 5.25/5.46 thf(fact_1418_order__less__imp__not__less,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_less
% 5.25/5.46 thf(fact_1419_order__less__imp__not__less,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_less
% 5.25/5.46 thf(fact_1420_order__less__imp__not__eq2,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( Y != X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq2
% 5.25/5.46 thf(fact_1421_order__less__imp__not__eq2,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( Y != X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq2
% 5.25/5.46 thf(fact_1422_order__less__imp__not__eq2,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( Y != X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq2
% 5.25/5.46 thf(fact_1423_order__less__imp__not__eq2,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( Y != X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq2
% 5.25/5.46 thf(fact_1424_order__less__imp__not__eq2,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( Y != X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq2
% 5.25/5.46 thf(fact_1425_order__less__imp__not__eq,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq
% 5.25/5.46 thf(fact_1426_order__less__imp__not__eq,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq
% 5.25/5.46 thf(fact_1427_order__less__imp__not__eq,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq
% 5.25/5.46 thf(fact_1428_order__less__imp__not__eq,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq
% 5.25/5.46 thf(fact_1429_order__less__imp__not__eq,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_not_eq
% 5.25/5.46 thf(fact_1430_linorder__less__linear,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 | ( X4 = Y )
% 5.25/5.46 | ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_linear
% 5.25/5.46 thf(fact_1431_linorder__less__linear,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 | ( X4 = Y )
% 5.25/5.46 | ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_linear
% 5.25/5.46 thf(fact_1432_linorder__less__linear,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 | ( X4 = Y )
% 5.25/5.46 | ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_linear
% 5.25/5.46 thf(fact_1433_linorder__less__linear,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 | ( X4 = Y )
% 5.25/5.46 | ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_linear
% 5.25/5.46 thf(fact_1434_linorder__less__linear,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 | ( X4 = Y )
% 5.25/5.46 | ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_linear
% 5.25/5.46 thf(fact_1435_order__less__imp__triv,axiom,
% 5.25/5.46 ! [X4: real,Y: real,P: $o] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_real @ Y @ X4 )
% 5.25/5.46 => P ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_triv
% 5.25/5.46 thf(fact_1436_order__less__imp__triv,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,P: $o] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ X4 )
% 5.25/5.46 => P ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_triv
% 5.25/5.46 thf(fact_1437_order__less__imp__triv,axiom,
% 5.25/5.46 ! [X4: num,Y: num,P: $o] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_num @ Y @ X4 )
% 5.25/5.46 => P ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_triv
% 5.25/5.46 thf(fact_1438_order__less__imp__triv,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat,P: $o] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_nat @ Y @ X4 )
% 5.25/5.46 => P ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_triv
% 5.25/5.46 thf(fact_1439_order__less__imp__triv,axiom,
% 5.25/5.46 ! [X4: int,Y: int,P: $o] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_int @ Y @ X4 )
% 5.25/5.46 => P ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_imp_triv
% 5.25/5.46 thf(fact_1440_order__less__not__sym,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_not_sym
% 5.25/5.46 thf(fact_1441_order__less__not__sym,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_not_sym
% 5.25/5.46 thf(fact_1442_order__less__not__sym,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_not_sym
% 5.25/5.46 thf(fact_1443_order__less__not__sym,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_not_sym
% 5.25/5.46 thf(fact_1444_order__less__not__sym,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_not_sym
% 5.25/5.46 thf(fact_1445_order__less__subst2,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1446_order__less__subst2,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1447_order__less__subst2,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > num,C: num] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1448_order__less__subst2,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1449_order__less__subst2,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > int,C: int] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1450_order__less__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1451_order__less__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1452_order__less__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1453_order__less__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1454_order__less__subst2,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst2
% 5.25/5.46 thf(fact_1455_order__less__subst1,axiom,
% 5.25/5.46 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1456_order__less__subst1,axiom,
% 5.25/5.46 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1457_order__less__subst1,axiom,
% 5.25/5.46 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1458_order__less__subst1,axiom,
% 5.25/5.46 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1459_order__less__subst1,axiom,
% 5.25/5.46 ! [A: real,F: int > real,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_int @ B @ C )
% 5.25/5.46 => ( ! [X5: int,Y3: int] :
% 5.25/5.46 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1460_order__less__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1461_order__less__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1462_order__less__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_num @ B @ C )
% 5.25/5.46 => ( ! [X5: num,Y3: num] :
% 5.25/5.46 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1463_order__less__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_nat @ B @ C )
% 5.25/5.46 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1464_order__less__subst1,axiom,
% 5.25/5.46 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_int @ B @ C )
% 5.25/5.46 => ( ! [X5: int,Y3: int] :
% 5.25/5.46 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_subst1
% 5.25/5.46 thf(fact_1465_order__less__irrefl,axiom,
% 5.25/5.46 ! [X4: real] :
% 5.25/5.46 ~ ( ord_less_real @ X4 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_irrefl
% 5.25/5.46 thf(fact_1466_order__less__irrefl,axiom,
% 5.25/5.46 ! [X4: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ X4 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_irrefl
% 5.25/5.46 thf(fact_1467_order__less__irrefl,axiom,
% 5.25/5.46 ! [X4: num] :
% 5.25/5.46 ~ ( ord_less_num @ X4 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_irrefl
% 5.25/5.46 thf(fact_1468_order__less__irrefl,axiom,
% 5.25/5.46 ! [X4: nat] :
% 5.25/5.46 ~ ( ord_less_nat @ X4 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_irrefl
% 5.25/5.46 thf(fact_1469_order__less__irrefl,axiom,
% 5.25/5.46 ! [X4: int] :
% 5.25/5.46 ~ ( ord_less_int @ X4 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_irrefl
% 5.25/5.46 thf(fact_1470_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1471_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1472_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > num,C: num] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1473_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1474_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: real,B: real,F: real > int,C: int] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1475_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1476_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1477_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1478_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1479_ord__less__eq__subst,axiom,
% 5.25/5.46 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( ( F @ B )
% 5.25/5.46 = C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_subst
% 5.25/5.46 thf(fact_1480_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1481_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1482_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: num,F: real > num,B: real,C: real] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1483_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1484_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: int,F: real > int,B: real,C: real] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ! [X5: real,Y3: real] :
% 5.25/5.46 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1485_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1486_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1487_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1488_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1489_ord__eq__less__subst,axiom,
% 5.25/5.46 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.46 ( ( A
% 5.25/5.46 = ( F @ B ) )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.46 => ( ord_less_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.46 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_subst
% 5.25/5.46 thf(fact_1490_order__less__trans,axiom,
% 5.25/5.46 ! [X4: real,Y: real,Z: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_real @ Y @ Z )
% 5.25/5.46 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_trans
% 5.25/5.46 thf(fact_1491_order__less__trans,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ Z )
% 5.25/5.46 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_trans
% 5.25/5.46 thf(fact_1492_order__less__trans,axiom,
% 5.25/5.46 ! [X4: num,Y: num,Z: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_num @ Y @ Z )
% 5.25/5.46 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_trans
% 5.25/5.46 thf(fact_1493_order__less__trans,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat,Z: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_nat @ Y @ Z )
% 5.25/5.46 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_trans
% 5.25/5.46 thf(fact_1494_order__less__trans,axiom,
% 5.25/5.46 ! [X4: int,Y: int,Z: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.46 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_trans
% 5.25/5.46 thf(fact_1495_order__less__asym_H,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym'
% 5.25/5.46 thf(fact_1496_order__less__asym_H,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym'
% 5.25/5.46 thf(fact_1497_order__less__asym_H,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( ord_less_num @ A @ B )
% 5.25/5.46 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym'
% 5.25/5.46 thf(fact_1498_order__less__asym_H,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym'
% 5.25/5.46 thf(fact_1499_order__less__asym_H,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym'
% 5.25/5.46 thf(fact_1500_linorder__neq__iff,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 = ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 | ( ord_less_real @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neq_iff
% 5.25/5.46 thf(fact_1501_linorder__neq__iff,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 = ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 | ( ord_less_rat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neq_iff
% 5.25/5.46 thf(fact_1502_linorder__neq__iff,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 = ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 | ( ord_less_num @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neq_iff
% 5.25/5.46 thf(fact_1503_linorder__neq__iff,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 = ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 | ( ord_less_nat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neq_iff
% 5.25/5.46 thf(fact_1504_linorder__neq__iff,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 = ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 | ( ord_less_int @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neq_iff
% 5.25/5.46 thf(fact_1505_order__less__asym,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym
% 5.25/5.46 thf(fact_1506_order__less__asym,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym
% 5.25/5.46 thf(fact_1507_order__less__asym,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym
% 5.25/5.46 thf(fact_1508_order__less__asym,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym
% 5.25/5.46 thf(fact_1509_order__less__asym,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ~ ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.46
% 5.25/5.46 % order_less_asym
% 5.25/5.46 thf(fact_1510_linorder__neqE,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 => ( ~ ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( ord_less_real @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neqE
% 5.25/5.46 thf(fact_1511_linorder__neqE,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 => ( ~ ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neqE
% 5.25/5.46 thf(fact_1512_linorder__neqE,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 => ( ~ ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( ord_less_num @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neqE
% 5.25/5.46 thf(fact_1513_linorder__neqE,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 => ( ~ ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neqE
% 5.25/5.46 thf(fact_1514_linorder__neqE,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( X4 != Y )
% 5.25/5.46 => ( ~ ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( ord_less_int @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_neqE
% 5.25/5.46 thf(fact_1515_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ B @ A )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1516_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ B @ A )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1517_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [B: num,A: num] :
% 5.25/5.46 ( ( ord_less_num @ B @ A )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1518_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ B @ A )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1519_dual__order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ B @ A )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1520_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1521_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1522_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( ord_less_num @ A @ B )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1523_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1524_order_Ostrict__implies__not__eq,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( A != B ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_implies_not_eq
% 5.25/5.46 thf(fact_1525_dual__order_Ostrict__trans,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 @ C @ B )
% 5.25/5.46 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_trans
% 5.25/5.46 thf(fact_1526_dual__order_Ostrict__trans,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 @ C @ B )
% 5.25/5.46 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_trans
% 5.25/5.46 thf(fact_1527_dual__order_Ostrict__trans,axiom,
% 5.25/5.46 ! [B: num,A: num,C: num] :
% 5.25/5.46 ( ( ord_less_num @ B @ A )
% 5.25/5.46 => ( ( ord_less_num @ C @ B )
% 5.25/5.46 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_trans
% 5.25/5.46 thf(fact_1528_dual__order_Ostrict__trans,axiom,
% 5.25/5.46 ! [B: nat,A: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_nat @ B @ A )
% 5.25/5.46 => ( ( ord_less_nat @ C @ B )
% 5.25/5.46 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_trans
% 5.25/5.46 thf(fact_1529_dual__order_Ostrict__trans,axiom,
% 5.25/5.46 ! [B: int,A: int,C: int] :
% 5.25/5.46 ( ( ord_less_int @ B @ A )
% 5.25/5.46 => ( ( ord_less_int @ C @ B )
% 5.25/5.46 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.strict_trans
% 5.25/5.46 thf(fact_1530_not__less__iff__gr__or__eq,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 5.25/5.46 = ( ( ord_less_real @ Y @ X4 )
% 5.25/5.46 | ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % not_less_iff_gr_or_eq
% 5.25/5.46 thf(fact_1531_not__less__iff__gr__or__eq,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 5.25/5.46 = ( ( ord_less_rat @ Y @ X4 )
% 5.25/5.46 | ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % not_less_iff_gr_or_eq
% 5.25/5.46 thf(fact_1532_not__less__iff__gr__or__eq,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 5.25/5.46 = ( ( ord_less_num @ Y @ X4 )
% 5.25/5.46 | ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % not_less_iff_gr_or_eq
% 5.25/5.46 thf(fact_1533_not__less__iff__gr__or__eq,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 5.25/5.46 = ( ( ord_less_nat @ Y @ X4 )
% 5.25/5.46 | ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % not_less_iff_gr_or_eq
% 5.25/5.46 thf(fact_1534_not__less__iff__gr__or__eq,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 5.25/5.46 = ( ( ord_less_int @ Y @ X4 )
% 5.25/5.46 | ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % not_less_iff_gr_or_eq
% 5.25/5.46 thf(fact_1535_order_Ostrict__trans,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 @ B @ C )
% 5.25/5.46 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_trans
% 5.25/5.46 thf(fact_1536_order_Ostrict__trans,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 @ B @ C )
% 5.25/5.46 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_trans
% 5.25/5.46 thf(fact_1537_order_Ostrict__trans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_num @ A @ B )
% 5.25/5.46 => ( ( ord_less_num @ B @ C )
% 5.25/5.46 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_trans
% 5.25/5.46 thf(fact_1538_order_Ostrict__trans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( ( ord_less_nat @ B @ C )
% 5.25/5.46 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_trans
% 5.25/5.46 thf(fact_1539_order_Ostrict__trans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( ( ord_less_int @ B @ C )
% 5.25/5.46 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.strict_trans
% 5.25/5.46 thf(fact_1540_linorder__less__wlog,axiom,
% 5.25/5.46 ! [P: real > real > $o,A: real,B: real] :
% 5.25/5.46 ( ! [A5: real,B5: real] :
% 5.25/5.46 ( ( ord_less_real @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 5.25/5.46 => ( ! [A5: real,B5: real] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_wlog
% 5.25/5.46 thf(fact_1541_linorder__less__wlog,axiom,
% 5.25/5.46 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.25/5.46 ( ! [A5: rat,B5: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 5.25/5.46 => ( ! [A5: rat,B5: rat] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_wlog
% 5.25/5.46 thf(fact_1542_linorder__less__wlog,axiom,
% 5.25/5.46 ! [P: num > num > $o,A: num,B: num] :
% 5.25/5.46 ( ! [A5: num,B5: num] :
% 5.25/5.46 ( ( ord_less_num @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 5.25/5.46 => ( ! [A5: num,B5: num] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_wlog
% 5.25/5.46 thf(fact_1543_linorder__less__wlog,axiom,
% 5.25/5.46 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.25/5.46 ( ! [A5: nat,B5: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 5.25/5.46 => ( ! [A5: nat,B5: nat] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_wlog
% 5.25/5.46 thf(fact_1544_linorder__less__wlog,axiom,
% 5.25/5.46 ! [P: int > int > $o,A: int,B: int] :
% 5.25/5.46 ( ! [A5: int,B5: int] :
% 5.25/5.46 ( ( ord_less_int @ A5 @ B5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 5.25/5.46 => ( ! [A5: int,B5: int] :
% 5.25/5.46 ( ( P @ B5 @ A5 )
% 5.25/5.46 => ( P @ A5 @ B5 ) )
% 5.25/5.46 => ( P @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_less_wlog
% 5.25/5.46 thf(fact_1545_exists__least__iff,axiom,
% 5.25/5.46 ( ( ^ [P3: nat > $o] :
% 5.25/5.46 ? [X6: nat] : ( P3 @ X6 ) )
% 5.25/5.46 = ( ^ [P4: nat > $o] :
% 5.25/5.46 ? [N: nat] :
% 5.25/5.46 ( ( P4 @ N )
% 5.25/5.46 & ! [M6: nat] :
% 5.25/5.46 ( ( ord_less_nat @ M6 @ N )
% 5.25/5.46 => ~ ( P4 @ M6 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % exists_least_iff
% 5.25/5.46 thf(fact_1546_dual__order_Oirrefl,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ~ ( ord_less_real @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.irrefl
% 5.25/5.46 thf(fact_1547_dual__order_Oirrefl,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.irrefl
% 5.25/5.46 thf(fact_1548_dual__order_Oirrefl,axiom,
% 5.25/5.46 ! [A: num] :
% 5.25/5.46 ~ ( ord_less_num @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.irrefl
% 5.25/5.46 thf(fact_1549_dual__order_Oirrefl,axiom,
% 5.25/5.46 ! [A: nat] :
% 5.25/5.46 ~ ( ord_less_nat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.irrefl
% 5.25/5.46 thf(fact_1550_dual__order_Oirrefl,axiom,
% 5.25/5.46 ! [A: int] :
% 5.25/5.46 ~ ( ord_less_int @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.irrefl
% 5.25/5.46 thf(fact_1551_dual__order_Oasym,axiom,
% 5.25/5.46 ! [B: real,A: real] :
% 5.25/5.46 ( ( ord_less_real @ B @ A )
% 5.25/5.46 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.asym
% 5.25/5.46 thf(fact_1552_dual__order_Oasym,axiom,
% 5.25/5.46 ! [B: rat,A: rat] :
% 5.25/5.46 ( ( ord_less_rat @ B @ A )
% 5.25/5.46 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.asym
% 5.25/5.46 thf(fact_1553_dual__order_Oasym,axiom,
% 5.25/5.46 ! [B: num,A: num] :
% 5.25/5.46 ( ( ord_less_num @ B @ A )
% 5.25/5.46 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.asym
% 5.25/5.46 thf(fact_1554_dual__order_Oasym,axiom,
% 5.25/5.46 ! [B: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ B @ A )
% 5.25/5.46 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.asym
% 5.25/5.46 thf(fact_1555_dual__order_Oasym,axiom,
% 5.25/5.46 ! [B: int,A: int] :
% 5.25/5.46 ( ( ord_less_int @ B @ A )
% 5.25/5.46 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.25/5.46
% 5.25/5.46 % dual_order.asym
% 5.25/5.46 thf(fact_1556_linorder__cases,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ~ ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( ( X4 != Y )
% 5.25/5.46 => ( ord_less_real @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_cases
% 5.25/5.46 thf(fact_1557_linorder__cases,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ~ ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( ( X4 != Y )
% 5.25/5.46 => ( ord_less_rat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_cases
% 5.25/5.46 thf(fact_1558_linorder__cases,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ~ ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( ( X4 != Y )
% 5.25/5.46 => ( ord_less_num @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_cases
% 5.25/5.46 thf(fact_1559_linorder__cases,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ~ ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( ( X4 != Y )
% 5.25/5.46 => ( ord_less_nat @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_cases
% 5.25/5.46 thf(fact_1560_linorder__cases,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ~ ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( ( X4 != Y )
% 5.25/5.46 => ( ord_less_int @ Y @ X4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % linorder_cases
% 5.25/5.46 thf(fact_1561_antisym__conv3,axiom,
% 5.25/5.46 ! [Y: real,X4: real] :
% 5.25/5.46 ( ~ ( ord_less_real @ Y @ X4 )
% 5.25/5.46 => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 5.25/5.46 = ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym_conv3
% 5.25/5.46 thf(fact_1562_antisym__conv3,axiom,
% 5.25/5.46 ! [Y: rat,X4: rat] :
% 5.25/5.46 ( ~ ( ord_less_rat @ Y @ X4 )
% 5.25/5.46 => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 5.25/5.46 = ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym_conv3
% 5.25/5.46 thf(fact_1563_antisym__conv3,axiom,
% 5.25/5.46 ! [Y: num,X4: num] :
% 5.25/5.46 ( ~ ( ord_less_num @ Y @ X4 )
% 5.25/5.46 => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 5.25/5.46 = ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym_conv3
% 5.25/5.46 thf(fact_1564_antisym__conv3,axiom,
% 5.25/5.46 ! [Y: nat,X4: nat] :
% 5.25/5.46 ( ~ ( ord_less_nat @ Y @ X4 )
% 5.25/5.46 => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 5.25/5.46 = ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym_conv3
% 5.25/5.46 thf(fact_1565_antisym__conv3,axiom,
% 5.25/5.46 ! [Y: int,X4: int] :
% 5.25/5.46 ( ~ ( ord_less_int @ Y @ X4 )
% 5.25/5.46 => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 5.25/5.46 = ( X4 = Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % antisym_conv3
% 5.25/5.46 thf(fact_1566_less__induct,axiom,
% 5.25/5.46 ! [P: nat > $o,A: nat] :
% 5.25/5.46 ( ! [X5: nat] :
% 5.25/5.46 ( ! [Y4: nat] :
% 5.25/5.46 ( ( ord_less_nat @ Y4 @ X5 )
% 5.25/5.46 => ( P @ Y4 ) )
% 5.25/5.46 => ( P @ X5 ) )
% 5.25/5.46 => ( P @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_induct
% 5.25/5.46 thf(fact_1567_ord__less__eq__trans,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_trans
% 5.25/5.46 thf(fact_1568_ord__less__eq__trans,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_trans
% 5.25/5.46 thf(fact_1569_ord__less__eq__trans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( ord_less_num @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_trans
% 5.25/5.46 thf(fact_1570_ord__less__eq__trans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_trans
% 5.25/5.46 thf(fact_1571_ord__less__eq__trans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ( ( B = C )
% 5.25/5.46 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_less_eq_trans
% 5.25/5.46 thf(fact_1572_ord__eq__less__trans,axiom,
% 5.25/5.46 ! [A: real,B: real,C: real] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_real @ B @ C )
% 5.25/5.46 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_trans
% 5.25/5.46 thf(fact_1573_ord__eq__less__trans,axiom,
% 5.25/5.46 ! [A: rat,B: rat,C: rat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_rat @ B @ C )
% 5.25/5.46 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_trans
% 5.25/5.46 thf(fact_1574_ord__eq__less__trans,axiom,
% 5.25/5.46 ! [A: num,B: num,C: num] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_num @ B @ C )
% 5.25/5.46 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_trans
% 5.25/5.46 thf(fact_1575_ord__eq__less__trans,axiom,
% 5.25/5.46 ! [A: nat,B: nat,C: nat] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_nat @ B @ C )
% 5.25/5.46 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_trans
% 5.25/5.46 thf(fact_1576_ord__eq__less__trans,axiom,
% 5.25/5.46 ! [A: int,B: int,C: int] :
% 5.25/5.46 ( ( A = B )
% 5.25/5.46 => ( ( ord_less_int @ B @ C )
% 5.25/5.46 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % ord_eq_less_trans
% 5.25/5.46 thf(fact_1577_order_Oasym,axiom,
% 5.25/5.46 ! [A: real,B: real] :
% 5.25/5.46 ( ( ord_less_real @ A @ B )
% 5.25/5.46 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.asym
% 5.25/5.46 thf(fact_1578_order_Oasym,axiom,
% 5.25/5.46 ! [A: rat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ A @ B )
% 5.25/5.46 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.asym
% 5.25/5.46 thf(fact_1579_order_Oasym,axiom,
% 5.25/5.46 ! [A: num,B: num] :
% 5.25/5.46 ( ( ord_less_num @ A @ B )
% 5.25/5.46 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.asym
% 5.25/5.46 thf(fact_1580_order_Oasym,axiom,
% 5.25/5.46 ! [A: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A @ B )
% 5.25/5.46 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.asym
% 5.25/5.46 thf(fact_1581_order_Oasym,axiom,
% 5.25/5.46 ! [A: int,B: int] :
% 5.25/5.46 ( ( ord_less_int @ A @ B )
% 5.25/5.46 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.25/5.46
% 5.25/5.46 % order.asym
% 5.25/5.46 thf(fact_1582_less__imp__neq,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_imp_neq
% 5.25/5.46 thf(fact_1583_less__imp__neq,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_imp_neq
% 5.25/5.46 thf(fact_1584_less__imp__neq,axiom,
% 5.25/5.46 ! [X4: num,Y: num] :
% 5.25/5.46 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_imp_neq
% 5.25/5.46 thf(fact_1585_less__imp__neq,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_imp_neq
% 5.25/5.46 thf(fact_1586_less__imp__neq,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.46 => ( X4 != Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % less_imp_neq
% 5.25/5.46 thf(fact_1587_dense,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.46 => ? [Z2: real] :
% 5.25/5.46 ( ( ord_less_real @ X4 @ Z2 )
% 5.25/5.46 & ( ord_less_real @ Z2 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dense
% 5.25/5.46 thf(fact_1588_dense,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.46 => ? [Z2: rat] :
% 5.25/5.46 ( ( ord_less_rat @ X4 @ Z2 )
% 5.25/5.46 & ( ord_less_rat @ Z2 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % dense
% 5.25/5.46 thf(fact_1589_gt__ex,axiom,
% 5.25/5.46 ! [X4: real] :
% 5.25/5.46 ? [X_12: real] : ( ord_less_real @ X4 @ X_12 ) ).
% 5.25/5.46
% 5.25/5.46 % gt_ex
% 5.25/5.46 thf(fact_1590_gt__ex,axiom,
% 5.25/5.46 ! [X4: rat] :
% 5.25/5.46 ? [X_12: rat] : ( ord_less_rat @ X4 @ X_12 ) ).
% 5.25/5.46
% 5.25/5.46 % gt_ex
% 5.25/5.46 thf(fact_1591_gt__ex,axiom,
% 5.25/5.46 ! [X4: nat] :
% 5.25/5.46 ? [X_12: nat] : ( ord_less_nat @ X4 @ X_12 ) ).
% 5.25/5.46
% 5.25/5.46 % gt_ex
% 5.25/5.46 thf(fact_1592_gt__ex,axiom,
% 5.25/5.46 ! [X4: int] :
% 5.25/5.46 ? [X_12: int] : ( ord_less_int @ X4 @ X_12 ) ).
% 5.25/5.46
% 5.25/5.46 % gt_ex
% 5.25/5.46 thf(fact_1593_lt__ex,axiom,
% 5.25/5.46 ! [X4: real] :
% 5.25/5.46 ? [Y3: real] : ( ord_less_real @ Y3 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % lt_ex
% 5.25/5.46 thf(fact_1594_lt__ex,axiom,
% 5.25/5.46 ! [X4: rat] :
% 5.25/5.46 ? [Y3: rat] : ( ord_less_rat @ Y3 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % lt_ex
% 5.25/5.46 thf(fact_1595_lt__ex,axiom,
% 5.25/5.46 ! [X4: int] :
% 5.25/5.46 ? [Y3: int] : ( ord_less_int @ Y3 @ X4 ) ).
% 5.25/5.46
% 5.25/5.46 % lt_ex
% 5.25/5.46 thf(fact_1596_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.46 ! [A: real] :
% 5.25/5.46 ~ ( ord_less_real @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(1)
% 5.25/5.46 thf(fact_1597_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.46 ! [A: rat] :
% 5.25/5.46 ~ ( ord_less_rat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(1)
% 5.25/5.46 thf(fact_1598_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.46 ! [A: num] :
% 5.25/5.46 ~ ( ord_less_num @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(1)
% 5.25/5.46 thf(fact_1599_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.46 ! [A: nat] :
% 5.25/5.46 ~ ( ord_less_nat @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(1)
% 5.25/5.46 thf(fact_1600_verit__comp__simplify1_I1_J,axiom,
% 5.25/5.46 ! [A: int] :
% 5.25/5.46 ~ ( ord_less_int @ A @ A ) ).
% 5.25/5.46
% 5.25/5.46 % verit_comp_simplify1(1)
% 5.25/5.46 thf(fact_1601_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_1602_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_1603_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_1604_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_1605_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_1606_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_1607_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_1608_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_1609_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_1610_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_1611_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_1612_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_1613_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_1614_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_1615_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_1616_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_1617_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_1618_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_1619_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_1620_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_1621_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_1622_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_1623_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_1624_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_1625_field__le__epsilon,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ! [E: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ E )
% 5.25/5.46 => ( ord_less_eq_real @ X4 @ ( plus_plus_real @ Y @ E ) ) )
% 5.25/5.46 => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_epsilon
% 5.25/5.46 thf(fact_1626_field__le__epsilon,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ! [E: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.25/5.46 => ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ Y @ E ) ) )
% 5.25/5.46 => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.25/5.46
% 5.25/5.46 % field_le_epsilon
% 5.25/5.46 thf(fact_1627_divide__nonpos__pos,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ X4 @ 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 @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_pos
% 5.25/5.46 thf(fact_1628_divide__nonpos__pos,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X4 @ 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 @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_pos
% 5.25/5.46 thf(fact_1629_divide__nonpos__neg,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_neg
% 5.25/5.46 thf(fact_1630_divide__nonpos__neg,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ X4 @ 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonpos_neg
% 5.25/5.46 thf(fact_1631_divide__nonneg__pos,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_pos
% 5.25/5.46 thf(fact_1632_divide__nonneg__pos,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 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 @ X4 @ Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_pos
% 5.25/5.46 thf(fact_1633_divide__nonneg__neg,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.46 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.25/5.46 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ zero_zero_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_neg
% 5.25/5.46 thf(fact_1634_divide__nonneg__neg,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.46 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.25/5.46 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ zero_zero_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % divide_nonneg_neg
% 5.25/5.46 thf(fact_1635_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_1636_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_1637_frac__less2,axiom,
% 5.25/5.46 ! [X4: real,Y: real,W: real,Z: real] :
% 5.25/5.46 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_real @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less2
% 5.25/5.46 thf(fact_1638_frac__less2,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less2
% 5.25/5.46 thf(fact_1639_frac__less,axiom,
% 5.25/5.46 ! [X4: real,Y: real,W: real,Z: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.46 => ( ( ord_less_real @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less
% 5.25/5.46 thf(fact_1640_frac__less,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat,W: rat,Z: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.46 => ( ( ord_less_rat @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_less
% 5.25/5.46 thf(fact_1641_frac__le,axiom,
% 5.25/5.46 ! [Y: real,X4: 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 @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_le
% 5.25/5.46 thf(fact_1642_frac__le,axiom,
% 5.25/5.46 ! [Y: rat,X4: 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 @ X4 @ 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 @ X4 @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % frac_le
% 5.25/5.46 thf(fact_1643_div__positive,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 @ B @ A )
% 5.25/5.46 => ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_positive
% 5.25/5.46 thf(fact_1644_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_1645_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_1646_unique__euclidean__semiring__numeral__class_Odiv__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 => ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.46 = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % unique_euclidean_semiring_numeral_class.div_less
% 5.25/5.46 thf(fact_1647_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_1648_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_1649_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: real,N2: nat,B: real] :
% 5.25/5.46 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) )
% 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_1650_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: rat,N2: nat,B: rat] :
% 5.25/5.46 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) )
% 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_1651_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: nat,N2: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 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_1652_power__less__imp__less__base,axiom,
% 5.25/5.46 ! [A: int,N2: nat,B: int] :
% 5.25/5.46 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 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_1653_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_1654_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_1655_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_1656_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_1657_power__le__one,axiom,
% 5.25/5.46 ! [A: real,N2: 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 @ N2 ) @ one_one_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_1658_power__le__one,axiom,
% 5.25/5.46 ! [A: rat,N2: 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 @ N2 ) @ one_one_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_1659_power__le__one,axiom,
% 5.25/5.46 ! [A: nat,N2: 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 @ N2 ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_1660_power__le__one,axiom,
% 5.25/5.46 ! [A: int,N2: 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 @ N2 ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_le_one
% 5.25/5.46 thf(fact_1661_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_1662_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_1663_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_1664_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_1665_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_1666_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_1667_div__add__self2,axiom,
% 5.25/5.46 ! [B: code_integer,A: code_integer] :
% 5.25/5.46 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.46 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.25/5.46 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self2
% 5.25/5.46 thf(fact_1668_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_1669_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_1670_div__add__self1,axiom,
% 5.25/5.46 ! [B: code_integer,A: code_integer] :
% 5.25/5.46 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.46 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.25/5.46 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_add_self1
% 5.25/5.46 thf(fact_1671_power__inject__base,axiom,
% 5.25/5.46 ! [A: real,N2: nat,B: real] :
% 5.25/5.46 ( ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.25/5.46 = ( power_power_real @ B @ ( suc @ N2 ) ) )
% 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_1672_power__inject__base,axiom,
% 5.25/5.46 ! [A: rat,N2: nat,B: rat] :
% 5.25/5.46 ( ( ( power_power_rat @ A @ ( suc @ N2 ) )
% 5.25/5.46 = ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 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_1673_power__inject__base,axiom,
% 5.25/5.46 ! [A: nat,N2: nat,B: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.25/5.46 = ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 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_1674_power__inject__base,axiom,
% 5.25/5.46 ! [A: int,N2: nat,B: int] :
% 5.25/5.46 ( ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.25/5.46 = ( power_power_int @ B @ ( suc @ N2 ) ) )
% 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_1675_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: real,N2: nat,B: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N2 ) ) @ ( power_power_real @ B @ ( suc @ N2 ) ) )
% 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_1676_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: rat,N2: nat,B: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N2 ) ) @ ( power_power_rat @ B @ ( suc @ N2 ) ) )
% 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_1677_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: nat,N2: nat,B: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N2 ) ) @ ( power_power_nat @ B @ ( suc @ N2 ) ) )
% 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_1678_power__le__imp__le__base,axiom,
% 5.25/5.46 ! [A: int,N2: nat,B: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N2 ) ) @ ( power_power_int @ B @ ( suc @ N2 ) ) )
% 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_1679_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_1680_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_1681_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_1682_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_1683_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_1684_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_1685_in__mono,axiom,
% 5.25/5.46 ! [A2: set_real,B3: set_real,X4: real] :
% 5.25/5.46 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.25/5.46 => ( ( member_real @ X4 @ A2 )
% 5.25/5.46 => ( member_real @ X4 @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % in_mono
% 5.25/5.46 thf(fact_1686_in__mono,axiom,
% 5.25/5.46 ! [A2: set_nat,B3: set_nat,X4: nat] :
% 5.25/5.46 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( member_nat @ X4 @ A2 )
% 5.25/5.46 => ( member_nat @ X4 @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % in_mono
% 5.25/5.46 thf(fact_1687_in__mono,axiom,
% 5.25/5.46 ! [A2: set_complex,B3: set_complex,X4: complex] :
% 5.25/5.46 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.25/5.46 => ( ( member_complex @ X4 @ A2 )
% 5.25/5.46 => ( member_complex @ X4 @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % in_mono
% 5.25/5.46 thf(fact_1688_in__mono,axiom,
% 5.25/5.46 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,X4: product_prod_nat_nat] :
% 5.25/5.46 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( member8440522571783428010at_nat @ X4 @ A2 )
% 5.25/5.46 => ( member8440522571783428010at_nat @ X4 @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % in_mono
% 5.25/5.46 thf(fact_1689_in__mono,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int,X4: int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ( member_int @ X4 @ A2 )
% 5.25/5.46 => ( member_int @ X4 @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % in_mono
% 5.25/5.46 thf(fact_1690_subsetD,axiom,
% 5.25/5.46 ! [A2: set_real,B3: set_real,C: real] :
% 5.25/5.46 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.25/5.46 => ( ( member_real @ C @ A2 )
% 5.25/5.46 => ( member_real @ C @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subsetD
% 5.25/5.46 thf(fact_1691_subsetD,axiom,
% 5.25/5.46 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.25/5.46 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( member_nat @ C @ A2 )
% 5.25/5.46 => ( member_nat @ C @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subsetD
% 5.25/5.46 thf(fact_1692_subsetD,axiom,
% 5.25/5.46 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.25/5.46 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.25/5.46 => ( ( member_complex @ C @ A2 )
% 5.25/5.46 => ( member_complex @ C @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subsetD
% 5.25/5.46 thf(fact_1693_subsetD,axiom,
% 5.25/5.46 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat,C: product_prod_nat_nat] :
% 5.25/5.46 ( ( ord_le3146513528884898305at_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( member8440522571783428010at_nat @ C @ A2 )
% 5.25/5.46 => ( member8440522571783428010at_nat @ C @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subsetD
% 5.25/5.46 thf(fact_1694_subsetD,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int,C: int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ( member_int @ C @ A2 )
% 5.25/5.46 => ( member_int @ C @ B3 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subsetD
% 5.25/5.46 thf(fact_1695_equalityE,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int] :
% 5.25/5.46 ( ( A2 = B3 )
% 5.25/5.46 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % equalityE
% 5.25/5.46 thf(fact_1696_subset__eq,axiom,
% 5.25/5.46 ( ord_less_eq_set_real
% 5.25/5.46 = ( ^ [A6: set_real,B6: set_real] :
% 5.25/5.46 ! [X: real] :
% 5.25/5.46 ( ( member_real @ X @ A6 )
% 5.25/5.46 => ( member_real @ X @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_eq
% 5.25/5.46 thf(fact_1697_subset__eq,axiom,
% 5.25/5.46 ( ord_less_eq_set_nat
% 5.25/5.46 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.25/5.46 ! [X: nat] :
% 5.25/5.46 ( ( member_nat @ X @ A6 )
% 5.25/5.46 => ( member_nat @ X @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_eq
% 5.25/5.46 thf(fact_1698_subset__eq,axiom,
% 5.25/5.46 ( ord_le211207098394363844omplex
% 5.25/5.46 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.25/5.46 ! [X: complex] :
% 5.25/5.46 ( ( member_complex @ X @ A6 )
% 5.25/5.46 => ( member_complex @ X @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_eq
% 5.25/5.46 thf(fact_1699_subset__eq,axiom,
% 5.25/5.46 ( ord_le3146513528884898305at_nat
% 5.25/5.46 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.25/5.46 ! [X: product_prod_nat_nat] :
% 5.25/5.46 ( ( member8440522571783428010at_nat @ X @ A6 )
% 5.25/5.46 => ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_eq
% 5.25/5.46 thf(fact_1700_subset__eq,axiom,
% 5.25/5.46 ( ord_less_eq_set_int
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ! [X: int] :
% 5.25/5.46 ( ( member_int @ X @ A6 )
% 5.25/5.46 => ( member_int @ X @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_eq
% 5.25/5.46 thf(fact_1701_equalityD1,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int] :
% 5.25/5.46 ( ( A2 = B3 )
% 5.25/5.46 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.46
% 5.25/5.46 % equalityD1
% 5.25/5.46 thf(fact_1702_equalityD2,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int] :
% 5.25/5.46 ( ( A2 = B3 )
% 5.25/5.46 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.25/5.46
% 5.25/5.46 % equalityD2
% 5.25/5.46 thf(fact_1703_subset__iff,axiom,
% 5.25/5.46 ( ord_less_eq_set_real
% 5.25/5.46 = ( ^ [A6: set_real,B6: set_real] :
% 5.25/5.46 ! [T: real] :
% 5.25/5.46 ( ( member_real @ T @ A6 )
% 5.25/5.46 => ( member_real @ T @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff
% 5.25/5.46 thf(fact_1704_subset__iff,axiom,
% 5.25/5.46 ( ord_less_eq_set_nat
% 5.25/5.46 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.25/5.46 ! [T: nat] :
% 5.25/5.46 ( ( member_nat @ T @ A6 )
% 5.25/5.46 => ( member_nat @ T @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff
% 5.25/5.46 thf(fact_1705_subset__iff,axiom,
% 5.25/5.46 ( ord_le211207098394363844omplex
% 5.25/5.46 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.25/5.46 ! [T: complex] :
% 5.25/5.46 ( ( member_complex @ T @ A6 )
% 5.25/5.46 => ( member_complex @ T @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff
% 5.25/5.46 thf(fact_1706_subset__iff,axiom,
% 5.25/5.46 ( ord_le3146513528884898305at_nat
% 5.25/5.46 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.25/5.46 ! [T: product_prod_nat_nat] :
% 5.25/5.46 ( ( member8440522571783428010at_nat @ T @ A6 )
% 5.25/5.46 => ( member8440522571783428010at_nat @ T @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff
% 5.25/5.46 thf(fact_1707_subset__iff,axiom,
% 5.25/5.46 ( ord_less_eq_set_int
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ! [T: int] :
% 5.25/5.46 ( ( member_int @ T @ A6 )
% 5.25/5.46 => ( member_int @ T @ B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff
% 5.25/5.46 thf(fact_1708_subset__refl,axiom,
% 5.25/5.46 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.25/5.46
% 5.25/5.46 % subset_refl
% 5.25/5.46 thf(fact_1709_Collect__mono,axiom,
% 5.25/5.46 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.46 ( ! [X5: complex] :
% 5.25/5.46 ( ( P @ X5 )
% 5.25/5.46 => ( Q @ X5 ) )
% 5.25/5.46 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono
% 5.25/5.46 thf(fact_1710_Collect__mono,axiom,
% 5.25/5.46 ! [P: real > $o,Q: real > $o] :
% 5.25/5.46 ( ! [X5: real] :
% 5.25/5.46 ( ( P @ X5 )
% 5.25/5.46 => ( Q @ X5 ) )
% 5.25/5.46 => ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono
% 5.25/5.46 thf(fact_1711_Collect__mono,axiom,
% 5.25/5.46 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.46 ( ! [X5: list_nat] :
% 5.25/5.46 ( ( P @ X5 )
% 5.25/5.46 => ( Q @ X5 ) )
% 5.25/5.46 => ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono
% 5.25/5.46 thf(fact_1712_Collect__mono,axiom,
% 5.25/5.46 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.46 ( ! [X5: nat] :
% 5.25/5.46 ( ( P @ X5 )
% 5.25/5.46 => ( Q @ X5 ) )
% 5.25/5.46 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono
% 5.25/5.46 thf(fact_1713_Collect__mono,axiom,
% 5.25/5.46 ! [P: int > $o,Q: int > $o] :
% 5.25/5.46 ( ! [X5: int] :
% 5.25/5.46 ( ( P @ X5 )
% 5.25/5.46 => ( Q @ X5 ) )
% 5.25/5.46 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono
% 5.25/5.46 thf(fact_1714_subset__trans,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.25/5.46 => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_trans
% 5.25/5.46 thf(fact_1715_set__eq__subset,axiom,
% 5.25/5.46 ( ( ^ [Y6: set_int,Z4: set_int] : ( Y6 = Z4 ) )
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.25/5.46 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % set_eq_subset
% 5.25/5.46 thf(fact_1716_Collect__mono__iff,axiom,
% 5.25/5.46 ! [P: complex > $o,Q: complex > $o] :
% 5.25/5.46 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.25/5.46 = ( ! [X: complex] :
% 5.25/5.46 ( ( P @ X )
% 5.25/5.46 => ( Q @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono_iff
% 5.25/5.46 thf(fact_1717_Collect__mono__iff,axiom,
% 5.25/5.46 ! [P: real > $o,Q: real > $o] :
% 5.25/5.46 ( ( ord_less_eq_set_real @ ( collect_real @ P ) @ ( collect_real @ Q ) )
% 5.25/5.46 = ( ! [X: real] :
% 5.25/5.46 ( ( P @ X )
% 5.25/5.46 => ( Q @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono_iff
% 5.25/5.46 thf(fact_1718_Collect__mono__iff,axiom,
% 5.25/5.46 ! [P: list_nat > $o,Q: list_nat > $o] :
% 5.25/5.46 ( ( ord_le6045566169113846134st_nat @ ( collect_list_nat @ P ) @ ( collect_list_nat @ Q ) )
% 5.25/5.46 = ( ! [X: list_nat] :
% 5.25/5.46 ( ( P @ X )
% 5.25/5.46 => ( Q @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono_iff
% 5.25/5.46 thf(fact_1719_Collect__mono__iff,axiom,
% 5.25/5.46 ! [P: nat > $o,Q: nat > $o] :
% 5.25/5.46 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.25/5.46 = ( ! [X: nat] :
% 5.25/5.46 ( ( P @ X )
% 5.25/5.46 => ( Q @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono_iff
% 5.25/5.46 thf(fact_1720_Collect__mono__iff,axiom,
% 5.25/5.46 ! [P: int > $o,Q: int > $o] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.25/5.46 = ( ! [X: int] :
% 5.25/5.46 ( ( P @ X )
% 5.25/5.46 => ( Q @ X ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % Collect_mono_iff
% 5.25/5.46 thf(fact_1721_subset__iff__psubset__eq,axiom,
% 5.25/5.46 ( ord_less_eq_set_int
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ( ( ord_less_set_int @ A6 @ B6 )
% 5.25/5.46 | ( A6 = B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_iff_psubset_eq
% 5.25/5.46 thf(fact_1722_subset__psubset__trans,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ( ord_less_set_int @ B3 @ C4 )
% 5.25/5.46 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_psubset_trans
% 5.25/5.46 thf(fact_1723_subset__not__subset__eq,axiom,
% 5.25/5.46 ( ord_less_set_int
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.25/5.46 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % subset_not_subset_eq
% 5.25/5.46 thf(fact_1724_psubset__subset__trans,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.25/5.46 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.25/5.46 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % psubset_subset_trans
% 5.25/5.46 thf(fact_1725_psubset__imp__subset,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int] :
% 5.25/5.46 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.25/5.46
% 5.25/5.46 % psubset_imp_subset
% 5.25/5.46 thf(fact_1726_psubset__eq,axiom,
% 5.25/5.46 ( ord_less_set_int
% 5.25/5.46 = ( ^ [A6: set_int,B6: set_int] :
% 5.25/5.46 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.25/5.46 & ( A6 != B6 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % psubset_eq
% 5.25/5.46 thf(fact_1727_psubsetE,axiom,
% 5.25/5.46 ! [A2: set_int,B3: set_int] :
% 5.25/5.46 ( ( ord_less_set_int @ A2 @ B3 )
% 5.25/5.46 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.25/5.46 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % psubsetE
% 5.25/5.46 thf(fact_1728_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N2: num,Q3: num] :
% 5.25/5.46 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.25/5.46 = zero_zero_nat )
% 5.25/5.46 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 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_1729_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N2: num,Q3: num] :
% 5.25/5.46 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.25/5.46 = zero_zero_int )
% 5.25/5.46 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 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_1730_cong__exp__iff__simps_I2_J,axiom,
% 5.25/5.46 ! [N2: num,Q3: num] :
% 5.25/5.46 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.25/5.46 = zero_z3403309356797280102nteger )
% 5.25/5.46 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 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_1731_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N2: num] :
% 5.25/5.46 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( 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_1732_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N2: num] :
% 5.25/5.46 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( 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_1733_cong__exp__iff__simps_I1_J,axiom,
% 5.25/5.46 ! [N2: num] :
% 5.25/5.46 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( 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_1734_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_1735_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_1736_ex__least__nat__less,axiom,
% 5.25/5.46 ! [P: nat > $o,N2: nat] :
% 5.25/5.46 ( ( P @ N2 )
% 5.25/5.46 => ( ~ ( P @ zero_zero_nat )
% 5.25/5.46 => ? [K2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ K2 @ N2 )
% 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_1737_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: real,Xs: list_real] :
% 5.25/5.46 ( ( member_real @ X4 @ ( 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_1738_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: complex,Xs: list_complex] :
% 5.25/5.46 ( ( member_complex @ X4 @ ( 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_1739_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: product_prod_nat_nat,Xs: list_P6011104703257516679at_nat] :
% 5.25/5.46 ( ( member8440522571783428010at_nat @ X4 @ ( 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_1740_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.25/5.46 ( ( member_VEBT_VEBT @ X4 @ ( 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_1741_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: $o,Xs: list_o] :
% 5.25/5.46 ( ( member_o @ X4 @ ( 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_1742_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: nat,Xs: list_nat] :
% 5.25/5.46 ( ( member_nat @ X4 @ ( 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_1743_length__pos__if__in__set,axiom,
% 5.25/5.46 ! [X4: int,Xs: list_int] :
% 5.25/5.46 ( ( member_int @ X4 @ ( 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_1744_nat__induct__non__zero,axiom,
% 5.25/5.46 ! [N2: nat,P: nat > $o] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 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 @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_induct_non_zero
% 5.25/5.46 thf(fact_1745_power__gt__expt,axiom,
% 5.25/5.46 ! [N2: nat,K: nat] :
% 5.25/5.46 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.25/5.46 => ( ord_less_nat @ K @ ( power_power_nat @ N2 @ K ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_gt_expt
% 5.25/5.46 thf(fact_1746_div__greater__zero__iff,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.25/5.46 = ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.46 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_greater_zero_iff
% 5.25/5.46 thf(fact_1747_div__le__mono2,axiom,
% 5.25/5.46 ! [M: nat,N2: nat,K: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N2 ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_le_mono2
% 5.25/5.46 thf(fact_1748_nat__one__le__power,axiom,
% 5.25/5.46 ! [I2: nat,N2: 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 @ N2 ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % nat_one_le_power
% 5.25/5.46 thf(fact_1749_mod__le__divisor,axiom,
% 5.25/5.46 ! [N2: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N2 ) @ N2 ) ) ).
% 5.25/5.46
% 5.25/5.46 % mod_le_divisor
% 5.25/5.46 thf(fact_1750_div__eq__dividend__iff,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ( ( divide_divide_nat @ M @ N2 )
% 5.25/5.46 = M )
% 5.25/5.46 = ( N2 = one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_eq_dividend_iff
% 5.25/5.46 thf(fact_1751_div__less__dividend,axiom,
% 5.25/5.46 ! [N2: nat,M: nat] :
% 5.25/5.46 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.46 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ M ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % div_less_dividend
% 5.25/5.46 thf(fact_1752_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.25/5.46 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.25/5.46 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.25/5.46
% 5.25/5.46 % VEBT_internal.membermima.simps(2)
% 5.25/5.46 thf(fact_1753_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_1754_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_1755_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_1756_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_1757_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: real,N2: 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 @ N2 ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_1758_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: rat,N2: 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 @ N2 ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_1759_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: nat,N2: 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 @ N2 ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_1760_power__Suc__le__self,axiom,
% 5.25/5.46 ! [A: int,N2: 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 @ N2 ) ) @ A ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_le_self
% 5.25/5.46 thf(fact_1761_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: real,N2: 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 @ N2 ) ) @ one_one_real ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_1762_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: rat,N2: 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 @ N2 ) ) @ one_one_rat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_1763_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: nat,N2: 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 @ N2 ) ) @ one_one_nat ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_1764_power__Suc__less__one,axiom,
% 5.25/5.46 ! [A: int,N2: 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 @ N2 ) ) @ one_one_int ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_Suc_less_one
% 5.25/5.46 thf(fact_1765_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: real] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_1766_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: rat] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_1767_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_1768_power__strict__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: int] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_strict_decreasing
% 5.25/5.46 thf(fact_1769_power__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: real] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_1770_power__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: rat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_1771_power__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_1772_power__decreasing,axiom,
% 5.25/5.46 ! [N2: nat,N4: nat,A: int] :
% 5.25/5.46 ( ( ord_less_eq_nat @ N2 @ N4 )
% 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 @ N4 ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power_decreasing
% 5.25/5.46 thf(fact_1773_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_1774_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_1775_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_1776_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_1777_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_1778_self__le__power,axiom,
% 5.25/5.46 ! [A: real,N2: nat] :
% 5.25/5.46 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_1779_self__le__power,axiom,
% 5.25/5.46 ! [A: rat,N2: nat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_1780_self__le__power,axiom,
% 5.25/5.46 ! [A: nat,N2: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_1781_self__le__power,axiom,
% 5.25/5.46 ! [A: int,N2: nat] :
% 5.25/5.46 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % self_le_power
% 5.25/5.46 thf(fact_1782_one__less__power,axiom,
% 5.25/5.46 ! [A: real,N2: nat] :
% 5.25/5.46 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_1783_one__less__power,axiom,
% 5.25/5.46 ! [A: rat,N2: nat] :
% 5.25/5.46 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_1784_one__less__power,axiom,
% 5.25/5.46 ! [A: nat,N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_1785_one__less__power,axiom,
% 5.25/5.46 ! [A: int,N2: nat] :
% 5.25/5.46 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % one_less_power
% 5.25/5.46 thf(fact_1786_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_1787_verit__le__mono__div,axiom,
% 5.25/5.46 ! [A2: nat,B3: nat,N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ A2 @ B3 )
% 5.25/5.46 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.46 => ( ord_less_eq_nat
% 5.25/5.46 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N2 )
% 5.25/5.46 @ ( if_nat
% 5.25/5.46 @ ( ( modulo_modulo_nat @ B3 @ N2 )
% 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 @ N2 ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % verit_le_mono_div
% 5.25/5.46 thf(fact_1788_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_1789_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_1790_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_1791_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_1792_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( 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 @ X4 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_1793_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( 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 @ X4 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_1794_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ord_less_eq_nat @ ( power_power_nat @ X4 @ ( 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 @ X4 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_1795_power2__le__imp__le,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( 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 @ X4 @ Y ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_le_imp_le
% 5.25/5.46 thf(fact_1796_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ( power_power_real @ X4 @ ( 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 @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.46 => ( X4 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_1797_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X4: rat,Y: rat] :
% 5.25/5.46 ( ( ( power_power_rat @ X4 @ ( 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 @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.46 => ( X4 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_1798_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X4: nat,Y: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ X4 @ ( 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 @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.46 => ( X4 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_1799_power2__eq__imp__eq,axiom,
% 5.25/5.46 ! [X4: int,Y: int] :
% 5.25/5.46 ( ( ( power_power_int @ X4 @ ( 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 @ X4 )
% 5.25/5.46 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.46 => ( X4 = Y ) ) ) ) ).
% 5.25/5.46
% 5.25/5.46 % power2_eq_imp_eq
% 5.25/5.46 thf(fact_1800_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_1801_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_1802_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_1803_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_1804_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_1805_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_1806_exp__add__not__zero__imp__right,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.46 != zero_zero_nat )
% 5.25/5.46 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 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_1807_exp__add__not__zero__imp__right,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.46 != zero_zero_int )
% 5.25/5.46 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 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_1808_exp__add__not__zero__imp__left,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 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_1809_exp__add__not__zero__imp__left,axiom,
% 5.25/5.46 ! [M: nat,N2: nat] :
% 5.25/5.46 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) )
% 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_1810_less__2__cases__iff,axiom,
% 5.25/5.46 ! [N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 = ( ( N2 = zero_zero_nat )
% 5.25/5.46 | ( N2
% 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_1811_less__2__cases,axiom,
% 5.25/5.46 ! [N2: nat] :
% 5.25/5.46 ( ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.46 => ( ( N2 = zero_zero_nat )
% 5.25/5.46 | ( N2
% 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_1812_power2__less__imp__less,axiom,
% 5.25/5.46 ! [X4: real,Y: real] :
% 5.25/5.46 ( ( ord_less_real @ ( power_power_real @ X4 @ ( 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 )
% 5.25/5.47 => ( ord_less_real @ X4 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power2_less_imp_less
% 5.25/5.47 thf(fact_1813_power2__less__imp__less,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.47 => ( ord_less_rat @ X4 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power2_less_imp_less
% 5.25/5.47 thf(fact_1814_power2__less__imp__less,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ord_less_nat @ ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.47 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.25/5.47 => ( ord_less_nat @ X4 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power2_less_imp_less
% 5.25/5.47 thf(fact_1815_power2__less__imp__less,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.47 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.47 => ( ord_less_int @ X4 @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power2_less_imp_less
% 5.25/5.47 thf(fact_1816_sum__power2__le__zero__iff,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.25/5.47 = ( ( X4 = zero_zero_real )
% 5.25/5.47 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_le_zero_iff
% 5.25/5.47 thf(fact_1817_sum__power2__le__zero__iff,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.25/5.47 = ( ( X4 = zero_zero_rat )
% 5.25/5.47 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_le_zero_iff
% 5.25/5.47 thf(fact_1818_sum__power2__le__zero__iff,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.25/5.47 = ( ( X4 = zero_zero_int )
% 5.25/5.47 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_le_zero_iff
% 5.25/5.47 thf(fact_1819_sum__power2__ge__zero,axiom,
% 5.25/5.47 ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_ge_zero
% 5.25/5.47 thf(fact_1820_sum__power2__ge__zero,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_ge_zero
% 5.25/5.47 thf(fact_1821_sum__power2__ge__zero,axiom,
% 5.25/5.47 ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_ge_zero
% 5.25/5.47 thf(fact_1822_sum__power2__gt__zero__iff,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.47 = ( ( X4 != zero_zero_real )
% 5.25/5.47 | ( Y != zero_zero_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_gt_zero_iff
% 5.25/5.47 thf(fact_1823_sum__power2__gt__zero__iff,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.47 = ( ( X4 != zero_zero_rat )
% 5.25/5.47 | ( Y != zero_zero_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_gt_zero_iff
% 5.25/5.47 thf(fact_1824_sum__power2__gt__zero__iff,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.47 = ( ( X4 != zero_zero_int )
% 5.25/5.47 | ( Y != zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_power2_gt_zero_iff
% 5.25/5.47 thf(fact_1825_not__sum__power2__lt__zero,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.25/5.47
% 5.25/5.47 % not_sum_power2_lt_zero
% 5.25/5.47 thf(fact_1826_not__sum__power2__lt__zero,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.25/5.47
% 5.25/5.47 % not_sum_power2_lt_zero
% 5.25/5.47 thf(fact_1827_not__sum__power2__lt__zero,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % not_sum_power2_lt_zero
% 5.25/5.47 thf(fact_1828_bits__stable__imp__add__self,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = A )
% 5.25/5.47 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.47 = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % bits_stable_imp_add_self
% 5.25/5.47 thf(fact_1829_bits__stable__imp__add__self,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.47 = A )
% 5.25/5.47 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.47 = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % bits_stable_imp_add_self
% 5.25/5.47 thf(fact_1830_bits__stable__imp__add__self,axiom,
% 5.25/5.47 ! [A: code_integer] :
% 5.25/5.47 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.47 = A )
% 5.25/5.47 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.25/5.47 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.47
% 5.25/5.47 % bits_stable_imp_add_self
% 5.25/5.47 thf(fact_1831_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_real @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1832_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_set_int @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1833_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1834_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_num @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1835_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1836_order__le__imp__less__or__eq,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_int @ X4 @ Y )
% 5.25/5.47 | ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_imp_less_or_eq
% 5.25/5.47 thf(fact_1837_linorder__le__less__linear,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X4 @ Y )
% 5.25/5.47 | ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_le_less_linear
% 5.25/5.47 thf(fact_1838_linorder__le__less__linear,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.47 | ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_le_less_linear
% 5.25/5.47 thf(fact_1839_linorder__le__less__linear,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.47 | ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_le_less_linear
% 5.25/5.47 thf(fact_1840_linorder__le__less__linear,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.47 | ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_le_less_linear
% 5.25/5.47 thf(fact_1841_linorder__le__less__linear,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.47 | ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_le_less_linear
% 5.25/5.47 thf(fact_1842_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: real,B: real,F: real > real,C: real] :
% 5.25/5.47 ( ( ord_less_real @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: real,Y3: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1843_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.47 ( ( ord_less_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1844_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > real,C: real] :
% 5.25/5.47 ( ( ord_less_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1845_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.25/5.47 ( ( ord_less_nat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1846_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: int,B: int,F: int > real,C: real] :
% 5.25/5.47 ( ( ord_less_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: int,Y3: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1847_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_real @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: real,Y3: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1848_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1849_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1850_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_nat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1851_order__less__le__subst2,axiom,
% 5.25/5.47 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: int,Y3: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst2
% 5.25/5.47 thf(fact_1852_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1853_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1854_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1855_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1856_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1857_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1858_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1859_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: num,F: num > num,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1860_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1861_order__less__le__subst1,axiom,
% 5.25/5.47 ! [A: int,F: num > int,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_subst1
% 5.25/5.47 thf(fact_1862_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1863_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1864_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1865_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1866_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1867_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1868_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1869_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_num @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1870_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_nat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1871_order__le__less__subst2,axiom,
% 5.25/5.47 ! [A: num,B: num,F: num > int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_eq_int @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst2
% 5.25/5.47 thf(fact_1872_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: real,F: real > real,B: real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_real @ B @ C )
% 5.25/5.47 => ( ! [X5: real,Y3: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1873_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1874_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: real,F: num > real,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1875_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_nat @ B @ C )
% 5.25/5.47 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1876_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: real,F: int > real,B: int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_int @ B @ C )
% 5.25/5.47 => ( ! [X5: int,Y3: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_real @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1877_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_real @ B @ C )
% 5.25/5.47 => ( ! [X5: real,Y3: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1878_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_rat @ B @ C )
% 5.25/5.47 => ( ! [X5: rat,Y3: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1879_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_num @ B @ C )
% 5.25/5.47 => ( ! [X5: num,Y3: num] :
% 5.25/5.47 ( ( ord_less_num @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1880_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_nat @ B @ C )
% 5.25/5.47 => ( ! [X5: nat,Y3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1881_order__le__less__subst1,axiom,
% 5.25/5.47 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.25/5.47 => ( ( ord_less_int @ B @ C )
% 5.25/5.47 => ( ! [X5: int,Y3: int] :
% 5.25/5.47 ( ( ord_less_int @ X5 @ Y3 )
% 5.25/5.47 => ( ord_less_rat @ ( F @ X5 ) @ ( F @ Y3 ) ) )
% 5.25/5.47 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_subst1
% 5.25/5.47 thf(fact_1882_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: real,Y: real,Z: real] :
% 5.25/5.47 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_real @ Y @ Z )
% 5.25/5.47 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1883_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int,Z: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.25/5.47 => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1884_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.25/5.47 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1885_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: num,Y: num,Z: num] :
% 5.25/5.47 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_num @ Y @ Z )
% 5.25/5.47 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1886_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat,Z: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.25/5.47 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1887_order__less__le__trans,axiom,
% 5.25/5.47 ! [X4: int,Y: int,Z: int] :
% 5.25/5.47 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_int @ Y @ Z )
% 5.25/5.47 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le_trans
% 5.25/5.47 thf(fact_1888_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: real,Y: real,Z: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_real @ Y @ Z )
% 5.25/5.47 => ( ord_less_real @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1889_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int,Z: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_set_int @ Y @ Z )
% 5.25/5.47 => ( ord_less_set_int @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1890_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_rat @ Y @ Z )
% 5.25/5.47 => ( ord_less_rat @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1891_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: num,Y: num,Z: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_num @ Y @ Z )
% 5.25/5.47 => ( ord_less_num @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1892_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat,Z: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_nat @ Y @ Z )
% 5.25/5.47 => ( ord_less_nat @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1893_order__le__less__trans,axiom,
% 5.25/5.47 ! [X4: int,Y: int,Z: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_int @ Y @ Z )
% 5.25/5.47 => ( ord_less_int @ X4 @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less_trans
% 5.25/5.47 thf(fact_1894_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_real @ A @ B )
% 5.25/5.47 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1895_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.47 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1896_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1897_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ord_less_num @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1898_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1899_order__neq__le__trans,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( A != B )
% 5.25/5.47 => ( ( ord_less_eq_int @ A @ B )
% 5.25/5.47 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_neq_le_trans
% 5.25/5.47 thf(fact_1900_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1901_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1902_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1903_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_num @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1904_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1905_order__le__neq__trans,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.47 => ( ( A != B )
% 5.25/5.47 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_neq_trans
% 5.25/5.47 thf(fact_1906_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1907_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1908_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1909_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ord_less_num @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_num @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1910_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1911_order__less__imp__le,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_int @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_int @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_imp_le
% 5.25/5.47 thf(fact_1912_linorder__not__less,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_eq_real @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_less
% 5.25/5.47 thf(fact_1913_linorder__not__less,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_less
% 5.25/5.47 thf(fact_1914_linorder__not__less,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_eq_num @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_less
% 5.25/5.47 thf(fact_1915_linorder__not__less,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_less
% 5.25/5.47 thf(fact_1916_linorder__not__less,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_eq_int @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_less
% 5.25/5.47 thf(fact_1917_linorder__not__le,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_real @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_real @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_le
% 5.25/5.47 thf(fact_1918_linorder__not__le,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_rat @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_rat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_le
% 5.25/5.47 thf(fact_1919_linorder__not__le,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_num @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_num @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_le
% 5.25/5.47 thf(fact_1920_linorder__not__le,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_nat @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_nat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_le
% 5.25/5.47 thf(fact_1921_linorder__not__le,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_int @ X4 @ Y ) )
% 5.25/5.47 = ( ord_less_int @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % linorder_not_le
% 5.25/5.47 thf(fact_1922_order__less__le,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [X: real,Y5: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1923_order__less__le,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [X: set_int,Y5: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1924_order__less__le,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [X: rat,Y5: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1925_order__less__le,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [X: num,Y5: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1926_order__less__le,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [X: nat,Y5: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1927_order__less__le,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [X: int,Y5: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X @ Y5 )
% 5.25/5.47 & ( X != Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_less_le
% 5.25/5.47 thf(fact_1928_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_real
% 5.25/5.47 = ( ^ [X: real,Y5: real] :
% 5.25/5.47 ( ( ord_less_real @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1929_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_set_int
% 5.25/5.47 = ( ^ [X: set_int,Y5: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1930_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_rat
% 5.25/5.47 = ( ^ [X: rat,Y5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1931_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_num
% 5.25/5.47 = ( ^ [X: num,Y5: num] :
% 5.25/5.47 ( ( ord_less_num @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1932_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_nat
% 5.25/5.47 = ( ^ [X: nat,Y5: nat] :
% 5.25/5.47 ( ( ord_less_nat @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1933_order__le__less,axiom,
% 5.25/5.47 ( ord_less_eq_int
% 5.25/5.47 = ( ^ [X: int,Y5: int] :
% 5.25/5.47 ( ( ord_less_int @ X @ Y5 )
% 5.25/5.47 | ( X = Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order_le_less
% 5.25/5.47 thf(fact_1934_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: real,A: real] :
% 5.25/5.47 ( ( ord_less_real @ B @ A )
% 5.25/5.47 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1935_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: set_int,A: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ B @ A )
% 5.25/5.47 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1936_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: rat,A: rat] :
% 5.25/5.47 ( ( ord_less_rat @ B @ A )
% 5.25/5.47 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1937_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: num,A: num] :
% 5.25/5.47 ( ( ord_less_num @ B @ A )
% 5.25/5.47 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1938_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: nat,A: nat] :
% 5.25/5.47 ( ( ord_less_nat @ B @ A )
% 5.25/5.47 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1939_dual__order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [B: int,A: int] :
% 5.25/5.47 ( ( ord_less_int @ B @ A )
% 5.25/5.47 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_implies_order
% 5.25/5.47 thf(fact_1940_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( ord_less_real @ A @ B )
% 5.25/5.47 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1941_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ A @ B )
% 5.25/5.47 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1942_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A @ B )
% 5.25/5.47 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1943_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( ord_less_num @ A @ B )
% 5.25/5.47 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1944_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ord_less_nat @ A @ B )
% 5.25/5.47 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1945_order_Ostrict__implies__order,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_int @ A @ B )
% 5.25/5.47 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_implies_order
% 5.25/5.47 thf(fact_1946_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [B2: real,A3: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1947_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1948_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1949_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [B2: num,A3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1950_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1951_dual__order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [B2: int,A3: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.47 & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_not
% 5.25/5.47 thf(fact_1952_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: real,A: real,C: real] :
% 5.25/5.47 ( ( ord_less_real @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_real @ C @ B )
% 5.25/5.47 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1953_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_set_int @ C @ B )
% 5.25/5.47 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1954_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: rat,A: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_rat @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_rat @ C @ B )
% 5.25/5.47 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1955_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: num,A: num,C: num] :
% 5.25/5.47 ( ( ord_less_num @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_num @ C @ B )
% 5.25/5.47 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1956_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: nat,A: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_nat @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_nat @ C @ B )
% 5.25/5.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1957_dual__order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [B: int,A: int,C: int] :
% 5.25/5.47 ( ( ord_less_int @ B @ A )
% 5.25/5.47 => ( ( ord_less_eq_int @ C @ B )
% 5.25/5.47 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans2
% 5.25/5.47 thf(fact_1958_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: real,A: real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.47 => ( ( ord_less_real @ C @ B )
% 5.25/5.47 => ( ord_less_real @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1959_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: set_int,A: set_int,C: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ B @ A )
% 5.25/5.47 => ( ( ord_less_set_int @ C @ B )
% 5.25/5.47 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1960_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: rat,A: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.47 => ( ( ord_less_rat @ C @ B )
% 5.25/5.47 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1961_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: num,A: num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ B @ A )
% 5.25/5.47 => ( ( ord_less_num @ C @ B )
% 5.25/5.47 => ( ord_less_num @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1962_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: nat,A: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ B @ A )
% 5.25/5.47 => ( ( ord_less_nat @ C @ B )
% 5.25/5.47 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1963_dual__order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [B: int,A: int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.47 => ( ( ord_less_int @ C @ B )
% 5.25/5.47 => ( ord_less_int @ C @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_trans1
% 5.25/5.47 thf(fact_1964_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [B2: real,A3: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1965_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1966_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1967_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [B2: num,A3: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1968_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1969_dual__order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [B2: int,A3: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.strict_iff_order
% 5.25/5.47 thf(fact_1970_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_real
% 5.25/5.47 = ( ^ [B2: real,A3: real] :
% 5.25/5.47 ( ( ord_less_real @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1971_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_set_int
% 5.25/5.47 = ( ^ [B2: set_int,A3: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1972_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_rat
% 5.25/5.47 = ( ^ [B2: rat,A3: rat] :
% 5.25/5.47 ( ( ord_less_rat @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1973_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_num
% 5.25/5.47 = ( ^ [B2: num,A3: num] :
% 5.25/5.47 ( ( ord_less_num @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1974_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_nat
% 5.25/5.47 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1975_dual__order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_int
% 5.25/5.47 = ( ^ [B2: int,A3: int] :
% 5.25/5.47 ( ( ord_less_int @ B2 @ A3 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dual_order.order_iff_strict
% 5.25/5.47 thf(fact_1976_dense__le__bounded,axiom,
% 5.25/5.47 ! [X4: real,Y: real,Z: real] :
% 5.25/5.47 ( ( ord_less_real @ X4 @ Y )
% 5.25/5.47 => ( ! [W2: real] :
% 5.25/5.47 ( ( ord_less_real @ X4 @ W2 )
% 5.25/5.47 => ( ( ord_less_real @ W2 @ Y )
% 5.25/5.47 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_le_bounded
% 5.25/5.47 thf(fact_1977_dense__le__bounded,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat,Z: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 => ( ! [W2: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X4 @ W2 )
% 5.25/5.47 => ( ( ord_less_rat @ W2 @ Y )
% 5.25/5.47 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_le_bounded
% 5.25/5.47 thf(fact_1978_dense__ge__bounded,axiom,
% 5.25/5.47 ! [Z: real,X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_real @ Z @ X4 )
% 5.25/5.47 => ( ! [W2: real] :
% 5.25/5.47 ( ( ord_less_real @ Z @ W2 )
% 5.25/5.47 => ( ( ord_less_real @ W2 @ X4 )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_ge_bounded
% 5.25/5.47 thf(fact_1979_dense__ge__bounded,axiom,
% 5.25/5.47 ! [Z: rat,X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z @ X4 )
% 5.25/5.47 => ( ! [W2: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z @ W2 )
% 5.25/5.47 => ( ( ord_less_rat @ W2 @ X4 )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_ge_bounded
% 5.25/5.47 thf(fact_1980_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [A3: real,B2: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1981_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1982_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1983_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [A3: num,B2: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1984_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1985_order_Ostrict__iff__not,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [A3: int,B2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.47 & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_not
% 5.25/5.47 thf(fact_1986_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: real,B: real,C: real] :
% 5.25/5.47 ( ( ord_less_real @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_real @ B @ C )
% 5.25/5.47 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1987_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_set_int @ B @ C )
% 5.25/5.47 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1988_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: rat,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_rat @ B @ C )
% 5.25/5.47 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1989_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: num,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_num @ B @ C )
% 5.25/5.47 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1990_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: nat,B: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_nat @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_nat @ B @ C )
% 5.25/5.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1991_order_Ostrict__trans2,axiom,
% 5.25/5.47 ! [A: int,B: int,C: int] :
% 5.25/5.47 ( ( ord_less_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_eq_int @ B @ C )
% 5.25/5.47 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans2
% 5.25/5.47 thf(fact_1992_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: real,B: real,C: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.47 => ( ( ord_less_real @ B @ C )
% 5.25/5.47 => ( ord_less_real @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1993_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int,C: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_set_int @ B @ C )
% 5.25/5.47 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1994_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: rat,B: rat,C: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 => ( ( ord_less_rat @ B @ C )
% 5.25/5.47 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1995_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: num,B: num,C: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A @ B )
% 5.25/5.47 => ( ( ord_less_num @ B @ C )
% 5.25/5.47 => ( ord_less_num @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1996_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: nat,B: nat,C: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.47 => ( ( ord_less_nat @ B @ C )
% 5.25/5.47 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1997_order_Ostrict__trans1,axiom,
% 5.25/5.47 ! [A: int,B: int,C: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.47 => ( ( ord_less_int @ B @ C )
% 5.25/5.47 => ( ord_less_int @ A @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_trans1
% 5.25/5.47 thf(fact_1998_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [A3: real,B2: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_1999_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_2000_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_2001_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [A3: num,B2: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_2002_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_2003_order_Ostrict__iff__order,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [A3: int,B2: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.25/5.47 & ( A3 != B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.strict_iff_order
% 5.25/5.47 thf(fact_2004_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_real
% 5.25/5.47 = ( ^ [A3: real,B2: real] :
% 5.25/5.47 ( ( ord_less_real @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2005_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_set_int
% 5.25/5.47 = ( ^ [A3: set_int,B2: set_int] :
% 5.25/5.47 ( ( ord_less_set_int @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2006_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_rat
% 5.25/5.47 = ( ^ [A3: rat,B2: rat] :
% 5.25/5.47 ( ( ord_less_rat @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2007_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_num
% 5.25/5.47 = ( ^ [A3: num,B2: num] :
% 5.25/5.47 ( ( ord_less_num @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2008_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_nat
% 5.25/5.47 = ( ^ [A3: nat,B2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2009_order_Oorder__iff__strict,axiom,
% 5.25/5.47 ( ord_less_eq_int
% 5.25/5.47 = ( ^ [A3: int,B2: int] :
% 5.25/5.47 ( ( ord_less_int @ A3 @ B2 )
% 5.25/5.47 | ( A3 = B2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % order.order_iff_strict
% 5.25/5.47 thf(fact_2010_not__le__imp__less,axiom,
% 5.25/5.47 ! [Y: real,X4: real] :
% 5.25/5.47 ( ~ ( ord_less_eq_real @ Y @ X4 )
% 5.25/5.47 => ( ord_less_real @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_le_imp_less
% 5.25/5.47 thf(fact_2011_not__le__imp__less,axiom,
% 5.25/5.47 ! [Y: rat,X4: rat] :
% 5.25/5.47 ( ~ ( ord_less_eq_rat @ Y @ X4 )
% 5.25/5.47 => ( ord_less_rat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_le_imp_less
% 5.25/5.47 thf(fact_2012_not__le__imp__less,axiom,
% 5.25/5.47 ! [Y: num,X4: num] :
% 5.25/5.47 ( ~ ( ord_less_eq_num @ Y @ X4 )
% 5.25/5.47 => ( ord_less_num @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_le_imp_less
% 5.25/5.47 thf(fact_2013_not__le__imp__less,axiom,
% 5.25/5.47 ! [Y: nat,X4: nat] :
% 5.25/5.47 ( ~ ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.47 => ( ord_less_nat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_le_imp_less
% 5.25/5.47 thf(fact_2014_not__le__imp__less,axiom,
% 5.25/5.47 ! [Y: int,X4: int] :
% 5.25/5.47 ( ~ ( ord_less_eq_int @ Y @ X4 )
% 5.25/5.47 => ( ord_less_int @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_le_imp_less
% 5.25/5.47 thf(fact_2015_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_real
% 5.25/5.47 = ( ^ [X: real,Y5: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_real @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2016_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_set_int
% 5.25/5.47 = ( ^ [X: set_int,Y5: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_set_int @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2017_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_rat
% 5.25/5.47 = ( ^ [X: rat,Y5: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_rat @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2018_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_num
% 5.25/5.47 = ( ^ [X: num,Y5: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_num @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2019_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_nat
% 5.25/5.47 = ( ^ [X: nat,Y5: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_nat @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2020_less__le__not__le,axiom,
% 5.25/5.47 ( ord_less_int
% 5.25/5.47 = ( ^ [X: int,Y5: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X @ Y5 )
% 5.25/5.47 & ~ ( ord_less_eq_int @ Y5 @ X ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % less_le_not_le
% 5.25/5.47 thf(fact_2021_dense__le,axiom,
% 5.25/5.47 ! [Y: real,Z: real] :
% 5.25/5.47 ( ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ X5 @ Y )
% 5.25/5.47 => ( ord_less_eq_real @ X5 @ Z ) )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_le
% 5.25/5.47 thf(fact_2022_dense__le,axiom,
% 5.25/5.47 ! [Y: rat,Z: rat] :
% 5.25/5.47 ( ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ X5 @ Y )
% 5.25/5.47 => ( ord_less_eq_rat @ X5 @ Z ) )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_le
% 5.25/5.47 thf(fact_2023_dense__ge,axiom,
% 5.25/5.47 ! [Z: real,Y: real] :
% 5.25/5.47 ( ! [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ Z @ X5 )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ X5 ) )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_ge
% 5.25/5.47 thf(fact_2024_dense__ge,axiom,
% 5.25/5.47 ! [Z: rat,Y: rat] :
% 5.25/5.47 ( ! [X5: rat] :
% 5.25/5.47 ( ( ord_less_rat @ Z @ X5 )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ X5 ) )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % dense_ge
% 5.25/5.47 thf(fact_2025_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_real @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2026_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_set_int @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2027_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_rat @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2028_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_num @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2029_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_nat @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2030_antisym__conv2,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.47 => ( ( ~ ( ord_less_int @ X4 @ Y ) )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv2
% 5.25/5.47 thf(fact_2031_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ~ ( ord_less_real @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2032_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: set_int,Y: set_int] :
% 5.25/5.47 ( ~ ( ord_less_set_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2033_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ~ ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_rat @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2034_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ~ ( ord_less_num @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_num @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2035_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ~ ( ord_less_nat @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_nat @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2036_antisym__conv1,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ~ ( ord_less_int @ X4 @ Y )
% 5.25/5.47 => ( ( ord_less_eq_int @ X4 @ Y )
% 5.25/5.47 = ( X4 = Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % antisym_conv1
% 5.25/5.47 thf(fact_2037_nless__le,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2038_nless__le,axiom,
% 5.25/5.47 ! [A: set_int,B: set_int] :
% 5.25/5.47 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2039_nless__le,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2040_nless__le,axiom,
% 5.25/5.47 ! [A: num,B: num] :
% 5.25/5.47 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2041_nless__le,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2042_nless__le,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.25/5.47 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nless_le
% 5.25/5.47 thf(fact_2043_leI,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ~ ( ord_less_real @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_real @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % leI
% 5.25/5.47 thf(fact_2044_leI,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ~ ( ord_less_rat @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_rat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % leI
% 5.25/5.47 thf(fact_2045_leI,axiom,
% 5.25/5.47 ! [X4: num,Y: num] :
% 5.25/5.47 ( ~ ( ord_less_num @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_num @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % leI
% 5.25/5.47 thf(fact_2046_leI,axiom,
% 5.25/5.47 ! [X4: nat,Y: nat] :
% 5.25/5.47 ( ~ ( ord_less_nat @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_nat @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % leI
% 5.25/5.47 thf(fact_2047_leI,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ~ ( ord_less_int @ X4 @ Y )
% 5.25/5.47 => ( ord_less_eq_int @ Y @ X4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % leI
% 5.25/5.47 thf(fact_2048_leD,axiom,
% 5.25/5.47 ! [Y: real,X4: real] :
% 5.25/5.47 ( ( ord_less_eq_real @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_real @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2049_leD,axiom,
% 5.25/5.47 ! [Y: set_int,X4: set_int] :
% 5.25/5.47 ( ( ord_less_eq_set_int @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_set_int @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2050_leD,axiom,
% 5.25/5.47 ! [Y: rat,X4: rat] :
% 5.25/5.47 ( ( ord_less_eq_rat @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_rat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2051_leD,axiom,
% 5.25/5.47 ! [Y: num,X4: num] :
% 5.25/5.47 ( ( ord_less_eq_num @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_num @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2052_leD,axiom,
% 5.25/5.47 ! [Y: nat,X4: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_nat @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2053_leD,axiom,
% 5.25/5.47 ! [Y: int,X4: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ Y @ X4 )
% 5.25/5.47 => ~ ( ord_less_int @ X4 @ Y ) ) ).
% 5.25/5.47
% 5.25/5.47 % leD
% 5.25/5.47 thf(fact_2054_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.47 ! [B4: real,A4: real] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.25/5.47 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_comp_simplify1(3)
% 5.25/5.47 thf(fact_2055_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.47 ! [B4: rat,A4: rat] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.25/5.47 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_comp_simplify1(3)
% 5.25/5.47 thf(fact_2056_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.47 ! [B4: num,A4: num] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.25/5.47 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_comp_simplify1(3)
% 5.25/5.47 thf(fact_2057_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.47 ! [B4: nat,A4: nat] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.25/5.47 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_comp_simplify1(3)
% 5.25/5.47 thf(fact_2058_verit__comp__simplify1_I3_J,axiom,
% 5.25/5.47 ! [B4: int,A4: int] :
% 5.25/5.47 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.25/5.47 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_comp_simplify1(3)
% 5.25/5.47 thf(fact_2059_Suc__n__div__2__gt__zero,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % Suc_n_div_2_gt_zero
% 5.25/5.47 thf(fact_2060_div__2__gt__zero,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.25/5.47 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_2_gt_zero
% 5.25/5.47 thf(fact_2061_verit__eq__simplify_I10_J,axiom,
% 5.25/5.47 ! [X22: num] :
% 5.25/5.47 ( one
% 5.25/5.47 != ( bit0 @ X22 ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_eq_simplify(10)
% 5.25/5.47 thf(fact_2062_invar__vebt_Ointros_I4_J,axiom,
% 5.25/5.47 ! [TreeList2: list_VEBT_VEBT,N2: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.25/5.47 ( ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X5 @ N2 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.25/5.47 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.47 => ( ( M = N2 )
% 5.25/5.47 => ( ( Deg
% 5.25/5.47 = ( plus_plus_nat @ N2 @ M ) )
% 5.25/5.47 => ( ! [I4: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.47 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X3 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.25/5.47 => ( ( ( Mi = Ma )
% 5.25/5.47 => ! [X5: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.25/5.47 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X5 @ X_12 ) ) )
% 5.25/5.47 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.25/5.47 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.25/5.47 => ( ( ( Mi != Ma )
% 5.25/5.47 => ! [I4: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma @ N2 )
% 5.25/5.47 = I4 )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N2 ) ) )
% 5.25/5.47 & ! [X5: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X5 @ N2 )
% 5.25/5.47 = I4 )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X5 @ N2 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi @ X5 )
% 5.25/5.47 & ( ord_less_eq_nat @ X5 @ Ma ) ) ) ) ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % invar_vebt.intros(4)
% 5.25/5.47 thf(fact_2063_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 != ( suc @ zero_zero_nat ) )
% 5.25/5.47 = ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod2_eq_Suc_0_eq_0
% 5.25/5.47 thf(fact_2064_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 != one_one_nat )
% 5.25/5.47 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_1_eq_0
% 5.25/5.47 thf(fact_2065_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.47 != one_one_int )
% 5.25/5.47 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.47 = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_1_eq_0
% 5.25/5.47 thf(fact_2066_not__mod__2__eq__1__eq__0,axiom,
% 5.25/5.47 ! [A: code_integer] :
% 5.25/5.47 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.47 != one_one_Code_integer )
% 5.25/5.47 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.47 = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_1_eq_0
% 5.25/5.47 thf(fact_2067_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 != zero_zero_nat )
% 5.25/5.47 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = one_one_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_0_eq_1
% 5.25/5.47 thf(fact_2068_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.47 != zero_zero_int )
% 5.25/5.47 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.47 = one_one_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_0_eq_1
% 5.25/5.47 thf(fact_2069_not__mod__2__eq__0__eq__1,axiom,
% 5.25/5.47 ! [A: code_integer] :
% 5.25/5.47 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.47 != zero_z3403309356797280102nteger )
% 5.25/5.47 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.47 = one_one_Code_integer ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_mod_2_eq_0_eq_1
% 5.25/5.47 thf(fact_2070_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 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary2 @ N )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N @ N ) )
% 5.25/5.47 & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.25/5.47 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary2 ) )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.25/5.47 & ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X3 )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.25/5.47 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary2 @ N )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N @ N ) )
% 5.25/5.47 & ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.47 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.47 & ( ( Mi2 = Ma2 )
% 5.25/5.47 => ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 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 ) ) @ A22 ) )
% 5.25/5.47 & ( ( Mi2 != Ma2 )
% 5.25/5.47 => ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 5.25/5.47 = I3 )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 5.25/5.47 & ! [X: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X @ N )
% 5.25/5.47 = I3 )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi2 @ X )
% 5.25/5.47 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) )
% 5.25/5.47 | ? [TreeList: list_VEBT_VEBT,N: nat,Summary2: vEBT_VEBT,Mi2: nat,Ma2: nat] :
% 5.25/5.47 ( ( A1
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ A22 @ TreeList @ Summary2 ) )
% 5.25/5.47 & ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X @ N ) )
% 5.25/5.47 & ( vEBT_invar_vebt @ Summary2 @ ( suc @ N ) )
% 5.25/5.47 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.25/5.47 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.25/5.47 & ( A22
% 5.25/5.47 = ( plus_plus_nat @ N @ ( suc @ N ) ) )
% 5.25/5.47 & ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.25/5.47 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ X3 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I3 ) ) )
% 5.25/5.47 & ( ( Mi2 = Ma2 )
% 5.25/5.47 => ! [X: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.25/5.47 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 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 ) ) @ A22 ) )
% 5.25/5.47 & ( ( Mi2 != Ma2 )
% 5.25/5.47 => ! [I3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ I3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) ) )
% 5.25/5.47 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N )
% 5.25/5.47 = I3 )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ Ma2 @ N ) ) )
% 5.25/5.47 & ! [X: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X @ N )
% 5.25/5.47 = I3 )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I3 ) @ ( vEBT_VEBT_low @ X @ N ) ) )
% 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.simps
% 5.25/5.47 thf(fact_2071_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,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary3 @ 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 @ Summary3 @ X_1 )
% 5.25/5.47 => ~ ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary3 @ 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 @ Summary3 @ X_1 )
% 5.25/5.47 => ~ ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary3 @ 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 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 5.25/5.47 => ( ( ( Mi3 = Ma3 )
% 5.25/5.47 => ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 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 ) ) @ Deg2 ) )
% 5.25/5.47 => ~ ( ( Mi3 != Ma3 )
% 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 @ Ma3 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.25/5.47 & ! [X2: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 5.25/5.47 => ( ( ord_less_nat @ Mi3 @ X2 )
% 5.25/5.47 & ( ord_less_eq_nat @ X2 @ Ma3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.25/5.47 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary3: vEBT_VEBT,M5: nat,Deg2: nat,Mi3: nat,Ma3: nat] :
% 5.25/5.47 ( ( A12
% 5.25/5.47 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.25/5.47 => ( ( A23 = Deg2 )
% 5.25/5.47 => ( ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ( vEBT_invar_vebt @ X2 @ N3 ) )
% 5.25/5.47 => ( ( vEBT_invar_vebt @ Summary3 @ 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 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ X3 ) )
% 5.25/5.47 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I ) ) )
% 5.25/5.47 => ( ( ( Mi3 = Ma3 )
% 5.25/5.47 => ! [X2: vEBT_VEBT] :
% 5.25/5.47 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.25/5.47 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X2 @ X_1 ) ) )
% 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 ) ) @ Deg2 ) )
% 5.25/5.47 => ~ ( ( Mi3 != Ma3 )
% 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 @ Ma3 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ Ma3 @ N3 ) ) )
% 5.25/5.47 & ! [X2: nat] :
% 5.25/5.47 ( ( ( ( vEBT_VEBT_high @ X2 @ N3 )
% 5.25/5.47 = I )
% 5.25/5.47 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I ) @ ( vEBT_VEBT_low @ X2 @ N3 ) ) )
% 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.cases
% 5.25/5.47 thf(fact_2072_nat__induct2,axiom,
% 5.25/5.47 ! [P: nat > $o,N2: nat] :
% 5.25/5.47 ( ( P @ zero_zero_nat )
% 5.25/5.47 => ( ( P @ one_one_nat )
% 5.25/5.47 => ( ! [N3: nat] :
% 5.25/5.47 ( ( P @ N3 )
% 5.25/5.47 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.25/5.47 => ( P @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_induct2
% 5.25/5.47 thf(fact_2073_not__Some__eq,axiom,
% 5.25/5.47 ! [X4: option4927543243414619207at_nat] :
% 5.25/5.47 ( ( ! [Y5: product_prod_nat_nat] :
% 5.25/5.47 ( X4
% 5.25/5.47 != ( some_P7363390416028606310at_nat @ Y5 ) ) )
% 5.25/5.47 = ( X4 = none_P5556105721700978146at_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_Some_eq
% 5.25/5.47 thf(fact_2074_not__Some__eq,axiom,
% 5.25/5.47 ! [X4: option_num] :
% 5.25/5.47 ( ( ! [Y5: num] :
% 5.25/5.47 ( X4
% 5.25/5.47 != ( some_num @ Y5 ) ) )
% 5.25/5.47 = ( X4 = none_num ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_Some_eq
% 5.25/5.47 thf(fact_2075_not__None__eq,axiom,
% 5.25/5.47 ! [X4: option4927543243414619207at_nat] :
% 5.25/5.47 ( ( X4 != none_P5556105721700978146at_nat )
% 5.25/5.47 = ( ? [Y5: product_prod_nat_nat] :
% 5.25/5.47 ( X4
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_None_eq
% 5.25/5.47 thf(fact_2076_not__None__eq,axiom,
% 5.25/5.47 ! [X4: option_num] :
% 5.25/5.47 ( ( X4 != none_num )
% 5.25/5.47 = ( ? [Y5: num] :
% 5.25/5.47 ( X4
% 5.25/5.47 = ( some_num @ Y5 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_None_eq
% 5.25/5.47 thf(fact_2077_pos2,axiom,
% 5.25/5.47 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos2
% 5.25/5.47 thf(fact_2078_double__eq__0__iff,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( ( plus_plus_real @ A @ A )
% 5.25/5.47 = zero_zero_real )
% 5.25/5.47 = ( A = zero_zero_real ) ) ).
% 5.25/5.47
% 5.25/5.47 % double_eq_0_iff
% 5.25/5.47 thf(fact_2079_double__eq__0__iff,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( ( plus_plus_rat @ A @ A )
% 5.25/5.47 = zero_zero_rat )
% 5.25/5.47 = ( A = zero_zero_rat ) ) ).
% 5.25/5.47
% 5.25/5.47 % double_eq_0_iff
% 5.25/5.47 thf(fact_2080_double__eq__0__iff,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( ( plus_plus_int @ A @ A )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 = ( A = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % double_eq_0_iff
% 5.25/5.47 thf(fact_2081_div__pos__pos__trivial,axiom,
% 5.25/5.47 ! [K: int,L: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.47 => ( ( ord_less_int @ K @ L )
% 5.25/5.47 => ( ( divide_divide_int @ K @ L )
% 5.25/5.47 = zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_pos_pos_trivial
% 5.25/5.47 thf(fact_2082_div__neg__neg__trivial,axiom,
% 5.25/5.47 ! [K: int,L: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ L @ K )
% 5.25/5.47 => ( ( divide_divide_int @ K @ L )
% 5.25/5.47 = zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_neg_neg_trivial
% 5.25/5.47 thf(fact_2083_VEBT_Oinject_I2_J,axiom,
% 5.25/5.47 ! [X21: $o,X222: $o,Y21: $o,Y22: $o] :
% 5.25/5.47 ( ( ( vEBT_Leaf @ X21 @ X222 )
% 5.25/5.47 = ( vEBT_Leaf @ Y21 @ Y22 ) )
% 5.25/5.47 = ( ( X21 = Y21 )
% 5.25/5.47 & ( X222 = Y22 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.inject(2)
% 5.25/5.47 thf(fact_2084_i0__less,axiom,
% 5.25/5.47 ! [N2: extended_enat] :
% 5.25/5.47 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.25/5.47 = ( N2 != zero_z5237406670263579293d_enat ) ) ).
% 5.25/5.47
% 5.25/5.47 % i0_less
% 5.25/5.47 thf(fact_2085_half__nonnegative__int__iff,axiom,
% 5.25/5.47 ! [K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.47 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.25/5.47
% 5.25/5.47 % half_nonnegative_int_iff
% 5.25/5.47 thf(fact_2086_half__negative__int__iff,axiom,
% 5.25/5.47 ! [K: int] :
% 5.25/5.47 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % half_negative_int_iff
% 5.25/5.47 thf(fact_2087_VEBT_Osize_I4_J,axiom,
% 5.25/5.47 ! [X21: $o,X222: $o] :
% 5.25/5.47 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.25/5.47 = zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.size(4)
% 5.25/5.47 thf(fact_2088_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 => ~ ! [X212: $o,X223: $o] :
% 5.25/5.47 ( Y
% 5.25/5.47 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.exhaust
% 5.25/5.47 thf(fact_2089_VEBT_Odistinct_I1_J,axiom,
% 5.25/5.47 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.25/5.47 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.25/5.47 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT.distinct(1)
% 5.25/5.47 thf(fact_2090_zdiv__mono__strict,axiom,
% 5.25/5.47 ! [A2: int,B3: int,N2: int] :
% 5.25/5.47 ( ( ord_less_int @ A2 @ B3 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.25/5.47 => ( ( ( modulo_modulo_int @ A2 @ N2 )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 => ( ( ( modulo_modulo_int @ B3 @ N2 )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 => ( ord_less_int @ ( divide_divide_int @ A2 @ N2 ) @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono_strict
% 5.25/5.47 thf(fact_2091_div__neg__pos__less0,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_neg_pos_less0
% 5.25/5.47 thf(fact_2092_neg__imp__zdiv__neg__iff,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_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % neg_imp_zdiv_neg_iff
% 5.25/5.47 thf(fact_2093_pos__imp__zdiv__neg__iff,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_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.25/5.47 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_imp_zdiv_neg_iff
% 5.25/5.47 thf(fact_2094_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.25/5.47 = ( ( ord_less_eq_int @ B @ A )
% 5.25/5.47 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nonneg1_imp_zdiv_pos_iff
% 5.25/5.47 thf(fact_2095_pos__imp__zdiv__nonneg__iff,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 @ ( divide_divide_int @ A @ B ) )
% 5.25/5.47 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_imp_zdiv_nonneg_iff
% 5.25/5.47 thf(fact_2096_neg__imp__zdiv__nonneg__iff,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 @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.25/5.47 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % neg_imp_zdiv_nonneg_iff
% 5.25/5.47 thf(fact_2097_pos__imp__zdiv__pos__iff,axiom,
% 5.25/5.47 ! [K: int,I2: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I2 @ K ) )
% 5.25/5.47 = ( ord_less_eq_int @ K @ I2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % pos_imp_zdiv_pos_iff
% 5.25/5.47 thf(fact_2098_div__nonpos__pos__le0,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_nonpos_pos_le0
% 5.25/5.47 thf(fact_2099_div__nonneg__neg__le0,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.47 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.47 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_nonneg_neg_le0
% 5.25/5.47 thf(fact_2100_verit__le__mono__div__int,axiom,
% 5.25/5.47 ! [A2: int,B3: int,N2: int] :
% 5.25/5.47 ( ( ord_less_int @ A2 @ B3 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.25/5.47 => ( ord_less_eq_int
% 5.25/5.47 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N2 )
% 5.25/5.47 @ ( if_int
% 5.25/5.47 @ ( ( modulo_modulo_int @ B3 @ N2 )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 @ one_one_int
% 5.25/5.47 @ zero_zero_int ) )
% 5.25/5.47 @ ( divide_divide_int @ B3 @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % verit_le_mono_div_int
% 5.25/5.47 thf(fact_2101_int__div__less__self,axiom,
% 5.25/5.47 ! [X4: int,K: int] :
% 5.25/5.47 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.25/5.47 => ( ( ord_less_int @ one_one_int @ K )
% 5.25/5.47 => ( ord_less_int @ ( divide_divide_int @ X4 @ K ) @ X4 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % int_div_less_self
% 5.25/5.47 thf(fact_2102_div__positive__int,axiom,
% 5.25/5.47 ! [L: int,K: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ L @ K )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ L )
% 5.25/5.47 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_positive_int
% 5.25/5.47 thf(fact_2103_div__int__pos__iff,axiom,
% 5.25/5.47 ! [K: int,L: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L ) )
% 5.25/5.47 = ( ( K = zero_zero_int )
% 5.25/5.47 | ( L = zero_zero_int )
% 5.25/5.47 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.47 & ( ord_less_eq_int @ zero_zero_int @ L ) )
% 5.25/5.47 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.47 & ( ord_less_int @ L @ zero_zero_int ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_int_pos_iff
% 5.25/5.47 thf(fact_2104_zdiv__mono2__neg,axiom,
% 5.25/5.47 ! [A: int,B4: int,B: int] :
% 5.25/5.47 ( ( ord_less_int @ A @ zero_zero_int )
% 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 @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono2_neg
% 5.25/5.47 thf(fact_2105_zdiv__mono1__neg,axiom,
% 5.25/5.47 ! [A: int,A4: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ A4 )
% 5.25/5.47 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.47 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono1_neg
% 5.25/5.47 thf(fact_2106_zdiv__eq__0__iff,axiom,
% 5.25/5.47 ! [I2: int,K: int] :
% 5.25/5.47 ( ( ( divide_divide_int @ I2 @ K )
% 5.25/5.47 = zero_zero_int )
% 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 % zdiv_eq_0_iff
% 5.25/5.47 thf(fact_2107_zdiv__mono2,axiom,
% 5.25/5.47 ! [A: int,B4: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 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 @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono2
% 5.25/5.47 thf(fact_2108_zdiv__mono1,axiom,
% 5.25/5.47 ! [A: int,A4: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ A @ A4 )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % zdiv_mono1
% 5.25/5.47 thf(fact_2109_VEBT__internal_Omembermima_Osimps_I1_J,axiom,
% 5.25/5.47 ! [Uu: $o,Uv: $o,Uw: nat] :
% 5.25/5.47 ~ ( vEBT_VEBT_membermima @ ( vEBT_Leaf @ Uu @ Uv ) @ Uw ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.membermima.simps(1)
% 5.25/5.47 thf(fact_2110_not__iless0,axiom,
% 5.25/5.47 ! [N2: extended_enat] :
% 5.25/5.47 ~ ( ord_le72135733267957522d_enat @ N2 @ zero_z5237406670263579293d_enat ) ).
% 5.25/5.47
% 5.25/5.47 % not_iless0
% 5.25/5.47 thf(fact_2111_i0__lb,axiom,
% 5.25/5.47 ! [N2: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N2 ) ).
% 5.25/5.47
% 5.25/5.47 % i0_lb
% 5.25/5.47 thf(fact_2112_ile0__eq,axiom,
% 5.25/5.47 ! [N2: extended_enat] :
% 5.25/5.47 ( ( ord_le2932123472753598470d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.25/5.47 = ( N2 = zero_z5237406670263579293d_enat ) ) ).
% 5.25/5.47
% 5.25/5.47 % ile0_eq
% 5.25/5.47 thf(fact_2113_realpow__pos__nth2,axiom,
% 5.25/5.47 ! [A: real,N2: nat] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.47 => ? [R2: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.47 & ( ( power_power_real @ R2 @ ( suc @ N2 ) )
% 5.25/5.47 = A ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % realpow_pos_nth2
% 5.25/5.47 thf(fact_2114_vebt__buildup_Osimps_I1_J,axiom,
% 5.25/5.47 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.25/5.47 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.25/5.47
% 5.25/5.47 % vebt_buildup.simps(1)
% 5.25/5.47 thf(fact_2115_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.25/5.47 ! [Uu: $o,Uv: $o,D: nat] :
% 5.25/5.47 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.25/5.47 = ( D = one_one_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.valid'.simps(1)
% 5.25/5.47 thf(fact_2116_realpow__pos__nth__unique,axiom,
% 5.25/5.47 ! [N2: nat,A: real] :
% 5.25/5.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.47 => ? [X5: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.25/5.47 & ( ( power_power_real @ X5 @ N2 )
% 5.25/5.47 = A )
% 5.25/5.47 & ! [Y4: real] :
% 5.25/5.47 ( ( ( ord_less_real @ zero_zero_real @ Y4 )
% 5.25/5.47 & ( ( power_power_real @ Y4 @ N2 )
% 5.25/5.47 = A ) )
% 5.25/5.47 => ( Y4 = X5 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % realpow_pos_nth_unique
% 5.25/5.47 thf(fact_2117_realpow__pos__nth,axiom,
% 5.25/5.47 ! [N2: nat,A: real] :
% 5.25/5.47 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.47 => ? [R2: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.25/5.47 & ( ( power_power_real @ R2 @ N2 )
% 5.25/5.47 = A ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % realpow_pos_nth
% 5.25/5.47 thf(fact_2118_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_2119_not__exp__less__eq__0__int,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % not_exp_less_eq_0_int
% 5.25/5.47 thf(fact_2120_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_2121_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.25/5.47 ! [A: $o,B: $o,X4: nat] :
% 5.25/5.47 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X4 )
% 5.25/5.47 = ( ( ( X4 = zero_zero_nat )
% 5.25/5.47 => A )
% 5.25/5.47 & ( ( X4 != zero_zero_nat )
% 5.25/5.47 => ( ( ( X4 = one_one_nat )
% 5.25/5.47 => B )
% 5.25/5.47 & ( X4 = one_one_nat ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % VEBT_internal.naive_member.simps(1)
% 5.25/5.47 thf(fact_2122_real__arch__pow__inv,axiom,
% 5.25/5.47 ! [Y: real,X4: real] :
% 5.25/5.47 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.47 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.25/5.47 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X4 @ N3 ) @ Y ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % real_arch_pow_inv
% 5.25/5.47 thf(fact_2123_option_Odistinct_I1_J,axiom,
% 5.25/5.47 ! [X22: product_prod_nat_nat] :
% 5.25/5.47 ( none_P5556105721700978146at_nat
% 5.25/5.47 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.distinct(1)
% 5.25/5.47 thf(fact_2124_option_Odistinct_I1_J,axiom,
% 5.25/5.47 ! [X22: num] :
% 5.25/5.47 ( none_num
% 5.25/5.47 != ( some_num @ X22 ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.distinct(1)
% 5.25/5.47 thf(fact_2125_option_OdiscI,axiom,
% 5.25/5.47 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.25/5.47 ( ( Option
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.25/5.47 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.discI
% 5.25/5.47 thf(fact_2126_option_OdiscI,axiom,
% 5.25/5.47 ! [Option: option_num,X22: num] :
% 5.25/5.47 ( ( Option
% 5.25/5.47 = ( some_num @ X22 ) )
% 5.25/5.47 => ( Option != none_num ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.discI
% 5.25/5.47 thf(fact_2127_option_Oexhaust,axiom,
% 5.25/5.47 ! [Y: option4927543243414619207at_nat] :
% 5.25/5.47 ( ( Y != none_P5556105721700978146at_nat )
% 5.25/5.47 => ~ ! [X23: product_prod_nat_nat] :
% 5.25/5.47 ( Y
% 5.25/5.47 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.exhaust
% 5.25/5.47 thf(fact_2128_option_Oexhaust,axiom,
% 5.25/5.47 ! [Y: option_num] :
% 5.25/5.47 ( ( Y != none_num )
% 5.25/5.47 => ~ ! [X23: num] :
% 5.25/5.47 ( Y
% 5.25/5.47 != ( some_num @ X23 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.exhaust
% 5.25/5.47 thf(fact_2129_split__option__ex,axiom,
% 5.25/5.47 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.25/5.47 ? [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.25/5.47 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.25/5.47 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.25/5.47 | ? [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % split_option_ex
% 5.25/5.47 thf(fact_2130_split__option__ex,axiom,
% 5.25/5.47 ( ( ^ [P3: option_num > $o] :
% 5.25/5.47 ? [X6: option_num] : ( P3 @ X6 ) )
% 5.25/5.47 = ( ^ [P4: option_num > $o] :
% 5.25/5.47 ( ( P4 @ none_num )
% 5.25/5.47 | ? [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % split_option_ex
% 5.25/5.47 thf(fact_2131_split__option__all,axiom,
% 5.25/5.47 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.25/5.47 ! [X6: option4927543243414619207at_nat] : ( P3 @ X6 ) )
% 5.25/5.47 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.25/5.47 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.25/5.47 & ! [X: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % split_option_all
% 5.25/5.47 thf(fact_2132_split__option__all,axiom,
% 5.25/5.47 ( ( ^ [P3: option_num > $o] :
% 5.25/5.47 ! [X6: option_num] : ( P3 @ X6 ) )
% 5.25/5.47 = ( ^ [P4: option_num > $o] :
% 5.25/5.47 ( ( P4 @ none_num )
% 5.25/5.47 & ! [X: num] : ( P4 @ ( some_num @ X ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % split_option_all
% 5.25/5.47 thf(fact_2133_combine__options__cases,axiom,
% 5.25/5.47 ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.25/5.47 ( ( ( X4 = none_P5556105721700978146at_nat )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.25/5.47 ( ( X4
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.25/5.47 => ( ( Y
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % combine_options_cases
% 5.25/5.47 thf(fact_2134_combine__options__cases,axiom,
% 5.25/5.47 ! [X4: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.25/5.47 ( ( ( X4 = none_P5556105721700978146at_nat )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ( ( Y = none_num )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ! [A5: product_prod_nat_nat,B5: num] :
% 5.25/5.47 ( ( X4
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.25/5.47 => ( ( Y
% 5.25/5.47 = ( some_num @ B5 ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % combine_options_cases
% 5.25/5.47 thf(fact_2135_combine__options__cases,axiom,
% 5.25/5.47 ! [X4: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.25/5.47 ( ( ( X4 = none_num )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ! [A5: num,B5: product_prod_nat_nat] :
% 5.25/5.47 ( ( X4
% 5.25/5.47 = ( some_num @ A5 ) )
% 5.25/5.47 => ( ( Y
% 5.25/5.47 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % combine_options_cases
% 5.25/5.47 thf(fact_2136_combine__options__cases,axiom,
% 5.25/5.47 ! [X4: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.25/5.47 ( ( ( X4 = none_num )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ( ( Y = none_num )
% 5.25/5.47 => ( P @ X4 @ Y ) )
% 5.25/5.47 => ( ! [A5: num,B5: num] :
% 5.25/5.47 ( ( X4
% 5.25/5.47 = ( some_num @ A5 ) )
% 5.25/5.47 => ( ( Y
% 5.25/5.47 = ( some_num @ B5 ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) )
% 5.25/5.47 => ( P @ X4 @ Y ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % combine_options_cases
% 5.25/5.47 thf(fact_2137_option_Osize_I3_J,axiom,
% 5.25/5.47 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size(3)
% 5.25/5.47 thf(fact_2138_option_Osize_I3_J,axiom,
% 5.25/5.47 ( ( size_size_option_num @ none_num )
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size(3)
% 5.25/5.47 thf(fact_2139_option_Osize_I4_J,axiom,
% 5.25/5.47 ! [X22: product_prod_nat_nat] :
% 5.25/5.47 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size(4)
% 5.25/5.47 thf(fact_2140_option_Osize_I4_J,axiom,
% 5.25/5.47 ! [X22: num] :
% 5.25/5.47 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size(4)
% 5.25/5.47 thf(fact_2141_divides__aux__eq,axiom,
% 5.25/5.47 ! [Q3: nat,R3: nat] :
% 5.25/5.47 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 5.25/5.47 = ( R3 = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % divides_aux_eq
% 5.25/5.47 thf(fact_2142_divides__aux__eq,axiom,
% 5.25/5.47 ! [Q3: int,R3: int] :
% 5.25/5.47 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.25/5.47 = ( R3 = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % divides_aux_eq
% 5.25/5.47 thf(fact_2143_gcd__nat__induct,axiom,
% 5.25/5.47 ! [P: nat > nat > $o,M: nat,N2: nat] :
% 5.25/5.47 ( ! [M5: nat] : ( P @ M5 @ zero_zero_nat )
% 5.25/5.47 => ( ! [M5: nat,N3: nat] :
% 5.25/5.47 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.25/5.47 => ( ( P @ N3 @ ( modulo_modulo_nat @ M5 @ N3 ) )
% 5.25/5.47 => ( P @ M5 @ N3 ) ) )
% 5.25/5.47 => ( P @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % gcd_nat_induct
% 5.25/5.47 thf(fact_2144_option_Osize__gen_I2_J,axiom,
% 5.25/5.47 ! [X4: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.25/5.47 ( ( size_o8335143837870341156at_nat @ X4 @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.25/5.47 = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size_gen(2)
% 5.25/5.47 thf(fact_2145_option_Osize__gen_I2_J,axiom,
% 5.25/5.47 ! [X4: num > nat,X22: num] :
% 5.25/5.47 ( ( size_option_num @ X4 @ ( some_num @ X22 ) )
% 5.25/5.47 = ( plus_plus_nat @ ( X4 @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % option.size_gen(2)
% 5.25/5.47 thf(fact_2146_even__succ__mod__exp,axiom,
% 5.25/5.47 ! [A: nat,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_mod_exp
% 5.25/5.47 thf(fact_2147_even__succ__mod__exp,axiom,
% 5.25/5.47 ! [A: int,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_mod_exp
% 5.25/5.47 thf(fact_2148_even__succ__mod__exp,axiom,
% 5.25/5.47 ! [A: code_integer,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_mod_exp
% 5.25/5.47 thf(fact_2149_even__succ__div__exp,axiom,
% 5.25/5.47 ! [A: nat,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_div_exp
% 5.25/5.47 thf(fact_2150_even__succ__div__exp,axiom,
% 5.25/5.47 ! [A: int,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_div_exp
% 5.25/5.47 thf(fact_2151_even__succ__div__exp,axiom,
% 5.25/5.47 ! [A: code_integer,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.47 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % even_succ_div_exp
% 5.25/5.47 thf(fact_2152_divmod__digit__1_I1_J,axiom,
% 5.25/5.47 ! [A: code_integer,B: code_integer] :
% 5.25/5.47 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.25/5.47 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.25/5.47 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.47 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.25/5.47 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % divmod_digit_1(1)
% 5.25/5.47 thf(fact_2153_divmod__digit__1_I1_J,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.47 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.47 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.47 => ( ( 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 )
% 5.25/5.47 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % divmod_digit_1(1)
% 5.25/5.47 thf(fact_2154_divmod__digit__1_I1_J,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.47 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.47 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.25/5.47 => ( ( 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 )
% 5.25/5.47 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % divmod_digit_1(1)
% 5.25/5.47 thf(fact_2155_num_Osize__gen_I2_J,axiom,
% 5.25/5.47 ! [X22: num] :
% 5.25/5.47 ( ( size_num @ ( bit0 @ X22 ) )
% 5.25/5.47 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % num.size_gen(2)
% 5.25/5.47 thf(fact_2156_power__le__zero__eq__numeral,axiom,
% 5.25/5.47 ! [A: real,W: num] :
% 5.25/5.47 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.25/5.47 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_le_zero_eq_numeral
% 5.25/5.47 thf(fact_2157_power__le__zero__eq__numeral,axiom,
% 5.25/5.47 ! [A: rat,W: num] :
% 5.25/5.47 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.25/5.47 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_le_zero_eq_numeral
% 5.25/5.47 thf(fact_2158_power__le__zero__eq__numeral,axiom,
% 5.25/5.47 ! [A: int,W: num] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.25/5.47 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.25/5.47 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_le_zero_eq_numeral
% 5.25/5.47 thf(fact_2159_one__mod__2__pow__eq,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % one_mod_2_pow_eq
% 5.25/5.47 thf(fact_2160_one__mod__2__pow__eq,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % one_mod_2_pow_eq
% 5.25/5.47 thf(fact_2161_one__mod__2__pow__eq,axiom,
% 5.25/5.47 ! [N2: nat] :
% 5.25/5.47 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.47 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % one_mod_2_pow_eq
% 5.25/5.47 thf(fact_2162_arith__geo__mean,axiom,
% 5.25/5.47 ! [U: real,X4: real,Y: real] :
% 5.25/5.47 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = ( times_times_real @ X4 @ Y ) )
% 5.25/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.47 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.47 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % arith_geo_mean
% 5.25/5.47 thf(fact_2163_arith__geo__mean,axiom,
% 5.25/5.47 ! [U: rat,X4: rat,Y: rat] :
% 5.25/5.47 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.47 = ( times_times_rat @ X4 @ Y ) )
% 5.25/5.47 => ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.47 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.47 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % arith_geo_mean
% 5.25/5.47 thf(fact_2164_semiring__norm_I13_J,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.25/5.47 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % semiring_norm(13)
% 5.25/5.47 thf(fact_2165_semiring__norm_I11_J,axiom,
% 5.25/5.47 ! [M: num] :
% 5.25/5.47 ( ( times_times_num @ M @ one )
% 5.25/5.47 = M ) ).
% 5.25/5.47
% 5.25/5.47 % semiring_norm(11)
% 5.25/5.47 thf(fact_2166_semiring__norm_I12_J,axiom,
% 5.25/5.47 ! [N2: num] :
% 5.25/5.47 ( ( times_times_num @ one @ N2 )
% 5.25/5.47 = N2 ) ).
% 5.25/5.47
% 5.25/5.47 % semiring_norm(12)
% 5.25/5.47 thf(fact_2167_mult__is__0,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ M @ N2 )
% 5.25/5.47 = zero_zero_nat )
% 5.25/5.47 = ( ( M = zero_zero_nat )
% 5.25/5.47 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_is_0
% 5.25/5.47 thf(fact_2168_mult__0__right,axiom,
% 5.25/5.47 ! [M: nat] :
% 5.25/5.47 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.25/5.47 = zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % mult_0_right
% 5.25/5.47 thf(fact_2169_mult__cancel1,axiom,
% 5.25/5.47 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ K @ M )
% 5.25/5.47 = ( times_times_nat @ K @ N2 ) )
% 5.25/5.47 = ( ( M = N2 )
% 5.25/5.47 | ( K = zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel1
% 5.25/5.47 thf(fact_2170_mult__cancel2,axiom,
% 5.25/5.47 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ M @ K )
% 5.25/5.47 = ( times_times_nat @ N2 @ K ) )
% 5.25/5.47 = ( ( M = N2 )
% 5.25/5.47 | ( K = zero_zero_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel2
% 5.25/5.47 thf(fact_2171_nat__mult__eq__1__iff,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ M @ N2 )
% 5.25/5.47 = one_one_nat )
% 5.25/5.47 = ( ( M = one_one_nat )
% 5.25/5.47 & ( N2 = one_one_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_eq_1_iff
% 5.25/5.47 thf(fact_2172_nat__1__eq__mult__iff,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( one_one_nat
% 5.25/5.47 = ( times_times_nat @ M @ N2 ) )
% 5.25/5.47 = ( ( M = one_one_nat )
% 5.25/5.47 & ( N2 = one_one_nat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_1_eq_mult_iff
% 5.25/5.47 thf(fact_2173_mult__zero__left,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.25/5.47 = zero_zero_rat ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_left
% 5.25/5.47 thf(fact_2174_mult__zero__left,axiom,
% 5.25/5.47 ! [A: complex] :
% 5.25/5.47 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.25/5.47 = zero_zero_complex ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_left
% 5.25/5.47 thf(fact_2175_mult__zero__left,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( times_times_real @ zero_zero_real @ A )
% 5.25/5.47 = zero_zero_real ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_left
% 5.25/5.47 thf(fact_2176_mult__zero__left,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.25/5.47 = zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_left
% 5.25/5.47 thf(fact_2177_mult__zero__left,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( times_times_int @ zero_zero_int @ A )
% 5.25/5.47 = zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_left
% 5.25/5.47 thf(fact_2178_mult__zero__right,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.25/5.47 = zero_zero_rat ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_right
% 5.25/5.47 thf(fact_2179_mult__zero__right,axiom,
% 5.25/5.47 ! [A: complex] :
% 5.25/5.47 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.25/5.47 = zero_zero_complex ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_right
% 5.25/5.47 thf(fact_2180_mult__zero__right,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( times_times_real @ A @ zero_zero_real )
% 5.25/5.47 = zero_zero_real ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_right
% 5.25/5.47 thf(fact_2181_mult__zero__right,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.25/5.47 = zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_right
% 5.25/5.47 thf(fact_2182_mult__zero__right,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( times_times_int @ A @ zero_zero_int )
% 5.25/5.47 = zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % mult_zero_right
% 5.25/5.47 thf(fact_2183_mult__eq__0__iff,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( ( times_times_rat @ A @ B )
% 5.25/5.47 = zero_zero_rat )
% 5.25/5.47 = ( ( A = zero_zero_rat )
% 5.25/5.47 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_eq_0_iff
% 5.25/5.47 thf(fact_2184_mult__eq__0__iff,axiom,
% 5.25/5.47 ! [A: complex,B: complex] :
% 5.25/5.47 ( ( ( times_times_complex @ A @ B )
% 5.25/5.47 = zero_zero_complex )
% 5.25/5.47 = ( ( A = zero_zero_complex )
% 5.25/5.47 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_eq_0_iff
% 5.25/5.47 thf(fact_2185_mult__eq__0__iff,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( ( times_times_real @ A @ B )
% 5.25/5.47 = zero_zero_real )
% 5.25/5.47 = ( ( A = zero_zero_real )
% 5.25/5.47 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_eq_0_iff
% 5.25/5.47 thf(fact_2186_mult__eq__0__iff,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( ( times_times_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 % mult_eq_0_iff
% 5.25/5.47 thf(fact_2187_mult__eq__0__iff,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( ( times_times_int @ A @ B )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 = ( ( A = zero_zero_int )
% 5.25/5.47 | ( B = zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_eq_0_iff
% 5.25/5.47 thf(fact_2188_mult__cancel__left,axiom,
% 5.25/5.47 ! [C: rat,A: rat,B: rat] :
% 5.25/5.47 ( ( ( times_times_rat @ C @ A )
% 5.25/5.47 = ( times_times_rat @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left
% 5.25/5.47 thf(fact_2189_mult__cancel__left,axiom,
% 5.25/5.47 ! [C: complex,A: complex,B: complex] :
% 5.25/5.47 ( ( ( times_times_complex @ C @ A )
% 5.25/5.47 = ( times_times_complex @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left
% 5.25/5.47 thf(fact_2190_mult__cancel__left,axiom,
% 5.25/5.47 ! [C: real,A: real,B: real] :
% 5.25/5.47 ( ( ( times_times_real @ C @ A )
% 5.25/5.47 = ( times_times_real @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left
% 5.25/5.47 thf(fact_2191_mult__cancel__left,axiom,
% 5.25/5.47 ! [C: nat,A: nat,B: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ C @ A )
% 5.25/5.47 = ( times_times_nat @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_nat )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left
% 5.25/5.47 thf(fact_2192_mult__cancel__left,axiom,
% 5.25/5.47 ! [C: int,A: int,B: int] :
% 5.25/5.47 ( ( ( times_times_int @ C @ A )
% 5.25/5.47 = ( times_times_int @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left
% 5.25/5.47 thf(fact_2193_mult__cancel__right,axiom,
% 5.25/5.47 ! [A: rat,C: rat,B: rat] :
% 5.25/5.47 ( ( ( times_times_rat @ A @ C )
% 5.25/5.47 = ( times_times_rat @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right
% 5.25/5.47 thf(fact_2194_mult__cancel__right,axiom,
% 5.25/5.47 ! [A: complex,C: complex,B: complex] :
% 5.25/5.47 ( ( ( times_times_complex @ A @ C )
% 5.25/5.47 = ( times_times_complex @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right
% 5.25/5.47 thf(fact_2195_mult__cancel__right,axiom,
% 5.25/5.47 ! [A: real,C: real,B: real] :
% 5.25/5.47 ( ( ( times_times_real @ A @ C )
% 5.25/5.47 = ( times_times_real @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right
% 5.25/5.47 thf(fact_2196_mult__cancel__right,axiom,
% 5.25/5.47 ! [A: nat,C: nat,B: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ A @ C )
% 5.25/5.47 = ( times_times_nat @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_nat )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right
% 5.25/5.47 thf(fact_2197_mult__cancel__right,axiom,
% 5.25/5.47 ! [A: int,C: int,B: int] :
% 5.25/5.47 ( ( ( times_times_int @ A @ C )
% 5.25/5.47 = ( times_times_int @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( A = B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right
% 5.25/5.47 thf(fact_2198_numeral__times__numeral,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N2 ) )
% 5.25/5.47 = ( numera1916890842035813515d_enat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % numeral_times_numeral
% 5.25/5.47 thf(fact_2199_numeral__times__numeral,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.25/5.47 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % numeral_times_numeral
% 5.25/5.47 thf(fact_2200_numeral__times__numeral,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.25/5.47 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % numeral_times_numeral
% 5.25/5.47 thf(fact_2201_numeral__times__numeral,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.47 = ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % numeral_times_numeral
% 5.25/5.47 thf(fact_2202_numeral__times__numeral,axiom,
% 5.25/5.47 ! [M: num,N2: num] :
% 5.25/5.47 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.25/5.47 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % numeral_times_numeral
% 5.25/5.47 thf(fact_2203_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.47 ! [V: num,W: num,Z: extended_enat] :
% 5.25/5.47 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ W ) @ Z ) )
% 5.25/5.47 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_numeral_left_semiring_numeral
% 5.25/5.47 thf(fact_2204_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.47 ! [V: num,W: num,Z: complex] :
% 5.25/5.47 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.25/5.47 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_numeral_left_semiring_numeral
% 5.25/5.47 thf(fact_2205_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.47 ! [V: num,W: num,Z: real] :
% 5.25/5.47 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.25/5.47 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_numeral_left_semiring_numeral
% 5.25/5.47 thf(fact_2206_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.47 ! [V: num,W: num,Z: nat] :
% 5.25/5.47 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.25/5.47 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_numeral_left_semiring_numeral
% 5.25/5.47 thf(fact_2207_mult__numeral__left__semiring__numeral,axiom,
% 5.25/5.47 ! [V: num,W: num,Z: int] :
% 5.25/5.47 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.25/5.47 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_numeral_left_semiring_numeral
% 5.25/5.47 thf(fact_2208_mult__1,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( times_times_rat @ one_one_rat @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult_1
% 5.25/5.47 thf(fact_2209_mult__1,axiom,
% 5.25/5.47 ! [A: complex] :
% 5.25/5.47 ( ( times_times_complex @ one_one_complex @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult_1
% 5.25/5.47 thf(fact_2210_mult__1,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( times_times_real @ one_one_real @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult_1
% 5.25/5.47 thf(fact_2211_mult__1,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( times_times_nat @ one_one_nat @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult_1
% 5.25/5.47 thf(fact_2212_mult__1,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( times_times_int @ one_one_int @ A )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult_1
% 5.25/5.47 thf(fact_2213_mult_Oright__neutral,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( times_times_rat @ A @ one_one_rat )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult.right_neutral
% 5.25/5.47 thf(fact_2214_mult_Oright__neutral,axiom,
% 5.25/5.47 ! [A: complex] :
% 5.25/5.47 ( ( times_times_complex @ A @ one_one_complex )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult.right_neutral
% 5.25/5.47 thf(fact_2215_mult_Oright__neutral,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( times_times_real @ A @ one_one_real )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult.right_neutral
% 5.25/5.47 thf(fact_2216_mult_Oright__neutral,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( times_times_nat @ A @ one_one_nat )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult.right_neutral
% 5.25/5.47 thf(fact_2217_mult_Oright__neutral,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( times_times_int @ A @ one_one_int )
% 5.25/5.47 = A ) ).
% 5.25/5.47
% 5.25/5.47 % mult.right_neutral
% 5.25/5.47 thf(fact_2218_num__double,axiom,
% 5.25/5.47 ! [N2: num] :
% 5.25/5.47 ( ( times_times_num @ ( bit0 @ one ) @ N2 )
% 5.25/5.47 = ( bit0 @ N2 ) ) ).
% 5.25/5.47
% 5.25/5.47 % num_double
% 5.25/5.47 thf(fact_2219_times__divide__eq__right,axiom,
% 5.25/5.47 ! [A: real,B: real,C: real] :
% 5.25/5.47 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.47 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.25/5.47
% 5.25/5.47 % times_divide_eq_right
% 5.25/5.47 thf(fact_2220_times__divide__eq__right,axiom,
% 5.25/5.47 ! [A: complex,B: complex,C: complex] :
% 5.25/5.47 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.47 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.25/5.47
% 5.25/5.47 % times_divide_eq_right
% 5.25/5.47 thf(fact_2221_divide__divide__eq__right,axiom,
% 5.25/5.47 ! [A: real,B: real,C: real] :
% 5.25/5.47 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.47 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % divide_divide_eq_right
% 5.25/5.47 thf(fact_2222_divide__divide__eq__right,axiom,
% 5.25/5.47 ! [A: complex,B: complex,C: complex] :
% 5.25/5.47 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.47 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % divide_divide_eq_right
% 5.25/5.47 thf(fact_2223_divide__divide__eq__left,axiom,
% 5.25/5.47 ! [A: real,B: real,C: real] :
% 5.25/5.47 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.25/5.47 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % divide_divide_eq_left
% 5.25/5.47 thf(fact_2224_divide__divide__eq__left,axiom,
% 5.25/5.47 ! [A: complex,B: complex,C: complex] :
% 5.25/5.47 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.25/5.47 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % divide_divide_eq_left
% 5.25/5.47 thf(fact_2225_times__divide__eq__left,axiom,
% 5.25/5.47 ! [B: real,C: real,A: real] :
% 5.25/5.47 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.47 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.25/5.47
% 5.25/5.47 % times_divide_eq_left
% 5.25/5.47 thf(fact_2226_times__divide__eq__left,axiom,
% 5.25/5.47 ! [B: complex,C: complex,A: complex] :
% 5.25/5.47 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.25/5.47 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.25/5.47
% 5.25/5.47 % times_divide_eq_left
% 5.25/5.47 thf(fact_2227_dvd__0__right,axiom,
% 5.25/5.47 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2228_dvd__0__right,axiom,
% 5.25/5.47 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2229_dvd__0__right,axiom,
% 5.25/5.47 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2230_dvd__0__right,axiom,
% 5.25/5.47 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2231_dvd__0__right,axiom,
% 5.25/5.47 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2232_dvd__0__right,axiom,
% 5.25/5.47 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_right
% 5.25/5.47 thf(fact_2233_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: code_integer] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.25/5.47 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2234_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: complex] :
% 5.25/5.47 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.25/5.47 = ( A = zero_zero_complex ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2235_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: real] :
% 5.25/5.47 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.25/5.47 = ( A = zero_zero_real ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2236_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: rat] :
% 5.25/5.47 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.25/5.47 = ( A = zero_zero_rat ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2237_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.25/5.47 = ( A = zero_zero_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2238_dvd__0__left__iff,axiom,
% 5.25/5.47 ! [A: int] :
% 5.25/5.47 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.25/5.47 = ( A = zero_zero_int ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_0_left_iff
% 5.25/5.47 thf(fact_2239_dvd__add__triv__right__iff,axiom,
% 5.25/5.47 ! [A: code_integer,B: code_integer] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.25/5.47 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_right_iff
% 5.25/5.47 thf(fact_2240_dvd__add__triv__right__iff,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.25/5.47 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_right_iff
% 5.25/5.47 thf(fact_2241_dvd__add__triv__right__iff,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.25/5.47 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_right_iff
% 5.25/5.47 thf(fact_2242_dvd__add__triv__right__iff,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.25/5.47 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_right_iff
% 5.25/5.47 thf(fact_2243_dvd__add__triv__right__iff,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.25/5.47 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_right_iff
% 5.25/5.47 thf(fact_2244_dvd__add__triv__left__iff,axiom,
% 5.25/5.47 ! [A: code_integer,B: code_integer] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.25/5.47 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_left_iff
% 5.25/5.47 thf(fact_2245_dvd__add__triv__left__iff,axiom,
% 5.25/5.47 ! [A: real,B: real] :
% 5.25/5.47 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.25/5.47 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_left_iff
% 5.25/5.47 thf(fact_2246_dvd__add__triv__left__iff,axiom,
% 5.25/5.47 ! [A: rat,B: rat] :
% 5.25/5.47 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.25/5.47 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_left_iff
% 5.25/5.47 thf(fact_2247_dvd__add__triv__left__iff,axiom,
% 5.25/5.47 ! [A: nat,B: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.47 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_left_iff
% 5.25/5.47 thf(fact_2248_dvd__add__triv__left__iff,axiom,
% 5.25/5.47 ! [A: int,B: int] :
% 5.25/5.47 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.25/5.47 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.25/5.47
% 5.25/5.47 % dvd_add_triv_left_iff
% 5.25/5.47 thf(fact_2249_mult__eq__1__iff,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( ( times_times_nat @ M @ N2 )
% 5.25/5.47 = ( suc @ zero_zero_nat ) )
% 5.25/5.47 = ( ( M
% 5.25/5.47 = ( suc @ zero_zero_nat ) )
% 5.25/5.47 & ( N2
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_eq_1_iff
% 5.25/5.47 thf(fact_2250_one__eq__mult__iff,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( ( suc @ zero_zero_nat )
% 5.25/5.47 = ( times_times_nat @ M @ N2 ) )
% 5.25/5.47 = ( ( M
% 5.25/5.47 = ( suc @ zero_zero_nat ) )
% 5.25/5.47 & ( N2
% 5.25/5.47 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % one_eq_mult_iff
% 5.25/5.47 thf(fact_2251_div__dvd__div,axiom,
% 5.25/5.47 ! [A: nat,B: nat,C: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.47 => ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.47 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.25/5.47 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_dvd_div
% 5.25/5.47 thf(fact_2252_div__dvd__div,axiom,
% 5.25/5.47 ! [A: int,B: int,C: int] :
% 5.25/5.47 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.47 => ( ( dvd_dvd_int @ A @ C )
% 5.25/5.47 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.25/5.47 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_dvd_div
% 5.25/5.47 thf(fact_2253_div__dvd__div,axiom,
% 5.25/5.47 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.47 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.47 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.47 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.25/5.47 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % div_dvd_div
% 5.25/5.47 thf(fact_2254_power__mult__numeral,axiom,
% 5.25/5.47 ! [A: nat,M: num,N2: num] :
% 5.25/5.47 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.47 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_mult_numeral
% 5.25/5.47 thf(fact_2255_power__mult__numeral,axiom,
% 5.25/5.47 ! [A: real,M: num,N2: num] :
% 5.25/5.47 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.47 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_mult_numeral
% 5.25/5.47 thf(fact_2256_power__mult__numeral,axiom,
% 5.25/5.47 ! [A: int,M: num,N2: num] :
% 5.25/5.47 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.47 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_mult_numeral
% 5.25/5.47 thf(fact_2257_power__mult__numeral,axiom,
% 5.25/5.47 ! [A: complex,M: num,N2: num] :
% 5.25/5.47 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.25/5.47 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % power_mult_numeral
% 5.25/5.47 thf(fact_2258_nat__mult__less__cancel__disj,axiom,
% 5.25/5.47 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.47 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_less_cancel_disj
% 5.25/5.47 thf(fact_2259_nat__0__less__mult__iff,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.47 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_0_less_mult_iff
% 5.25/5.47 thf(fact_2260_mult__less__cancel2,axiom,
% 5.25/5.47 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.47 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.25/5.47 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.47 & ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_less_cancel2
% 5.25/5.47 thf(fact_2261_not__real__square__gt__zero,axiom,
% 5.25/5.47 ! [X4: real] :
% 5.25/5.47 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X4 @ X4 ) ) )
% 5.25/5.47 = ( X4 = zero_zero_real ) ) ).
% 5.25/5.47
% 5.25/5.47 % not_real_square_gt_zero
% 5.25/5.47 thf(fact_2262_mult__Suc__right,axiom,
% 5.25/5.47 ! [M: nat,N2: nat] :
% 5.25/5.47 ( ( times_times_nat @ M @ ( suc @ N2 ) )
% 5.25/5.47 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_Suc_right
% 5.25/5.47 thf(fact_2263_nat__mult__dvd__cancel__disj,axiom,
% 5.25/5.47 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.47 = ( ( K = zero_zero_nat )
% 5.25/5.47 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_dvd_cancel_disj
% 5.25/5.47 thf(fact_2264_of__bool__less__eq__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.25/5.47 = ( P
% 5.25/5.47 => Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_eq_iff
% 5.25/5.47 thf(fact_2265_of__bool__less__eq__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.25/5.47 = ( P
% 5.25/5.47 => Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_eq_iff
% 5.25/5.47 thf(fact_2266_of__bool__less__eq__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.25/5.47 = ( P
% 5.25/5.47 => Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_eq_iff
% 5.25/5.47 thf(fact_2267_of__bool__less__eq__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.25/5.47 = ( P
% 5.25/5.47 => Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_eq_iff
% 5.25/5.47 thf(fact_2268_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n1201886186963655149omplex @ $false )
% 5.25/5.47 = zero_zero_complex ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2269_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n3304061248610475627l_real @ $false )
% 5.25/5.47 = zero_zero_real ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2270_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.25/5.47 = zero_zero_rat ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2271_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.25/5.47 = zero_zero_nat ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2272_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.25/5.47 = zero_zero_int ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2273_of__bool__eq_I1_J,axiom,
% 5.25/5.47 ( ( zero_n356916108424825756nteger @ $false )
% 5.25/5.47 = zero_z3403309356797280102nteger ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(1)
% 5.25/5.47 thf(fact_2274_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.25/5.47 = zero_zero_complex )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2275_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.25/5.47 = zero_zero_real )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2276_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.25/5.47 = zero_zero_rat )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2277_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.25/5.47 = zero_zero_nat )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2278_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2279_of__bool__eq__0__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n356916108424825756nteger @ P )
% 5.25/5.47 = zero_z3403309356797280102nteger )
% 5.25/5.47 = ~ P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_0_iff
% 5.25/5.47 thf(fact_2280_nat__mult__div__cancel__disj,axiom,
% 5.25/5.47 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.47 ( ( ( K = zero_zero_nat )
% 5.25/5.47 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.47 = zero_zero_nat ) )
% 5.25/5.47 & ( ( K != zero_zero_nat )
% 5.25/5.47 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.47 = ( divide_divide_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_mult_div_cancel_disj
% 5.25/5.47 thf(fact_2281_of__bool__less__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.25/5.47 = ( ~ P
% 5.25/5.47 & Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_iff
% 5.25/5.47 thf(fact_2282_of__bool__less__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.25/5.47 = ( ~ P
% 5.25/5.47 & Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_iff
% 5.25/5.47 thf(fact_2283_of__bool__less__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.25/5.47 = ( ~ P
% 5.25/5.47 & Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_iff
% 5.25/5.47 thf(fact_2284_of__bool__less__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.25/5.47 = ( ~ P
% 5.25/5.47 & Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_iff
% 5.25/5.47 thf(fact_2285_of__bool__less__iff,axiom,
% 5.25/5.47 ! [P: $o,Q: $o] :
% 5.25/5.47 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.25/5.47 = ( ~ P
% 5.25/5.47 & Q ) ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_less_iff
% 5.25/5.47 thf(fact_2286_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.25/5.47 = one_one_complex )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2287_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.25/5.47 = one_one_real )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2288_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.25/5.47 = one_one_rat )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2289_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.25/5.47 = one_one_nat )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2290_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.25/5.47 = one_one_int )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2291_of__bool__eq__1__iff,axiom,
% 5.25/5.47 ! [P: $o] :
% 5.25/5.47 ( ( ( zero_n356916108424825756nteger @ P )
% 5.25/5.47 = one_one_Code_integer )
% 5.25/5.47 = P ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq_1_iff
% 5.25/5.47 thf(fact_2292_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n1201886186963655149omplex @ $true )
% 5.25/5.47 = one_one_complex ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2293_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n3304061248610475627l_real @ $true )
% 5.25/5.47 = one_one_real ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2294_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.25/5.47 = one_one_rat ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2295_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.25/5.47 = one_one_nat ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2296_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.25/5.47 = one_one_int ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2297_of__bool__eq_I2_J,axiom,
% 5.25/5.47 ( ( zero_n356916108424825756nteger @ $true )
% 5.25/5.47 = one_one_Code_integer ) ).
% 5.25/5.47
% 5.25/5.47 % of_bool_eq(2)
% 5.25/5.47 thf(fact_2298_nat__dvd__1__iff__1,axiom,
% 5.25/5.47 ! [M: nat] :
% 5.25/5.47 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.25/5.47 = ( M = one_one_nat ) ) ).
% 5.25/5.47
% 5.25/5.47 % nat_dvd_1_iff_1
% 5.25/5.47 thf(fact_2299_mult__cancel__right2,axiom,
% 5.25/5.47 ! [A: rat,C: rat] :
% 5.25/5.47 ( ( ( times_times_rat @ A @ C )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( A = one_one_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right2
% 5.25/5.47 thf(fact_2300_mult__cancel__right2,axiom,
% 5.25/5.47 ! [A: complex,C: complex] :
% 5.25/5.47 ( ( ( times_times_complex @ A @ C )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( A = one_one_complex ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right2
% 5.25/5.47 thf(fact_2301_mult__cancel__right2,axiom,
% 5.25/5.47 ! [A: real,C: real] :
% 5.25/5.47 ( ( ( times_times_real @ A @ C )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( A = one_one_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right2
% 5.25/5.47 thf(fact_2302_mult__cancel__right2,axiom,
% 5.25/5.47 ! [A: int,C: int] :
% 5.25/5.47 ( ( ( times_times_int @ A @ C )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( A = one_one_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right2
% 5.25/5.47 thf(fact_2303_mult__cancel__right1,axiom,
% 5.25/5.47 ! [C: rat,B: rat] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_rat @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( B = one_one_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right1
% 5.25/5.47 thf(fact_2304_mult__cancel__right1,axiom,
% 5.25/5.47 ! [C: complex,B: complex] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_complex @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( B = one_one_complex ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right1
% 5.25/5.47 thf(fact_2305_mult__cancel__right1,axiom,
% 5.25/5.47 ! [C: real,B: real] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_real @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( B = one_one_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right1
% 5.25/5.47 thf(fact_2306_mult__cancel__right1,axiom,
% 5.25/5.47 ! [C: int,B: int] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_int @ B @ C ) )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( B = one_one_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_right1
% 5.25/5.47 thf(fact_2307_mult__cancel__left2,axiom,
% 5.25/5.47 ! [C: rat,A: rat] :
% 5.25/5.47 ( ( ( times_times_rat @ C @ A )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( A = one_one_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left2
% 5.25/5.47 thf(fact_2308_mult__cancel__left2,axiom,
% 5.25/5.47 ! [C: complex,A: complex] :
% 5.25/5.47 ( ( ( times_times_complex @ C @ A )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( A = one_one_complex ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left2
% 5.25/5.47 thf(fact_2309_mult__cancel__left2,axiom,
% 5.25/5.47 ! [C: real,A: real] :
% 5.25/5.47 ( ( ( times_times_real @ C @ A )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( A = one_one_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left2
% 5.25/5.47 thf(fact_2310_mult__cancel__left2,axiom,
% 5.25/5.47 ! [C: int,A: int] :
% 5.25/5.47 ( ( ( times_times_int @ C @ A )
% 5.25/5.47 = C )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( A = one_one_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left2
% 5.25/5.47 thf(fact_2311_mult__cancel__left1,axiom,
% 5.25/5.47 ! [C: rat,B: rat] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_rat @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_rat )
% 5.25/5.47 | ( B = one_one_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left1
% 5.25/5.47 thf(fact_2312_mult__cancel__left1,axiom,
% 5.25/5.47 ! [C: complex,B: complex] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_complex @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_complex )
% 5.25/5.47 | ( B = one_one_complex ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left1
% 5.25/5.47 thf(fact_2313_mult__cancel__left1,axiom,
% 5.25/5.47 ! [C: real,B: real] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_real @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_real )
% 5.25/5.47 | ( B = one_one_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left1
% 5.25/5.47 thf(fact_2314_mult__cancel__left1,axiom,
% 5.25/5.47 ! [C: int,B: int] :
% 5.25/5.47 ( ( C
% 5.25/5.47 = ( times_times_int @ C @ B ) )
% 5.25/5.47 = ( ( C = zero_zero_int )
% 5.25/5.47 | ( B = one_one_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % mult_cancel_left1
% 5.25/5.47 thf(fact_2315_sum__squares__eq__zero__iff,axiom,
% 5.25/5.47 ! [X4: rat,Y: rat] :
% 5.25/5.47 ( ( ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 5.25/5.47 = zero_zero_rat )
% 5.25/5.47 = ( ( X4 = zero_zero_rat )
% 5.25/5.47 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_squares_eq_zero_iff
% 5.25/5.47 thf(fact_2316_sum__squares__eq__zero__iff,axiom,
% 5.25/5.47 ! [X4: real,Y: real] :
% 5.25/5.47 ( ( ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 5.25/5.47 = zero_zero_real )
% 5.25/5.47 = ( ( X4 = zero_zero_real )
% 5.25/5.47 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_squares_eq_zero_iff
% 5.25/5.47 thf(fact_2317_sum__squares__eq__zero__iff,axiom,
% 5.25/5.47 ! [X4: int,Y: int] :
% 5.25/5.47 ( ( ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 5.25/5.47 = zero_zero_int )
% 5.25/5.47 = ( ( X4 = zero_zero_int )
% 5.25/5.47 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % sum_squares_eq_zero_iff
% 5.25/5.47 thf(fact_2318_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.47 ! [C: rat,A: rat,B: rat] :
% 5.25/5.47 ( ( C != zero_zero_rat )
% 5.25/5.47 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.47 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.47
% 5.25/5.47 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.47 thf(fact_2319_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.47 ! [C: real,A: real,B: real] :
% 5.25/5.47 ( ( C != zero_zero_real )
% 5.25/5.47 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.25/5.48 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.48 thf(fact_2320_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( C != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_right2
% 5.25/5.48 thf(fact_2321_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: rat,A: rat] :
% 5.25/5.48 ( ( B != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2322_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2323_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2324_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: real,A: real] :
% 5.25/5.48 ( ( B != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2325_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: complex,A: complex] :
% 5.25/5.48 ( ( B != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2326_nonzero__mult__div__cancel__right,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.25/5.48 = A ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_right
% 5.25/5.48 thf(fact_2327_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( C != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2328_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( C != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.48 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2329_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( C != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2330_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( C != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.48 thf(fact_2331_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( C != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.25/5.48 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.48 thf(fact_2332_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( C != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left2
% 5.25/5.48 thf(fact_2333_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( A != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2334_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( A != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2335_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( A != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2336_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( A != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2337_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: complex,B: complex] :
% 5.25/5.48 ( ( A != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2338_nonzero__mult__div__cancel__left,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ A )
% 5.25/5.48 = B ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_div_cancel_left
% 5.25/5.48 thf(fact_2339_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( C != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.48 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2340_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( C != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.48 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2341_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( C != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_mult_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2342_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.48 ! [C: rat,A: rat,B: rat] :
% 5.25/5.48 ( ( ( C = zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.48 = zero_zero_rat ) )
% 5.25/5.48 & ( ( C != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.48 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_divide_mult_cancel_left_if
% 5.25/5.48 thf(fact_2343_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.48 ! [C: real,A: real,B: real] :
% 5.25/5.48 ( ( ( C = zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.48 = zero_zero_real ) )
% 5.25/5.48 & ( ( C != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.48 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_divide_mult_cancel_left_if
% 5.25/5.48 thf(fact_2344_mult__divide__mult__cancel__left__if,axiom,
% 5.25/5.48 ! [C: complex,A: complex,B: complex] :
% 5.25/5.48 ( ( ( C = zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.48 = zero_zero_complex ) )
% 5.25/5.48 & ( ( C != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_divide_mult_cancel_left_if
% 5.25/5.48 thf(fact_2345_div__mult__mult1,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( C != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1
% 5.25/5.48 thf(fact_2346_div__mult__mult1,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( C != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.48 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1
% 5.25/5.48 thf(fact_2347_div__mult__mult1,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1
% 5.25/5.48 thf(fact_2348_div__mult__mult2,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( C != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult2
% 5.25/5.48 thf(fact_2349_div__mult__mult2,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( C != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult2
% 5.25/5.48 thf(fact_2350_div__mult__mult2,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult2
% 5.25/5.48 thf(fact_2351_div__mult__mult1__if,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( ( C = zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.48 = zero_zero_nat ) )
% 5.25/5.48 & ( ( C != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1_if
% 5.25/5.48 thf(fact_2352_div__mult__mult1__if,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( ( C = zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.48 = zero_zero_int ) )
% 5.25/5.48 & ( ( C != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.48 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1_if
% 5.25/5.48 thf(fact_2353_div__mult__mult1__if,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( ( C = zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.48 = zero_z3403309356797280102nteger ) )
% 5.25/5.48 & ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_mult1_if
% 5.25/5.48 thf(fact_2354_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: rat,B: rat,V: num] :
% 5.25/5.48 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_right_numeral
% 5.25/5.48 thf(fact_2355_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: extended_enat,B: extended_enat,V: num] :
% 5.25/5.48 ( ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ A @ B ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.25/5.48 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ V ) ) @ ( times_7803423173614009249d_enat @ B @ ( numera1916890842035813515d_enat @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_right_numeral
% 5.25/5.48 thf(fact_2356_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: complex,B: complex,V: num] :
% 5.25/5.48 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.25/5.48 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_right_numeral
% 5.25/5.48 thf(fact_2357_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: real,B: real,V: num] :
% 5.25/5.48 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_right_numeral
% 5.25/5.48 thf(fact_2358_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: nat,B: nat,V: num] :
% 5.25/5.48 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_right_numeral
% 5.25/5.48 thf(fact_2359_distrib__right__numeral,axiom,
% 5.25/5.48 ! [A: int,B: int,V: num] :
% 5.25/5.48 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_right_numeral
% 5.25/5.48 thf(fact_2360_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: rat,C: rat] :
% 5.25/5.48 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_left_numeral
% 5.25/5.48 thf(fact_2361_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: extended_enat,C: extended_enat] :
% 5.25/5.48 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ ( plus_p3455044024723400733d_enat @ B @ C ) )
% 5.25/5.48 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ B ) @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_left_numeral
% 5.25/5.48 thf(fact_2362_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: complex,C: complex] :
% 5.25/5.48 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.25/5.48 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_left_numeral
% 5.25/5.48 thf(fact_2363_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: real,C: real] :
% 5.25/5.48 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_left_numeral
% 5.25/5.48 thf(fact_2364_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: nat,C: nat] :
% 5.25/5.48 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % distrib_left_numeral
% 5.25/5.48 thf(fact_2365_distrib__left__numeral,axiom,
% 5.25/5.48 ! [V: num,B: int,C: int] :
% 5.25/5.48 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.25/5.48 = ( plus_plus_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 % distrib_left_numeral
% 5.25/5.48 thf(fact_2366_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_2367_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_2368_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_2369_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_2370_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_2371_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_2372_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_2373_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_2374_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_2375_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_2376_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_2377_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_2378_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_2379_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_2380_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_2381_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_2382_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_2383_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_2384_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_2385_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_2386_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_2387_dvd__add__times__triv__right__iff,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ B @ ( times_times_complex @ C @ A ) ) )
% 5.25/5.48 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_right_iff
% 5.25/5.48 thf(fact_2388_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_2389_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_2390_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_2391_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_2392_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_2393_dvd__add__times__triv__left__iff,axiom,
% 5.25/5.48 ! [A: complex,C: complex,B: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ A @ ( plus_plus_complex @ ( times_times_complex @ C @ A ) @ B ) )
% 5.25/5.48 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_times_triv_left_iff
% 5.25/5.48 thf(fact_2394_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_2395_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_2396_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_2397_mod__mult__self1__is__0,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1_is_0
% 5.25/5.48 thf(fact_2398_mod__mult__self1__is__0,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1_is_0
% 5.25/5.48 thf(fact_2399_mod__mult__self1__is__0,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.25/5.48 = zero_z3403309356797280102nteger ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1_is_0
% 5.25/5.48 thf(fact_2400_mod__mult__self2__is__0,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2_is_0
% 5.25/5.48 thf(fact_2401_mod__mult__self2__is__0,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2_is_0
% 5.25/5.48 thf(fact_2402_mod__mult__self2__is__0,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.25/5.48 = zero_z3403309356797280102nteger ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2_is_0
% 5.25/5.48 thf(fact_2403_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_2404_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_2405_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_2406_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_2407_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_2408_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_2409_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_2410_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_2411_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_2412_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_2413_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_2414_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_2415_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_2416_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_2417_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_2418_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_2419_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_2420_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_2421_mod__mult__self1,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.25/5.48 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1
% 5.25/5.48 thf(fact_2422_mod__mult__self1,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.25/5.48 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1
% 5.25/5.48 thf(fact_2423_mod__mult__self1,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.25/5.48 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self1
% 5.25/5.48 thf(fact_2424_mod__mult__self2,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.25/5.48 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2
% 5.25/5.48 thf(fact_2425_mod__mult__self2,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.25/5.48 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2
% 5.25/5.48 thf(fact_2426_mod__mult__self2,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.25/5.48 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self2
% 5.25/5.48 thf(fact_2427_mod__mult__self3,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self3
% 5.25/5.48 thf(fact_2428_mod__mult__self3,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self3
% 5.25/5.48 thf(fact_2429_mod__mult__self3,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self3
% 5.25/5.48 thf(fact_2430_mod__mult__self4,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self4
% 5.25/5.48 thf(fact_2431_mod__mult__self4,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self4
% 5.25/5.48 thf(fact_2432_mod__mult__self4,axiom,
% 5.25/5.48 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.48 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_mult_self4
% 5.25/5.48 thf(fact_2433_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_2434_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_2435_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_2436_one__le__mult__iff,axiom,
% 5.25/5.48 ! [M: nat,N2: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.48 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.48 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % one_le_mult_iff
% 5.25/5.48 thf(fact_2437_mult__le__cancel2,axiom,
% 5.25/5.48 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) )
% 5.25/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.48 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_le_cancel2
% 5.25/5.48 thf(fact_2438_nat__mult__le__cancel__disj,axiom,
% 5.25/5.48 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.48 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.48 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.48 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nat_mult_le_cancel_disj
% 5.25/5.48 thf(fact_2439_zero__less__of__bool__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.25/5.48 = P ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_of_bool_iff
% 5.25/5.48 thf(fact_2440_zero__less__of__bool__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.25/5.48 = P ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_of_bool_iff
% 5.25/5.48 thf(fact_2441_zero__less__of__bool__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.25/5.48 = P ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_of_bool_iff
% 5.25/5.48 thf(fact_2442_zero__less__of__bool__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.25/5.48 = P ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_of_bool_iff
% 5.25/5.48 thf(fact_2443_zero__less__of__bool__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.25/5.48 = P ) ).
% 5.25/5.48
% 5.25/5.48 % zero_less_of_bool_iff
% 5.25/5.48 thf(fact_2444_of__bool__less__one__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.25/5.48 = ~ P ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_less_one_iff
% 5.25/5.48 thf(fact_2445_of__bool__less__one__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.25/5.48 = ~ P ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_less_one_iff
% 5.25/5.48 thf(fact_2446_of__bool__less__one__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.25/5.48 = ~ P ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_less_one_iff
% 5.25/5.48 thf(fact_2447_of__bool__less__one__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.25/5.48 = ~ P ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_less_one_iff
% 5.25/5.48 thf(fact_2448_of__bool__less__one__iff,axiom,
% 5.25/5.48 ! [P: $o] :
% 5.25/5.48 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.25/5.48 = ~ P ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_less_one_iff
% 5.25/5.48 thf(fact_2449_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_2450_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_2451_div__mult__self1__is__m,axiom,
% 5.25/5.48 ! [N2: nat,M: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ N2 @ M ) @ N2 )
% 5.25/5.48 = M ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self1_is_m
% 5.25/5.48 thf(fact_2452_div__mult__self__is__m,axiom,
% 5.25/5.48 ! [N2: nat,M: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.48 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N2 ) @ N2 )
% 5.25/5.48 = M ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self_is_m
% 5.25/5.48 thf(fact_2453_Suc__0__mod__eq,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.25/5.48 = ( zero_n2687167440665602831ol_nat
% 5.25/5.48 @ ( N2
% 5.25/5.48 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_0_mod_eq
% 5.25/5.48 thf(fact_2454_Suc__mod__mult__self1,axiom,
% 5.25/5.48 ! [M: nat,K: nat,N2: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N2 ) ) ) @ N2 )
% 5.25/5.48 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_mod_mult_self1
% 5.25/5.48 thf(fact_2455_Suc__mod__mult__self2,axiom,
% 5.25/5.48 ! [M: nat,N2: nat,K: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N2 @ K ) ) ) @ N2 )
% 5.25/5.48 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_mod_mult_self2
% 5.25/5.48 thf(fact_2456_Suc__mod__mult__self3,axiom,
% 5.25/5.48 ! [K: nat,N2: nat,M: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N2 ) @ M ) ) @ N2 )
% 5.25/5.48 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_mod_mult_self3
% 5.25/5.48 thf(fact_2457_Suc__mod__mult__self4,axiom,
% 5.25/5.48 ! [N2: nat,K: nat,M: nat] :
% 5.25/5.48 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N2 @ K ) @ M ) ) @ N2 )
% 5.25/5.48 = ( modulo_modulo_nat @ ( suc @ M ) @ N2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_mod_mult_self4
% 5.25/5.48 thf(fact_2458_le__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: real,B: real,W: num] :
% 5.25/5.48 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.48 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2459_le__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: rat,B: rat,W: num] :
% 5.25/5.48 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.48 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2460_divide__le__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: real,W: num,A: real] :
% 5.25/5.48 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.25/5.48 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_le_eq_numeral1(1)
% 5.25/5.48 thf(fact_2461_divide__le__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: rat,W: num,A: rat] :
% 5.25/5.48 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.25/5.48 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_le_eq_numeral1(1)
% 5.25/5.48 thf(fact_2462_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: rat,B: rat,W: num] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.48 = ( ( ( ( numeral_numeral_rat @ W )
% 5.25/5.48 != zero_zero_rat )
% 5.25/5.48 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.25/5.48 = B ) )
% 5.25/5.48 & ( ( ( numeral_numeral_rat @ W )
% 5.25/5.48 = zero_zero_rat )
% 5.25/5.48 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % eq_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2463_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: real,B: real,W: num] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.48 = ( ( ( ( numeral_numeral_real @ W )
% 5.25/5.48 != zero_zero_real )
% 5.25/5.48 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.25/5.48 = B ) )
% 5.25/5.48 & ( ( ( numeral_numeral_real @ W )
% 5.25/5.48 = zero_zero_real )
% 5.25/5.48 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % eq_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2464_eq__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: complex,B: complex,W: num] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.25/5.48 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.48 != zero_zero_complex )
% 5.25/5.48 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.48 = B ) )
% 5.25/5.48 & ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.48 = zero_zero_complex )
% 5.25/5.48 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % eq_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2465_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: rat,W: num,A: rat] :
% 5.25/5.48 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.25/5.48 = A )
% 5.25/5.48 = ( ( ( ( numeral_numeral_rat @ W )
% 5.25/5.48 != zero_zero_rat )
% 5.25/5.48 => ( B
% 5.25/5.48 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.25/5.48 & ( ( ( numeral_numeral_rat @ W )
% 5.25/5.48 = zero_zero_rat )
% 5.25/5.48 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_eq_eq_numeral1(1)
% 5.25/5.48 thf(fact_2466_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: real,W: num,A: real] :
% 5.25/5.48 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.25/5.48 = A )
% 5.25/5.48 = ( ( ( ( numeral_numeral_real @ W )
% 5.25/5.48 != zero_zero_real )
% 5.25/5.48 => ( B
% 5.25/5.48 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.25/5.48 & ( ( ( numeral_numeral_real @ W )
% 5.25/5.48 = zero_zero_real )
% 5.25/5.48 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_eq_eq_numeral1(1)
% 5.25/5.48 thf(fact_2467_divide__eq__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: complex,W: num,A: complex] :
% 5.25/5.48 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.25/5.48 = A )
% 5.25/5.48 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.48 != zero_zero_complex )
% 5.25/5.48 => ( B
% 5.25/5.48 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.25/5.48 & ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.48 = zero_zero_complex )
% 5.25/5.48 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_eq_eq_numeral1(1)
% 5.25/5.48 thf(fact_2468_less__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: rat,B: rat,W: num] :
% 5.25/5.48 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.25/5.48 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2469_less__divide__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [A: real,B: real,W: num] :
% 5.25/5.48 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.25/5.48 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % less_divide_eq_numeral1(1)
% 5.25/5.48 thf(fact_2470_divide__less__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: rat,W: num,A: rat] :
% 5.25/5.48 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.25/5.48 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_less_eq_numeral1(1)
% 5.25/5.48 thf(fact_2471_divide__less__eq__numeral1_I1_J,axiom,
% 5.25/5.48 ! [B: real,W: num,A: real] :
% 5.25/5.48 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.25/5.48 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % divide_less_eq_numeral1(1)
% 5.25/5.48 thf(fact_2472_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [B: rat,A: rat] :
% 5.25/5.48 ( ( B != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.25/5.48 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2473_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [B: real,A: real] :
% 5.25/5.48 ( ( B != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.25/5.48 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2474_nonzero__divide__mult__cancel__right,axiom,
% 5.25/5.48 ! [B: complex,A: complex] :
% 5.25/5.48 ( ( B != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_right
% 5.25/5.48 thf(fact_2475_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [A: rat,B: rat] :
% 5.25/5.48 ( ( A != zero_zero_rat )
% 5.25/5.48 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.25/5.48 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2476_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [A: real,B: real] :
% 5.25/5.48 ( ( A != zero_zero_real )
% 5.25/5.48 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.25/5.48 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2477_nonzero__divide__mult__cancel__left,axiom,
% 5.25/5.48 ! [A: complex,B: complex] :
% 5.25/5.48 ( ( A != zero_zero_complex )
% 5.25/5.48 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.25/5.48 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nonzero_divide_mult_cancel_left
% 5.25/5.48 thf(fact_2478_div__mult__self4,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self4
% 5.25/5.48 thf(fact_2479_div__mult__self4,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self4
% 5.25/5.48 thf(fact_2480_div__mult__self4,axiom,
% 5.25/5.48 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self4
% 5.25/5.48 thf(fact_2481_div__mult__self3,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self3
% 5.25/5.48 thf(fact_2482_div__mult__self3,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self3
% 5.25/5.48 thf(fact_2483_div__mult__self3,axiom,
% 5.25/5.48 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self3
% 5.25/5.48 thf(fact_2484_div__mult__self2,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.25/5.48 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self2
% 5.25/5.48 thf(fact_2485_div__mult__self2,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.25/5.48 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self2
% 5.25/5.48 thf(fact_2486_div__mult__self2,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self2
% 5.25/5.48 thf(fact_2487_div__mult__self1,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.25/5.48 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self1
% 5.25/5.48 thf(fact_2488_div__mult__self1,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.25/5.48 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self1
% 5.25/5.48 thf(fact_2489_div__mult__self1,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.25/5.48 = ( plus_p5714425477246183910nteger @ C @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_self1
% 5.25/5.48 thf(fact_2490_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_2491_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_2492_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_2493_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_2494_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_2495_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_2496_pow__divides__pow__iff,axiom,
% 5.25/5.48 ! [N2: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) )
% 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_2497_pow__divides__pow__iff,axiom,
% 5.25/5.48 ! [N2: nat,A: int,B: int] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) )
% 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_2498_zmod__numeral__Bit0,axiom,
% 5.25/5.48 ! [V: num,W: num] :
% 5.25/5.48 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.25/5.48 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_numeral_Bit0
% 5.25/5.48 thf(fact_2499_power__add__numeral2,axiom,
% 5.25/5.48 ! [A: complex,M: num,N2: num,B: complex] :
% 5.25/5.48 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.25/5.48 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral2
% 5.25/5.48 thf(fact_2500_power__add__numeral2,axiom,
% 5.25/5.48 ! [A: real,M: num,N2: num,B: real] :
% 5.25/5.48 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.25/5.48 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral2
% 5.25/5.48 thf(fact_2501_power__add__numeral2,axiom,
% 5.25/5.48 ! [A: nat,M: num,N2: num,B: nat] :
% 5.25/5.48 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.25/5.48 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral2
% 5.25/5.48 thf(fact_2502_power__add__numeral2,axiom,
% 5.25/5.48 ! [A: int,M: num,N2: num,B: int] :
% 5.25/5.48 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) @ B ) )
% 5.25/5.48 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral2
% 5.25/5.48 thf(fact_2503_power__add__numeral,axiom,
% 5.25/5.48 ! [A: complex,M: num,N2: num] :
% 5.25/5.48 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.25/5.48 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral
% 5.25/5.48 thf(fact_2504_power__add__numeral,axiom,
% 5.25/5.48 ! [A: real,M: num,N2: num] :
% 5.25/5.48 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.25/5.48 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral
% 5.25/5.48 thf(fact_2505_power__add__numeral,axiom,
% 5.25/5.48 ! [A: nat,M: num,N2: num] :
% 5.25/5.48 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.25/5.48 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral
% 5.25/5.48 thf(fact_2506_power__add__numeral,axiom,
% 5.25/5.48 ! [A: int,M: num,N2: num] :
% 5.25/5.48 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N2 ) ) )
% 5.25/5.48 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % power_add_numeral
% 5.25/5.48 thf(fact_2507_Suc__times__numeral__mod__eq,axiom,
% 5.25/5.48 ! [K: num,N2: nat] :
% 5.25/5.48 ( ( ( numeral_numeral_nat @ K )
% 5.25/5.48 != one_one_nat )
% 5.25/5.48 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N2 ) ) @ ( numeral_numeral_nat @ K ) )
% 5.25/5.48 = one_one_nat ) ) ).
% 5.25/5.48
% 5.25/5.48 % Suc_times_numeral_mod_eq
% 5.25/5.48 thf(fact_2508_zle__add1__eq__le,axiom,
% 5.25/5.48 ! [W: int,Z: int] :
% 5.25/5.48 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.25/5.48 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.25/5.48
% 5.25/5.48 % zle_add1_eq_le
% 5.25/5.48 thf(fact_2509_mod__neg__neg__trivial,axiom,
% 5.25/5.48 ! [K: int,L: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.25/5.48 => ( ( ord_less_int @ L @ K )
% 5.25/5.48 => ( ( modulo_modulo_int @ K @ L )
% 5.25/5.48 = K ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_neg_neg_trivial
% 5.25/5.48 thf(fact_2510_mod__pos__pos__trivial,axiom,
% 5.25/5.48 ! [K: int,L: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.25/5.48 => ( ( ord_less_int @ K @ L )
% 5.25/5.48 => ( ( modulo_modulo_int @ K @ L )
% 5.25/5.48 = K ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_pos_pos_trivial
% 5.25/5.48 thf(fact_2511_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_2512_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_2513_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_2514_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_2515_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_2516_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_2517_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_2518_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_2519_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_2520_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_2521_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_2522_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_2523_even__Suc__Suc__iff,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N2 ) ) )
% 5.25/5.48 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc_Suc_iff
% 5.25/5.48 thf(fact_2524_even__Suc,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc
% 5.25/5.48 thf(fact_2525_odd__of__bool__self,axiom,
% 5.25/5.48 ! [P2: $o] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P2 ) ) )
% 5.25/5.48 = P2 ) ).
% 5.25/5.48
% 5.25/5.48 % odd_of_bool_self
% 5.25/5.48 thf(fact_2526_odd__of__bool__self,axiom,
% 5.25/5.48 ! [P2: $o] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P2 ) ) )
% 5.25/5.48 = P2 ) ).
% 5.25/5.48
% 5.25/5.48 % odd_of_bool_self
% 5.25/5.48 thf(fact_2527_odd__of__bool__self,axiom,
% 5.25/5.48 ! [P2: $o] :
% 5.25/5.48 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P2 ) ) )
% 5.25/5.48 = P2 ) ).
% 5.25/5.48
% 5.25/5.48 % odd_of_bool_self
% 5.25/5.48 thf(fact_2528_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_2529_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_2530_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_2531_of__bool__half__eq__0,axiom,
% 5.25/5.48 ! [B: $o] :
% 5.25/5.48 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = zero_zero_nat ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_half_eq_0
% 5.25/5.48 thf(fact_2532_of__bool__half__eq__0,axiom,
% 5.25/5.48 ! [B: $o] :
% 5.25/5.48 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.48 = zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_half_eq_0
% 5.25/5.48 thf(fact_2533_of__bool__half__eq__0,axiom,
% 5.25/5.48 ! [B: $o] :
% 5.25/5.48 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.48 = zero_z3403309356797280102nteger ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_half_eq_0
% 5.25/5.48 thf(fact_2534_even__Suc__div__two,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.48 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_Suc_div_two
% 5.25/5.48 thf(fact_2535_odd__Suc__div__two,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.25/5.48 => ( ( divide_divide_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.48 = ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_Suc_div_two
% 5.25/5.48 thf(fact_2536_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_2537_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_2538_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_2539_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_2540_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_2541_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_2542_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_2543_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_2544_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_2545_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_2546_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_2547_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_2548_even__power,axiom,
% 5.25/5.48 ! [A: code_integer,N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.25/5.48 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_2549_even__power,axiom,
% 5.25/5.48 ! [A: nat,N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N2 ) )
% 5.25/5.48 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_2550_even__power,axiom,
% 5.25/5.48 ! [A: int,N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N2 ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.48 & ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % even_power
% 5.25/5.48 thf(fact_2551_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_2552_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_2553_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_2554_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: real,N2: nat] :
% 5.25/5.48 ( ( ord_less_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 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_2555_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: rat,N2: nat] :
% 5.25/5.48 ( ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 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_2556_power__less__zero__eq,axiom,
% 5.25/5.48 ! [A: int,N2: nat] :
% 5.25/5.48 ( ( ord_less_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.25/5.48 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 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_2557_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_2558_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_2559_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_2560_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_2561_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_2562_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_2563_one__div__2__pow__eq,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % one_div_2_pow_eq
% 5.25/5.48 thf(fact_2564_one__div__2__pow__eq,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % one_div_2_pow_eq
% 5.25/5.48 thf(fact_2565_one__div__2__pow__eq,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % one_div_2_pow_eq
% 5.25/5.48 thf(fact_2566_bits__1__div__exp,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bits_1_div_exp
% 5.25/5.48 thf(fact_2567_bits__1__div__exp,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n2684676970156552555ol_int @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bits_1_div_exp
% 5.25/5.48 thf(fact_2568_bits__1__div__exp,axiom,
% 5.25/5.48 ! [N2: nat] :
% 5.25/5.48 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.48 = ( zero_n356916108424825756nteger @ ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bits_1_div_exp
% 5.25/5.48 thf(fact_2569_add1__zle__eq,axiom,
% 5.25/5.48 ! [W: int,Z: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.25/5.48 = ( ord_less_int @ W @ Z ) ) ).
% 5.25/5.48
% 5.25/5.48 % add1_zle_eq
% 5.25/5.48 thf(fact_2570_zdvd__imp__le,axiom,
% 5.25/5.48 ! [Z: int,N2: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ Z @ N2 )
% 5.25/5.48 => ( ( ord_less_int @ zero_zero_int @ N2 )
% 5.25/5.48 => ( ord_less_eq_int @ Z @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdvd_imp_le
% 5.25/5.48 thf(fact_2571_int__gr__induct,axiom,
% 5.25/5.48 ! [K: int,I2: int,P: int > $o] :
% 5.25/5.48 ( ( ord_less_int @ K @ I2 )
% 5.25/5.48 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.25/5.48 => ( ! [I4: int] :
% 5.25/5.48 ( ( ord_less_int @ K @ I4 )
% 5.25/5.48 => ( ( P @ I4 )
% 5.25/5.48 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.48 => ( P @ I2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % int_gr_induct
% 5.25/5.48 thf(fact_2572_le__imp__0__less,axiom,
% 5.25/5.48 ! [Z: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.25/5.48 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % le_imp_0_less
% 5.25/5.48 thf(fact_2573_zless__add1__eq,axiom,
% 5.25/5.48 ! [W: int,Z: int] :
% 5.25/5.48 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.25/5.48 = ( ( ord_less_int @ W @ Z )
% 5.25/5.48 | ( W = Z ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zless_add1_eq
% 5.25/5.48 thf(fact_2574_split__zmod,axiom,
% 5.25/5.48 ! [P: int > $o,N2: int,K: int] :
% 5.25/5.48 ( ( P @ ( modulo_modulo_int @ N2 @ K ) )
% 5.25/5.48 = ( ( ( K = zero_zero_int )
% 5.25/5.48 => ( P @ N2 ) )
% 5.25/5.48 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.48 => ! [I3: int,J3: int] :
% 5.25/5.48 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.48 & ( ord_less_int @ J3 @ K )
% 5.25/5.48 & ( N2
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.48 => ( P @ J3 ) ) )
% 5.25/5.48 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.48 => ! [I3: int,J3: int] :
% 5.25/5.48 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.48 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.48 & ( N2
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.48 => ( P @ J3 ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % split_zmod
% 5.25/5.48 thf(fact_2575_odd__less__0__iff,axiom,
% 5.25/5.48 ! [Z: int] :
% 5.25/5.48 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.25/5.48 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % odd_less_0_iff
% 5.25/5.48 thf(fact_2576_q__pos__lemma,axiom,
% 5.25/5.48 ! [B4: int,Q4: int,R4: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 5.25/5.48 => ( ( ord_less_int @ R4 @ B4 )
% 5.25/5.48 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.48 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % q_pos_lemma
% 5.25/5.48 thf(fact_2577_neg__mod__conj,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.48 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.25/5.48 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % neg_mod_conj
% 5.25/5.48 thf(fact_2578_pos__mod__conj,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.48 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % pos_mod_conj
% 5.25/5.48 thf(fact_2579_int__mod__neg__eq,axiom,
% 5.25/5.48 ! [A: int,B: int,Q3: int,R3: int] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.25/5.48 => ( ( ord_less_int @ B @ R3 )
% 5.25/5.48 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.48 = R3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % int_mod_neg_eq
% 5.25/5.48 thf(fact_2580_int__mod__pos__eq,axiom,
% 5.25/5.48 ! [A: int,B: int,Q3: int,R3: int] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.25/5.48 => ( ( ord_less_int @ R3 @ B )
% 5.25/5.48 => ( ( modulo_modulo_int @ A @ B )
% 5.25/5.48 = R3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % int_mod_pos_eq
% 5.25/5.48 thf(fact_2581_pos__zmult__eq__1__iff,axiom,
% 5.25/5.48 ! [M: int,N2: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ M )
% 5.25/5.48 => ( ( ( times_times_int @ M @ N2 )
% 5.25/5.48 = one_one_int )
% 5.25/5.48 = ( ( M = one_one_int )
% 5.25/5.48 & ( N2 = one_one_int ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % pos_zmult_eq_1_iff
% 5.25/5.48 thf(fact_2582_zless__imp__add1__zle,axiom,
% 5.25/5.48 ! [W: int,Z: int] :
% 5.25/5.48 ( ( ord_less_int @ W @ Z )
% 5.25/5.48 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.25/5.48
% 5.25/5.48 % zless_imp_add1_zle
% 5.25/5.48 thf(fact_2583_mod__int__pos__iff,axiom,
% 5.25/5.48 ! [K: int,L: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) )
% 5.25/5.48 = ( ( dvd_dvd_int @ L @ K )
% 5.25/5.48 | ( ( L = zero_zero_int )
% 5.25/5.48 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.25/5.48 | ( ord_less_int @ zero_zero_int @ L ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_int_pos_iff
% 5.25/5.48 thf(fact_2584_zdiv__mono2__lemma,axiom,
% 5.25/5.48 ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 5.25/5.48 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 5.25/5.48 => ( ( ord_less_int @ R4 @ B4 )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.25/5.48 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.48 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.48 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdiv_mono2_lemma
% 5.25/5.48 thf(fact_2585_zmod__trivial__iff,axiom,
% 5.25/5.48 ! [I2: int,K: int] :
% 5.25/5.48 ( ( ( modulo_modulo_int @ I2 @ K )
% 5.25/5.48 = I2 )
% 5.25/5.48 = ( ( K = zero_zero_int )
% 5.25/5.48 | ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.25/5.48 & ( ord_less_int @ I2 @ K ) )
% 5.25/5.48 | ( ( ord_less_eq_int @ I2 @ zero_zero_int )
% 5.25/5.48 & ( ord_less_int @ K @ I2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_trivial_iff
% 5.25/5.48 thf(fact_2586_zdiv__mono2__neg__lemma,axiom,
% 5.25/5.48 ! [B: int,Q3: int,R3: int,B4: int,Q4: int,R4: int] :
% 5.25/5.48 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 )
% 5.25/5.48 = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) )
% 5.25/5.48 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R4 ) @ zero_zero_int )
% 5.25/5.48 => ( ( ord_less_int @ R3 @ B )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.25/5.48 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.25/5.48 => ( ( ord_less_eq_int @ B4 @ B )
% 5.25/5.48 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdiv_mono2_neg_lemma
% 5.25/5.48 thf(fact_2587_int__one__le__iff__zero__less,axiom,
% 5.25/5.48 ! [Z: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.25/5.48 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.25/5.48
% 5.25/5.48 % int_one_le_iff_zero_less
% 5.25/5.48 thf(fact_2588_unique__quotient__lemma,axiom,
% 5.25/5.48 ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ R4 )
% 5.25/5.48 => ( ( ord_less_int @ R4 @ B )
% 5.25/5.48 => ( ( ord_less_int @ R3 @ B )
% 5.25/5.48 => ( ord_less_eq_int @ Q4 @ Q3 ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unique_quotient_lemma
% 5.25/5.48 thf(fact_2589_neg__mod__sign,axiom,
% 5.25/5.48 ! [L: int,K: int] :
% 5.25/5.48 ( ( ord_less_int @ L @ zero_zero_int )
% 5.25/5.48 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L ) @ zero_zero_int ) ) ).
% 5.25/5.48
% 5.25/5.48 % neg_mod_sign
% 5.25/5.48 thf(fact_2590_Euclidean__Division_Opos__mod__sign,axiom,
% 5.25/5.48 ! [L: int,K: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ L )
% 5.25/5.48 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % Euclidean_Division.pos_mod_sign
% 5.25/5.48 thf(fact_2591_unique__quotient__lemma__neg,axiom,
% 5.25/5.48 ! [B: int,Q4: int,R4: int,Q3: int,R3: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R4 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.48 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.25/5.48 => ( ( ord_less_int @ B @ R3 )
% 5.25/5.48 => ( ( ord_less_int @ B @ R4 )
% 5.25/5.48 => ( ord_less_eq_int @ Q3 @ Q4 ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unique_quotient_lemma_neg
% 5.25/5.48 thf(fact_2592_mod__pos__neg__trivial,axiom,
% 5.25/5.48 ! [K: int,L: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.48 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.25/5.48 => ( ( modulo_modulo_int @ K @ L )
% 5.25/5.48 = ( plus_plus_int @ K @ L ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mod_pos_neg_trivial
% 5.25/5.48 thf(fact_2593_zmod__le__nonneg__dividend,axiom,
% 5.25/5.48 ! [M: int,K: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.25/5.48 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_le_nonneg_dividend
% 5.25/5.48 thf(fact_2594_zdvd__antisym__nonneg,axiom,
% 5.25/5.48 ! [M: int,N2: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.25/5.48 => ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.25/5.48 => ( ( dvd_dvd_int @ M @ N2 )
% 5.25/5.48 => ( ( dvd_dvd_int @ N2 @ M )
% 5.25/5.48 => ( M = N2 ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdvd_antisym_nonneg
% 5.25/5.48 thf(fact_2595_verit__la__generic,axiom,
% 5.25/5.48 ! [A: int,X4: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ A @ X4 )
% 5.25/5.48 | ( A = X4 )
% 5.25/5.48 | ( ord_less_eq_int @ X4 @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % verit_la_generic
% 5.25/5.48 thf(fact_2596_less__eq__int__code_I1_J,axiom,
% 5.25/5.48 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.25/5.48
% 5.25/5.48 % less_eq_int_code(1)
% 5.25/5.48 thf(fact_2597_zmod__eq__0D,axiom,
% 5.25/5.48 ! [M: int,D: int] :
% 5.25/5.48 ( ( ( modulo_modulo_int @ M @ D )
% 5.25/5.48 = zero_zero_int )
% 5.25/5.48 => ? [Q2: int] :
% 5.25/5.48 ( M
% 5.25/5.48 = ( times_times_int @ D @ Q2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_eq_0D
% 5.25/5.48 thf(fact_2598_zmod__eq__0__iff,axiom,
% 5.25/5.48 ! [M: int,D: int] :
% 5.25/5.48 ( ( ( modulo_modulo_int @ M @ D )
% 5.25/5.48 = zero_zero_int )
% 5.25/5.48 = ( ? [Q5: int] :
% 5.25/5.48 ( M
% 5.25/5.48 = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmod_eq_0_iff
% 5.25/5.48 thf(fact_2599_Euclidean__Division_Opos__mod__bound,axiom,
% 5.25/5.48 ! [L: int,K: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ L )
% 5.25/5.48 => ( ord_less_int @ ( modulo_modulo_int @ K @ L ) @ L ) ) ).
% 5.25/5.48
% 5.25/5.48 % Euclidean_Division.pos_mod_bound
% 5.25/5.48 thf(fact_2600_neg__mod__bound,axiom,
% 5.25/5.48 ! [L: int,K: int] :
% 5.25/5.48 ( ( ord_less_int @ L @ zero_zero_int )
% 5.25/5.48 => ( ord_less_int @ L @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % neg_mod_bound
% 5.25/5.48 thf(fact_2601_zmult__zless__mono2,axiom,
% 5.25/5.48 ! [I2: int,J: int,K: int] :
% 5.25/5.48 ( ( ord_less_int @ I2 @ J )
% 5.25/5.48 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.48 => ( ord_less_int @ ( times_times_int @ K @ I2 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zmult_zless_mono2
% 5.25/5.48 thf(fact_2602_zdvd__not__zless,axiom,
% 5.25/5.48 ! [M: int,N2: int] :
% 5.25/5.48 ( ( ord_less_int @ zero_zero_int @ M )
% 5.25/5.48 => ( ( ord_less_int @ M @ N2 )
% 5.25/5.48 => ~ ( dvd_dvd_int @ N2 @ M ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % zdvd_not_zless
% 5.25/5.48 thf(fact_2603_less__int__code_I1_J,axiom,
% 5.25/5.48 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.25/5.48
% 5.25/5.48 % less_int_code(1)
% 5.25/5.48 thf(fact_2604_iadd__is__0,axiom,
% 5.25/5.48 ! [M: extended_enat,N2: extended_enat] :
% 5.25/5.48 ( ( ( plus_p3455044024723400733d_enat @ M @ N2 )
% 5.25/5.48 = zero_z5237406670263579293d_enat )
% 5.25/5.48 = ( ( M = zero_z5237406670263579293d_enat )
% 5.25/5.48 & ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % iadd_is_0
% 5.25/5.48 thf(fact_2605_imult__is__0,axiom,
% 5.25/5.48 ! [M: extended_enat,N2: extended_enat] :
% 5.25/5.48 ( ( ( times_7803423173614009249d_enat @ M @ N2 )
% 5.25/5.48 = zero_z5237406670263579293d_enat )
% 5.25/5.48 = ( ( M = zero_z5237406670263579293d_enat )
% 5.25/5.48 | ( N2 = zero_z5237406670263579293d_enat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % imult_is_0
% 5.25/5.48 thf(fact_2606_zero__one__enat__neq_I1_J,axiom,
% 5.25/5.48 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.25/5.48
% 5.25/5.48 % zero_one_enat_neq(1)
% 5.25/5.48 thf(fact_2607_int__ge__induct,axiom,
% 5.25/5.48 ! [K: int,I2: int,P: int > $o] :
% 5.25/5.48 ( ( ord_less_eq_int @ K @ I2 )
% 5.25/5.48 => ( ( P @ K )
% 5.25/5.48 => ( ! [I4: int] :
% 5.25/5.48 ( ( ord_less_eq_int @ K @ I4 )
% 5.25/5.48 => ( ( P @ I4 )
% 5.25/5.48 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.25/5.48 => ( P @ I2 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % int_ge_induct
% 5.25/5.48 thf(fact_2608_is__unit__mult__iff,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_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
% 5.25/5.48 % is_unit_mult_iff
% 5.25/5.48 thf(fact_2609_is__unit__mult__iff,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_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
% 5.25/5.48 % is_unit_mult_iff
% 5.25/5.48 thf(fact_2610_is__unit__mult__iff,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_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
% 5.25/5.48 % is_unit_mult_iff
% 5.25/5.48 thf(fact_2611_dvd__mult__unit__iff,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff
% 5.25/5.48 thf(fact_2612_dvd__mult__unit__iff,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff
% 5.25/5.48 thf(fact_2613_dvd__mult__unit__iff,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff
% 5.25/5.48 thf(fact_2614_mult__unit__dvd__iff,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: 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 ) @ C )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff
% 5.25/5.48 thf(fact_2615_mult__unit__dvd__iff,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff
% 5.25/5.48 thf(fact_2616_mult__unit__dvd__iff,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff
% 5.25/5.48 thf(fact_2617_dvd__mult__unit__iff_H,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff'
% 5.25/5.48 thf(fact_2618_dvd__mult__unit__iff_H,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff'
% 5.25/5.48 thf(fact_2619_dvd__mult__unit__iff_H,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_unit_iff'
% 5.25/5.48 thf(fact_2620_mult__unit__dvd__iff_H,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff'
% 5.25/5.48 thf(fact_2621_mult__unit__dvd__iff_H,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff'
% 5.25/5.48 thf(fact_2622_mult__unit__dvd__iff_H,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_unit_dvd_iff'
% 5.25/5.48 thf(fact_2623_unit__mult__left__cancel,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.25/5.48 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_left_cancel
% 5.25/5.48 thf(fact_2624_unit__mult__left__cancel,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( ( times_times_nat @ A @ B )
% 5.25/5.48 = ( times_times_nat @ A @ C ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_left_cancel
% 5.25/5.48 thf(fact_2625_unit__mult__left__cancel,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( ( times_times_int @ A @ B )
% 5.25/5.48 = ( times_times_int @ A @ C ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_left_cancel
% 5.25/5.48 thf(fact_2626_unit__mult__right__cancel,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.48 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.25/5.48 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_right_cancel
% 5.25/5.48 thf(fact_2627_unit__mult__right__cancel,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ( ( ( times_times_nat @ B @ A )
% 5.25/5.48 = ( times_times_nat @ C @ A ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_right_cancel
% 5.25/5.48 thf(fact_2628_unit__mult__right__cancel,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ( ( ( times_times_int @ B @ A )
% 5.25/5.48 = ( times_times_int @ C @ A ) )
% 5.25/5.48 = ( B = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_mult_right_cancel
% 5.25/5.48 thf(fact_2629_dvd__div__mult,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.25/5.48 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult
% 5.25/5.48 thf(fact_2630_dvd__div__mult,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.25/5.48 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult
% 5.25/5.48 thf(fact_2631_dvd__div__mult,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult
% 5.25/5.48 thf(fact_2632_div__mult__swap,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_swap
% 5.25/5.48 thf(fact_2633_div__mult__swap,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_swap
% 5.25/5.48 thf(fact_2634_div__mult__swap,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_swap
% 5.25/5.48 thf(fact_2635_div__div__eq__right,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.48 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_eq_right
% 5.25/5.48 thf(fact_2636_div__div__eq__right,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.48 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_eq_right
% 5.25/5.48 thf(fact_2637_div__div__eq__right,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.48 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_eq_right
% 5.25/5.48 thf(fact_2638_dvd__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult2_eq
% 5.25/5.48 thf(fact_2639_dvd__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.25/5.48 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult2_eq
% 5.25/5.48 thf(fact_2640_dvd__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_mult2_eq
% 5.25/5.48 thf(fact_2641_dvd__mult__imp__div,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.25/5.48 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_imp_div
% 5.25/5.48 thf(fact_2642_dvd__mult__imp__div,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.25/5.48 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_imp_div
% 5.25/5.48 thf(fact_2643_dvd__mult__imp__div,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 ) @ B )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_imp_div
% 5.25/5.48 thf(fact_2644_div__mult__div__if__dvd,axiom,
% 5.25/5.48 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_nat @ D @ C )
% 5.25/5.48 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.25/5.48 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_div_if_dvd
% 5.25/5.48 thf(fact_2645_div__mult__div__if__dvd,axiom,
% 5.25/5.48 ! [B: int,A: int,D: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_int @ D @ C )
% 5.25/5.48 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.25/5.48 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_div_if_dvd
% 5.25/5.48 thf(fact_2646_div__mult__div__if__dvd,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_div_if_dvd
% 5.25/5.48 thf(fact_2647_dvd__antisym,axiom,
% 5.25/5.48 ! [M: nat,N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ M @ N2 )
% 5.25/5.48 => ( ( dvd_dvd_nat @ N2 @ M )
% 5.25/5.48 => ( M = N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_antisym
% 5.25/5.48 thf(fact_2648_bezout__lemma__nat,axiom,
% 5.25/5.48 ! [D: nat,A: nat,B: nat,X4: nat,Y: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ D @ A )
% 5.25/5.48 => ( ( dvd_dvd_nat @ D @ B )
% 5.25/5.48 => ( ( ( ( times_times_nat @ A @ X4 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.25/5.48 | ( ( times_times_nat @ B @ X4 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.25/5.48 => ? [X5: nat,Y3: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ D @ A )
% 5.25/5.48 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.25/5.48 & ( ( ( times_times_nat @ A @ X5 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y3 ) @ D ) )
% 5.25/5.48 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X5 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bezout_lemma_nat
% 5.25/5.48 thf(fact_2649_bezout__add__nat,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ? [D3: nat,X5: nat,Y3: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ D3 @ A )
% 5.25/5.48 & ( dvd_dvd_nat @ D3 @ B )
% 5.25/5.48 & ( ( ( times_times_nat @ A @ X5 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) )
% 5.25/5.48 | ( ( times_times_nat @ B @ X5 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ A @ Y3 ) @ D3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bezout_add_nat
% 5.25/5.48 thf(fact_2650_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.48 thf(fact_2651_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.48 thf(fact_2652_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.48 thf(fact_2653_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % ab_semigroup_mult_class.mult_ac(1)
% 5.25/5.48 thf(fact_2654_dvdE,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ~ ! [K2: code_integer] :
% 5.25/5.48 ( A
% 5.25/5.48 != ( times_3573771949741848930nteger @ B @ K2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdE
% 5.25/5.48 thf(fact_2655_dvdE,axiom,
% 5.25/5.48 ! [B: complex,A: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ B @ A )
% 5.25/5.48 => ~ ! [K2: complex] :
% 5.25/5.48 ( A
% 5.25/5.48 != ( times_times_complex @ B @ K2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdE
% 5.25/5.48 thf(fact_2656_dvdE,axiom,
% 5.25/5.48 ! [B: real,A: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ B @ A )
% 5.25/5.48 => ~ ! [K2: real] :
% 5.25/5.48 ( A
% 5.25/5.48 != ( times_times_real @ B @ K2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdE
% 5.25/5.48 thf(fact_2657_dvdE,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ~ ! [K2: nat] :
% 5.25/5.48 ( A
% 5.25/5.48 != ( times_times_nat @ B @ K2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdE
% 5.25/5.48 thf(fact_2658_dvdE,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ~ ! [K2: int] :
% 5.25/5.48 ( A
% 5.25/5.48 != ( times_times_int @ B @ K2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdE
% 5.25/5.48 thf(fact_2659_dvdI,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdI
% 5.25/5.48 thf(fact_2660_dvdI,axiom,
% 5.25/5.48 ! [A: complex,B: complex,K: complex] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( times_times_complex @ B @ K ) )
% 5.25/5.48 => ( dvd_dvd_complex @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdI
% 5.25/5.48 thf(fact_2661_dvdI,axiom,
% 5.25/5.48 ! [A: real,B: real,K: real] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( times_times_real @ B @ K ) )
% 5.25/5.48 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdI
% 5.25/5.48 thf(fact_2662_dvdI,axiom,
% 5.25/5.48 ! [A: nat,B: nat,K: nat] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( times_times_nat @ B @ K ) )
% 5.25/5.48 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdI
% 5.25/5.48 thf(fact_2663_dvdI,axiom,
% 5.25/5.48 ! [A: int,B: int,K: int] :
% 5.25/5.48 ( ( A
% 5.25/5.48 = ( times_times_int @ B @ K ) )
% 5.25/5.48 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvdI
% 5.25/5.48 thf(fact_2664_dvd__def,axiom,
% 5.25/5.48 ( dvd_dvd_Code_integer
% 5.25/5.48 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.25/5.48 ? [K3: code_integer] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( times_3573771949741848930nteger @ B2 @ K3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_def
% 5.25/5.48 thf(fact_2665_dvd__def,axiom,
% 5.25/5.48 ( dvd_dvd_complex
% 5.25/5.48 = ( ^ [B2: complex,A3: complex] :
% 5.25/5.48 ? [K3: complex] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( times_times_complex @ B2 @ K3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_def
% 5.25/5.48 thf(fact_2666_dvd__def,axiom,
% 5.25/5.48 ( dvd_dvd_real
% 5.25/5.48 = ( ^ [B2: real,A3: real] :
% 5.25/5.48 ? [K3: real] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( times_times_real @ B2 @ K3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_def
% 5.25/5.48 thf(fact_2667_dvd__def,axiom,
% 5.25/5.48 ( dvd_dvd_nat
% 5.25/5.48 = ( ^ [B2: nat,A3: nat] :
% 5.25/5.48 ? [K3: nat] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( times_times_nat @ B2 @ K3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_def
% 5.25/5.48 thf(fact_2668_dvd__def,axiom,
% 5.25/5.48 ( dvd_dvd_int
% 5.25/5.48 = ( ^ [B2: int,A3: int] :
% 5.25/5.48 ? [K3: int] :
% 5.25/5.48 ( A3
% 5.25/5.48 = ( times_times_int @ B2 @ K3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_def
% 5.25/5.48 thf(fact_2669_of__bool__conj,axiom,
% 5.25/5.48 ! [P: $o,Q: $o] :
% 5.25/5.48 ( ( zero_n1201886186963655149omplex
% 5.25/5.48 @ ( P
% 5.25/5.48 & Q ) )
% 5.25/5.48 = ( times_times_complex @ ( zero_n1201886186963655149omplex @ P ) @ ( zero_n1201886186963655149omplex @ Q ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_conj
% 5.25/5.48 thf(fact_2670_of__bool__conj,axiom,
% 5.25/5.48 ! [P: $o,Q: $o] :
% 5.25/5.48 ( ( zero_n3304061248610475627l_real
% 5.25/5.48 @ ( P
% 5.25/5.48 & Q ) )
% 5.25/5.48 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_conj
% 5.25/5.48 thf(fact_2671_of__bool__conj,axiom,
% 5.25/5.48 ! [P: $o,Q: $o] :
% 5.25/5.48 ( ( zero_n2687167440665602831ol_nat
% 5.25/5.48 @ ( P
% 5.25/5.48 & Q ) )
% 5.25/5.48 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_conj
% 5.25/5.48 thf(fact_2672_of__bool__conj,axiom,
% 5.25/5.48 ! [P: $o,Q: $o] :
% 5.25/5.48 ( ( zero_n2684676970156552555ol_int
% 5.25/5.48 @ ( P
% 5.25/5.48 & Q ) )
% 5.25/5.48 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_conj
% 5.25/5.48 thf(fact_2673_of__bool__conj,axiom,
% 5.25/5.48 ! [P: $o,Q: $o] :
% 5.25/5.48 ( ( zero_n356916108424825756nteger
% 5.25/5.48 @ ( P
% 5.25/5.48 & Q ) )
% 5.25/5.48 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_conj
% 5.25/5.48 thf(fact_2674_dvd__mult,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult
% 5.25/5.48 thf(fact_2675_dvd__mult,axiom,
% 5.25/5.48 ! [A: complex,C: complex,B: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ A @ C )
% 5.25/5.48 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult
% 5.25/5.48 thf(fact_2676_dvd__mult,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ C )
% 5.25/5.48 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult
% 5.25/5.48 thf(fact_2677_dvd__mult,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.48 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult
% 5.25/5.48 thf(fact_2678_dvd__mult,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ C )
% 5.25/5.48 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult
% 5.25/5.48 thf(fact_2679_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_2680_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_2681_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_2682_mult_Oassoc,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( times_times_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.assoc
% 5.25/5.48 thf(fact_2683_mult_Oassoc,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.assoc
% 5.25/5.48 thf(fact_2684_mult_Oassoc,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.assoc
% 5.25/5.48 thf(fact_2685_mult_Oassoc,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.assoc
% 5.25/5.48 thf(fact_2686_dvd__mult2,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 @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult2
% 5.25/5.48 thf(fact_2687_dvd__mult2,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ A @ B )
% 5.25/5.48 => ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult2
% 5.25/5.48 thf(fact_2688_dvd__mult2,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.48 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult2
% 5.25/5.48 thf(fact_2689_dvd__mult2,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 @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult2
% 5.25/5.48 thf(fact_2690_dvd__mult2,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 @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult2
% 5.25/5.48 thf(fact_2691_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_2692_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_2693_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_2694_of__bool__eq__iff,axiom,
% 5.25/5.48 ! [P2: $o,Q3: $o] :
% 5.25/5.48 ( ( ( zero_n2687167440665602831ol_nat @ P2 )
% 5.25/5.48 = ( zero_n2687167440665602831ol_nat @ Q3 ) )
% 5.25/5.48 = ( P2 = Q3 ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_eq_iff
% 5.25/5.48 thf(fact_2695_of__bool__eq__iff,axiom,
% 5.25/5.48 ! [P2: $o,Q3: $o] :
% 5.25/5.48 ( ( ( zero_n2684676970156552555ol_int @ P2 )
% 5.25/5.48 = ( zero_n2684676970156552555ol_int @ Q3 ) )
% 5.25/5.48 = ( P2 = Q3 ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_eq_iff
% 5.25/5.48 thf(fact_2696_of__bool__eq__iff,axiom,
% 5.25/5.48 ! [P2: $o,Q3: $o] :
% 5.25/5.48 ( ( ( zero_n356916108424825756nteger @ P2 )
% 5.25/5.48 = ( zero_n356916108424825756nteger @ Q3 ) )
% 5.25/5.48 = ( P2 = Q3 ) ) ).
% 5.25/5.48
% 5.25/5.48 % of_bool_eq_iff
% 5.25/5.48 thf(fact_2697_dvd__mult__left,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_left
% 5.25/5.48 thf(fact_2698_dvd__mult__left,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_complex @ A @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_left
% 5.25/5.48 thf(fact_2699_dvd__mult__left,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_left
% 5.25/5.48 thf(fact_2700_dvd__mult__left,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_left
% 5.25/5.48 thf(fact_2701_dvd__mult__left,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_left
% 5.25/5.48 thf(fact_2702_dvd__triv__left,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_left
% 5.25/5.48 thf(fact_2703_dvd__triv__left,axiom,
% 5.25/5.48 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_left
% 5.25/5.48 thf(fact_2704_dvd__triv__left,axiom,
% 5.25/5.48 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_left
% 5.25/5.48 thf(fact_2705_dvd__triv__left,axiom,
% 5.25/5.48 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_left
% 5.25/5.48 thf(fact_2706_dvd__triv__left,axiom,
% 5.25/5.48 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_left
% 5.25/5.48 thf(fact_2707_mult__dvd__mono,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_dvd_mono
% 5.25/5.48 thf(fact_2708_mult__dvd__mono,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_complex @ C @ D )
% 5.25/5.48 => ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_dvd_mono
% 5.25/5.48 thf(fact_2709_mult__dvd__mono,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_real @ C @ D )
% 5.25/5.48 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_dvd_mono
% 5.25/5.48 thf(fact_2710_mult__dvd__mono,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ D )
% 5.25/5.48 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_dvd_mono
% 5.25/5.48 thf(fact_2711_mult__dvd__mono,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ D )
% 5.25/5.48 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult_dvd_mono
% 5.25/5.48 thf(fact_2712_mult_Ocommute,axiom,
% 5.25/5.48 ( times_times_complex
% 5.25/5.48 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.commute
% 5.25/5.48 thf(fact_2713_mult_Ocommute,axiom,
% 5.25/5.48 ( times_times_real
% 5.25/5.48 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.commute
% 5.25/5.48 thf(fact_2714_mult_Ocommute,axiom,
% 5.25/5.48 ( times_times_nat
% 5.25/5.48 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.commute
% 5.25/5.48 thf(fact_2715_mult_Ocommute,axiom,
% 5.25/5.48 ( times_times_int
% 5.25/5.48 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.commute
% 5.25/5.48 thf(fact_2716_dvd__mult__right,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_right
% 5.25/5.48 thf(fact_2717_dvd__mult__right,axiom,
% 5.25/5.48 ! [A: complex,B: complex,C: complex] :
% 5.25/5.48 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_complex @ B @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_right
% 5.25/5.48 thf(fact_2718_dvd__mult__right,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_right
% 5.25/5.48 thf(fact_2719_dvd__mult__right,axiom,
% 5.25/5.48 ! [A: nat,B: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_right
% 5.25/5.48 thf(fact_2720_dvd__mult__right,axiom,
% 5.25/5.48 ! [A: int,B: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.48 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_right
% 5.25/5.48 thf(fact_2721_dvd__triv__right,axiom,
% 5.25/5.48 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_right
% 5.25/5.48 thf(fact_2722_dvd__triv__right,axiom,
% 5.25/5.48 ! [A: complex,B: complex] : ( dvd_dvd_complex @ A @ ( times_times_complex @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_right
% 5.25/5.48 thf(fact_2723_dvd__triv__right,axiom,
% 5.25/5.48 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_right
% 5.25/5.48 thf(fact_2724_dvd__triv__right,axiom,
% 5.25/5.48 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_right
% 5.25/5.48 thf(fact_2725_dvd__triv__right,axiom,
% 5.25/5.48 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_triv_right
% 5.25/5.48 thf(fact_2726_mult_Oleft__commute,axiom,
% 5.25/5.48 ! [B: complex,A: complex,C: complex] :
% 5.25/5.48 ( ( times_times_complex @ B @ ( times_times_complex @ A @ C ) )
% 5.25/5.48 = ( times_times_complex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.left_commute
% 5.25/5.48 thf(fact_2727_mult_Oleft__commute,axiom,
% 5.25/5.48 ! [B: real,A: real,C: real] :
% 5.25/5.48 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.25/5.48 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.left_commute
% 5.25/5.48 thf(fact_2728_mult_Oleft__commute,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.25/5.48 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.left_commute
% 5.25/5.48 thf(fact_2729_mult_Oleft__commute,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.25/5.48 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % mult.left_commute
% 5.25/5.48 thf(fact_2730_bezout__add__strong__nat,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( A != zero_zero_nat )
% 5.25/5.48 => ? [D3: nat,X5: nat,Y3: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ D3 @ A )
% 5.25/5.48 & ( dvd_dvd_nat @ D3 @ B )
% 5.25/5.48 & ( ( times_times_nat @ A @ X5 )
% 5.25/5.48 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ D3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % bezout_add_strong_nat
% 5.25/5.48 thf(fact_2731_unit__dvdE,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 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.48 => ! [C3: code_integer] :
% 5.25/5.48 ( B
% 5.25/5.48 != ( times_3573771949741848930nteger @ A @ C3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_dvdE
% 5.25/5.48 thf(fact_2732_unit__dvdE,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.48 => ~ ( ( A != zero_zero_nat )
% 5.25/5.48 => ! [C3: nat] :
% 5.25/5.48 ( B
% 5.25/5.48 != ( times_times_nat @ A @ C3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_dvdE
% 5.25/5.48 thf(fact_2733_unit__dvdE,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.48 => ~ ( ( A != zero_zero_int )
% 5.25/5.48 => ! [C3: int] :
% 5.25/5.48 ( B
% 5.25/5.48 != ( times_times_int @ A @ C3 ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_dvdE
% 5.25/5.48 thf(fact_2734_dvd__div__eq__mult,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 @ A @ B )
% 5.25/5.48 => ( ( ( divide_divide_nat @ B @ A )
% 5.25/5.48 = C )
% 5.25/5.48 = ( B
% 5.25/5.48 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_mult
% 5.25/5.48 thf(fact_2735_dvd__div__eq__mult,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 @ A @ B )
% 5.25/5.48 => ( ( ( divide_divide_int @ B @ A )
% 5.25/5.48 = C )
% 5.25/5.48 = ( B
% 5.25/5.48 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_mult
% 5.25/5.48 thf(fact_2736_dvd__div__eq__mult,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 @ A @ B )
% 5.25/5.48 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.25/5.48 = C )
% 5.25/5.48 = ( B
% 5.25/5.48 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_mult
% 5.25/5.48 thf(fact_2737_div__dvd__iff__mult,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( B != zero_zero_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_iff_mult
% 5.25/5.48 thf(fact_2738_div__dvd__iff__mult,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( B != zero_zero_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_iff_mult
% 5.25/5.48 thf(fact_2739_div__dvd__iff__mult,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( B != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_dvd_iff_mult
% 5.25/5.48 thf(fact_2740_dvd__div__iff__mult,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( C != zero_zero_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_iff_mult
% 5.25/5.48 thf(fact_2741_dvd__div__iff__mult,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( C != zero_zero_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_iff_mult
% 5.25/5.48 thf(fact_2742_dvd__div__iff__mult,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_iff_mult
% 5.25/5.48 thf(fact_2743_dvd__div__div__eq__mult,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.25/5.48 ( ( A != zero_zero_nat )
% 5.25/5.48 => ( ( C != zero_zero_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ D )
% 5.25/5.48 => ( ( ( divide_divide_nat @ B @ A )
% 5.25/5.48 = ( divide_divide_nat @ D @ C ) )
% 5.25/5.48 = ( ( times_times_nat @ B @ C )
% 5.25/5.48 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_div_eq_mult
% 5.25/5.48 thf(fact_2744_dvd__div__div__eq__mult,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int,D: int] :
% 5.25/5.48 ( ( A != zero_zero_int )
% 5.25/5.48 => ( ( C != zero_zero_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ D )
% 5.25/5.48 => ( ( ( divide_divide_int @ B @ A )
% 5.25/5.48 = ( divide_divide_int @ D @ C ) )
% 5.25/5.48 = ( ( times_times_int @ B @ C )
% 5.25/5.48 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_div_eq_mult
% 5.25/5.48 thf(fact_2745_dvd__div__div__eq__mult,axiom,
% 5.25/5.48 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.25/5.48 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( C != zero_z3403309356797280102nteger )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.25/5.48 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.25/5.48 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.25/5.48 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.25/5.48 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_div_eq_mult
% 5.25/5.48 thf(fact_2746_is__unit__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: nat,C: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.48 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % is_unit_div_mult2_eq
% 5.25/5.48 thf(fact_2747_is__unit__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: int,C: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.48 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % is_unit_div_mult2_eq
% 5.25/5.48 thf(fact_2748_is__unit__div__mult2__eq,axiom,
% 5.25/5.48 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % is_unit_div_mult2_eq
% 5.25/5.48 thf(fact_2749_unit__div__mult__swap,axiom,
% 5.25/5.48 ! [C: nat,A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.48 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_swap
% 5.25/5.48 thf(fact_2750_unit__div__mult__swap,axiom,
% 5.25/5.48 ! [C: int,A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.48 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_swap
% 5.25/5.48 thf(fact_2751_unit__div__mult__swap,axiom,
% 5.25/5.48 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_mult_swap
% 5.25/5.48 thf(fact_2752_unit__div__commute,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.25/5.48 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_commute
% 5.25/5.48 thf(fact_2753_unit__div__commute,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.25/5.48 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_commute
% 5.25/5.48 thf(fact_2754_unit__div__commute,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_div_commute
% 5.25/5.48 thf(fact_2755_div__mult__unit2,axiom,
% 5.25/5.48 ! [C: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.25/5.48 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_unit2
% 5.25/5.48 thf(fact_2756_div__mult__unit2,axiom,
% 5.25/5.48 ! [C: int,B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.48 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_unit2
% 5.25/5.48 thf(fact_2757_div__mult__unit2,axiom,
% 5.25/5.48 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_mult_unit2
% 5.25/5.48 thf(fact_2758_unit__eq__div2,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( A
% 5.25/5.48 = ( divide_divide_nat @ C @ B ) )
% 5.25/5.48 = ( ( times_times_nat @ A @ B )
% 5.25/5.48 = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div2
% 5.25/5.48 thf(fact_2759_unit__eq__div2,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( A
% 5.25/5.48 = ( divide_divide_int @ C @ B ) )
% 5.25/5.48 = ( ( times_times_int @ A @ B )
% 5.25/5.48 = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div2
% 5.25/5.48 thf(fact_2760_unit__eq__div2,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( A
% 5.25/5.48 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.25/5.48 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.25/5.48 = C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div2
% 5.25/5.48 thf(fact_2761_unit__eq__div1,axiom,
% 5.25/5.48 ! [B: nat,A: nat,C: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( ( ( divide_divide_nat @ A @ B )
% 5.25/5.48 = C )
% 5.25/5.48 = ( A
% 5.25/5.48 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div1
% 5.25/5.48 thf(fact_2762_unit__eq__div1,axiom,
% 5.25/5.48 ! [B: int,A: int,C: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( ( ( divide_divide_int @ A @ B )
% 5.25/5.48 = C )
% 5.25/5.48 = ( A
% 5.25/5.48 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div1
% 5.25/5.48 thf(fact_2763_unit__eq__div1,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.48 = C )
% 5.25/5.48 = ( A
% 5.25/5.48 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_eq_div1
% 5.25/5.48 thf(fact_2764_nat__mult__dvd__cancel1,axiom,
% 5.25/5.48 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.48 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.48 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.48 = ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % nat_mult_dvd_cancel1
% 5.25/5.48 thf(fact_2765_dvd__mult__cancel,axiom,
% 5.25/5.48 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.48 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.48 => ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_mult_cancel
% 5.25/5.48 thf(fact_2766_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_2767_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_2768_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_2769_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_2770_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_2771_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_2772_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_2773_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_2774_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_2775_dvd__unit__imp__unit,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 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_unit_imp_unit
% 5.25/5.48 thf(fact_2776_dvd__unit__imp__unit,axiom,
% 5.25/5.48 ! [A: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_unit_imp_unit
% 5.25/5.48 thf(fact_2777_dvd__unit__imp__unit,axiom,
% 5.25/5.48 ! [A: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_unit_imp_unit
% 5.25/5.48 thf(fact_2778_unit__imp__dvd,axiom,
% 5.25/5.48 ! [B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.48 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_imp_dvd
% 5.25/5.48 thf(fact_2779_unit__imp__dvd,axiom,
% 5.25/5.48 ! [B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.48 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_imp_dvd
% 5.25/5.48 thf(fact_2780_unit__imp__dvd,axiom,
% 5.25/5.48 ! [B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.48 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.25/5.48
% 5.25/5.48 % unit_imp_dvd
% 5.25/5.48 thf(fact_2781_one__dvd,axiom,
% 5.25/5.48 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2782_one__dvd,axiom,
% 5.25/5.48 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2783_one__dvd,axiom,
% 5.25/5.48 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2784_one__dvd,axiom,
% 5.25/5.48 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2785_one__dvd,axiom,
% 5.25/5.48 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2786_one__dvd,axiom,
% 5.25/5.48 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.25/5.48
% 5.25/5.48 % one_dvd
% 5.25/5.48 thf(fact_2787_dvd__add__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 @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_right_iff
% 5.25/5.48 thf(fact_2788_dvd__add__right__iff,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_right_iff
% 5.25/5.48 thf(fact_2789_dvd__add__right__iff,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_right_iff
% 5.25/5.48 thf(fact_2790_dvd__add__right__iff,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 @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_right_iff
% 5.25/5.48 thf(fact_2791_dvd__add__right__iff,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 @ ( plus_plus_int @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_right_iff
% 5.25/5.48 thf(fact_2792_dvd__add__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 @ C )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_left_iff
% 5.25/5.48 thf(fact_2793_dvd__add__left__iff,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_left_iff
% 5.25/5.48 thf(fact_2794_dvd__add__left__iff,axiom,
% 5.25/5.48 ! [A: rat,C: rat,B: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_left_iff
% 5.25/5.48 thf(fact_2795_dvd__add__left__iff,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_left_iff
% 5.25/5.48 thf(fact_2796_dvd__add__left__iff,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ A @ C )
% 5.25/5.48 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.48 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add_left_iff
% 5.25/5.48 thf(fact_2797_dvd__add,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 @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add
% 5.25/5.48 thf(fact_2798_dvd__add,axiom,
% 5.25/5.48 ! [A: real,B: real,C: real] :
% 5.25/5.48 ( ( dvd_dvd_real @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_real @ A @ C )
% 5.25/5.48 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add
% 5.25/5.48 thf(fact_2799_dvd__add,axiom,
% 5.25/5.48 ! [A: rat,B: rat,C: rat] :
% 5.25/5.48 ( ( dvd_dvd_rat @ A @ B )
% 5.25/5.48 => ( ( dvd_dvd_rat @ A @ C )
% 5.25/5.48 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add
% 5.25/5.48 thf(fact_2800_dvd__add,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 @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add
% 5.25/5.48 thf(fact_2801_dvd__add,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 @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_add
% 5.25/5.48 thf(fact_2802_div__div__div__same,axiom,
% 5.25/5.48 ! [D: nat,B: nat,A: nat] :
% 5.25/5.48 ( ( dvd_dvd_nat @ D @ B )
% 5.25/5.48 => ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.48 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.25/5.48 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_div_same
% 5.25/5.48 thf(fact_2803_div__div__div__same,axiom,
% 5.25/5.48 ! [D: int,B: int,A: int] :
% 5.25/5.48 ( ( dvd_dvd_int @ D @ B )
% 5.25/5.48 => ( ( dvd_dvd_int @ B @ A )
% 5.25/5.48 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.25/5.48 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_div_same
% 5.25/5.48 thf(fact_2804_div__div__div__same,axiom,
% 5.25/5.48 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.25/5.48 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.25/5.48 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.48 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.25/5.48 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % div_div_div_same
% 5.25/5.48 thf(fact_2805_dvd__div__eq__cancel,axiom,
% 5.25/5.48 ! [A: nat,C: nat,B: nat] :
% 5.25/5.48 ( ( ( divide_divide_nat @ A @ C )
% 5.25/5.48 = ( divide_divide_nat @ B @ C ) )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_nat @ C @ B )
% 5.25/5.48 => ( A = B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_cancel
% 5.25/5.48 thf(fact_2806_dvd__div__eq__cancel,axiom,
% 5.25/5.48 ! [A: int,C: int,B: int] :
% 5.25/5.48 ( ( ( divide_divide_int @ A @ C )
% 5.25/5.48 = ( divide_divide_int @ B @ C ) )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_int @ C @ B )
% 5.25/5.48 => ( A = B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_cancel
% 5.25/5.48 thf(fact_2807_dvd__div__eq__cancel,axiom,
% 5.25/5.48 ! [A: real,C: real,B: real] :
% 5.25/5.48 ( ( ( divide_divide_real @ A @ C )
% 5.25/5.48 = ( divide_divide_real @ B @ C ) )
% 5.25/5.48 => ( ( dvd_dvd_real @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_real @ C @ B )
% 5.25/5.48 => ( A = B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_cancel
% 5.25/5.48 thf(fact_2808_dvd__div__eq__cancel,axiom,
% 5.25/5.48 ! [A: complex,C: complex,B: complex] :
% 5.25/5.48 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.25/5.48 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.48 => ( ( dvd_dvd_complex @ C @ A )
% 5.25/5.48 => ( ( dvd_dvd_complex @ C @ B )
% 5.25/5.48 => ( A = B ) ) ) ) ).
% 5.25/5.48
% 5.25/5.48 % dvd_div_eq_cancel
% 5.25/5.49 thf(fact_2809_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_2810_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_2811_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_2812_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_2813_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_2814_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_2815_dvd__power__same,axiom,
% 5.25/5.49 ! [X4: code_integer,Y: code_integer,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_2816_dvd__power__same,axiom,
% 5.25/5.49 ! [X4: nat,Y: nat,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ X4 @ Y )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_2817_dvd__power__same,axiom,
% 5.25/5.49 ! [X4: real,Y: real,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ X4 @ Y )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_2818_dvd__power__same,axiom,
% 5.25/5.49 ! [X4: int,Y: int,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ X4 @ Y )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_2819_dvd__power__same,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ X4 @ Y )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_same
% 5.25/5.49 thf(fact_2820_mult__not__zero,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ( times_times_rat @ A @ B )
% 5.25/5.49 != zero_zero_rat )
% 5.25/5.49 => ( ( A != zero_zero_rat )
% 5.25/5.49 & ( B != zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_not_zero
% 5.25/5.49 thf(fact_2821_mult__not__zero,axiom,
% 5.25/5.49 ! [A: complex,B: complex] :
% 5.25/5.49 ( ( ( times_times_complex @ A @ B )
% 5.25/5.49 != zero_zero_complex )
% 5.25/5.49 => ( ( A != zero_zero_complex )
% 5.25/5.49 & ( B != zero_zero_complex ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_not_zero
% 5.25/5.49 thf(fact_2822_mult__not__zero,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ( times_times_real @ A @ B )
% 5.25/5.49 != zero_zero_real )
% 5.25/5.49 => ( ( A != zero_zero_real )
% 5.25/5.49 & ( B != zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_not_zero
% 5.25/5.49 thf(fact_2823_mult__not__zero,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ( times_times_nat @ A @ B )
% 5.25/5.49 != zero_zero_nat )
% 5.25/5.49 => ( ( A != zero_zero_nat )
% 5.25/5.49 & ( B != zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_not_zero
% 5.25/5.49 thf(fact_2824_mult__not__zero,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( times_times_int @ A @ B )
% 5.25/5.49 != zero_zero_int )
% 5.25/5.49 => ( ( A != zero_zero_int )
% 5.25/5.49 & ( B != zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_not_zero
% 5.25/5.49 thf(fact_2825_divisors__zero,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ( times_times_rat @ A @ B )
% 5.25/5.49 = zero_zero_rat )
% 5.25/5.49 => ( ( A = zero_zero_rat )
% 5.25/5.49 | ( B = zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divisors_zero
% 5.25/5.49 thf(fact_2826_divisors__zero,axiom,
% 5.25/5.49 ! [A: complex,B: complex] :
% 5.25/5.49 ( ( ( times_times_complex @ A @ B )
% 5.25/5.49 = zero_zero_complex )
% 5.25/5.49 => ( ( A = zero_zero_complex )
% 5.25/5.49 | ( B = zero_zero_complex ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divisors_zero
% 5.25/5.49 thf(fact_2827_divisors__zero,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ( times_times_real @ A @ B )
% 5.25/5.49 = zero_zero_real )
% 5.25/5.49 => ( ( A = zero_zero_real )
% 5.25/5.49 | ( B = zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divisors_zero
% 5.25/5.49 thf(fact_2828_divisors__zero,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ( times_times_nat @ A @ B )
% 5.25/5.49 = zero_zero_nat )
% 5.25/5.49 => ( ( A = zero_zero_nat )
% 5.25/5.49 | ( B = zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divisors_zero
% 5.25/5.49 thf(fact_2829_divisors__zero,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( times_times_int @ A @ B )
% 5.25/5.49 = zero_zero_int )
% 5.25/5.49 => ( ( A = zero_zero_int )
% 5.25/5.49 | ( B = zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divisors_zero
% 5.25/5.49 thf(fact_2830_no__zero__divisors,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( A != zero_zero_rat )
% 5.25/5.49 => ( ( B != zero_zero_rat )
% 5.25/5.49 => ( ( times_times_rat @ A @ B )
% 5.25/5.49 != zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % no_zero_divisors
% 5.25/5.49 thf(fact_2831_no__zero__divisors,axiom,
% 5.25/5.49 ! [A: complex,B: complex] :
% 5.25/5.49 ( ( A != zero_zero_complex )
% 5.25/5.49 => ( ( B != zero_zero_complex )
% 5.25/5.49 => ( ( times_times_complex @ A @ B )
% 5.25/5.49 != zero_zero_complex ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % no_zero_divisors
% 5.25/5.49 thf(fact_2832_no__zero__divisors,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( A != zero_zero_real )
% 5.25/5.49 => ( ( B != zero_zero_real )
% 5.25/5.49 => ( ( times_times_real @ A @ B )
% 5.25/5.49 != zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % no_zero_divisors
% 5.25/5.49 thf(fact_2833_no__zero__divisors,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( A != zero_zero_nat )
% 5.25/5.49 => ( ( B != zero_zero_nat )
% 5.25/5.49 => ( ( times_times_nat @ A @ B )
% 5.25/5.49 != zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % no_zero_divisors
% 5.25/5.49 thf(fact_2834_no__zero__divisors,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( A != zero_zero_int )
% 5.25/5.49 => ( ( B != zero_zero_int )
% 5.25/5.49 => ( ( times_times_int @ A @ B )
% 5.25/5.49 != zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % no_zero_divisors
% 5.25/5.49 thf(fact_2835_mult__left__cancel,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( ( times_times_rat @ C @ A )
% 5.25/5.49 = ( times_times_rat @ C @ B ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_cancel
% 5.25/5.49 thf(fact_2836_mult__left__cancel,axiom,
% 5.25/5.49 ! [C: complex,A: complex,B: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( ( times_times_complex @ C @ A )
% 5.25/5.49 = ( times_times_complex @ C @ B ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_cancel
% 5.25/5.49 thf(fact_2837_mult__left__cancel,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( ( times_times_real @ C @ A )
% 5.25/5.49 = ( times_times_real @ C @ B ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_cancel
% 5.25/5.49 thf(fact_2838_mult__left__cancel,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( C != zero_zero_nat )
% 5.25/5.49 => ( ( ( times_times_nat @ C @ A )
% 5.25/5.49 = ( times_times_nat @ C @ B ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_cancel
% 5.25/5.49 thf(fact_2839_mult__left__cancel,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( C != zero_zero_int )
% 5.25/5.49 => ( ( ( times_times_int @ C @ A )
% 5.25/5.49 = ( times_times_int @ C @ B ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_cancel
% 5.25/5.49 thf(fact_2840_mult__right__cancel,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( ( times_times_rat @ A @ C )
% 5.25/5.49 = ( times_times_rat @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_cancel
% 5.25/5.49 thf(fact_2841_mult__right__cancel,axiom,
% 5.25/5.49 ! [C: complex,A: complex,B: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( ( times_times_complex @ A @ C )
% 5.25/5.49 = ( times_times_complex @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_cancel
% 5.25/5.49 thf(fact_2842_mult__right__cancel,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( ( times_times_real @ A @ C )
% 5.25/5.49 = ( times_times_real @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_cancel
% 5.25/5.49 thf(fact_2843_mult__right__cancel,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( C != zero_zero_nat )
% 5.25/5.49 => ( ( ( times_times_nat @ A @ C )
% 5.25/5.49 = ( times_times_nat @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_cancel
% 5.25/5.49 thf(fact_2844_mult__right__cancel,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( C != zero_zero_int )
% 5.25/5.49 => ( ( ( times_times_int @ A @ C )
% 5.25/5.49 = ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( A = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_cancel
% 5.25/5.49 thf(fact_2845_mult_Ocomm__neutral,axiom,
% 5.25/5.49 ! [A: rat] :
% 5.25/5.49 ( ( times_times_rat @ A @ one_one_rat )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult.comm_neutral
% 5.25/5.49 thf(fact_2846_mult_Ocomm__neutral,axiom,
% 5.25/5.49 ! [A: complex] :
% 5.25/5.49 ( ( times_times_complex @ A @ one_one_complex )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult.comm_neutral
% 5.25/5.49 thf(fact_2847_mult_Ocomm__neutral,axiom,
% 5.25/5.49 ! [A: real] :
% 5.25/5.49 ( ( times_times_real @ A @ one_one_real )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult.comm_neutral
% 5.25/5.49 thf(fact_2848_mult_Ocomm__neutral,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( times_times_nat @ A @ one_one_nat )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult.comm_neutral
% 5.25/5.49 thf(fact_2849_mult_Ocomm__neutral,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( times_times_int @ A @ one_one_int )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult.comm_neutral
% 5.25/5.49 thf(fact_2850_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.49 ! [A: rat] :
% 5.25/5.49 ( ( times_times_rat @ one_one_rat @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % comm_monoid_mult_class.mult_1
% 5.25/5.49 thf(fact_2851_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.49 ! [A: complex] :
% 5.25/5.49 ( ( times_times_complex @ one_one_complex @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % comm_monoid_mult_class.mult_1
% 5.25/5.49 thf(fact_2852_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.49 ! [A: real] :
% 5.25/5.49 ( ( times_times_real @ one_one_real @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % comm_monoid_mult_class.mult_1
% 5.25/5.49 thf(fact_2853_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( times_times_nat @ one_one_nat @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % comm_monoid_mult_class.mult_1
% 5.25/5.49 thf(fact_2854_comm__monoid__mult__class_Omult__1,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( times_times_int @ one_one_int @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % comm_monoid_mult_class.mult_1
% 5.25/5.49 thf(fact_2855_combine__common__factor,axiom,
% 5.25/5.49 ! [A: rat,E2: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ C ) )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % combine_common_factor
% 5.25/5.49 thf(fact_2856_combine__common__factor,axiom,
% 5.25/5.49 ! [A: complex,E2: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ C ) )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ E2 ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % combine_common_factor
% 5.25/5.49 thf(fact_2857_combine__common__factor,axiom,
% 5.25/5.49 ! [A: real,E2: real,B: real,C: real] :
% 5.25/5.49 ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ C ) )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E2 ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % combine_common_factor
% 5.25/5.49 thf(fact_2858_combine__common__factor,axiom,
% 5.25/5.49 ! [A: nat,E2: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( plus_plus_nat @ ( times_times_nat @ A @ E2 ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E2 ) @ C ) )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E2 ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % combine_common_factor
% 5.25/5.49 thf(fact_2859_combine__common__factor,axiom,
% 5.25/5.49 ! [A: int,E2: int,B: int,C: int] :
% 5.25/5.49 ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ C ) )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E2 ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % combine_common_factor
% 5.25/5.49 thf(fact_2860_distrib__right,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_right
% 5.25/5.49 thf(fact_2861_distrib__right,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_right
% 5.25/5.49 thf(fact_2862_distrib__right,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_right
% 5.25/5.49 thf(fact_2863_distrib__right,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_right
% 5.25/5.49 thf(fact_2864_distrib__right,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_right
% 5.25/5.49 thf(fact_2865_distrib__left,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_left
% 5.25/5.49 thf(fact_2866_distrib__left,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_left
% 5.25/5.49 thf(fact_2867_distrib__left,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_left
% 5.25/5.49 thf(fact_2868_distrib__left,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_left
% 5.25/5.49 thf(fact_2869_distrib__left,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % distrib_left
% 5.25/5.49 thf(fact_2870_comm__semiring__class_Odistrib,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % comm_semiring_class.distrib
% 5.25/5.49 thf(fact_2871_comm__semiring__class_Odistrib,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % comm_semiring_class.distrib
% 5.25/5.49 thf(fact_2872_comm__semiring__class_Odistrib,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % comm_semiring_class.distrib
% 5.25/5.49 thf(fact_2873_comm__semiring__class_Odistrib,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % comm_semiring_class.distrib
% 5.25/5.49 thf(fact_2874_comm__semiring__class_Odistrib,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % comm_semiring_class.distrib
% 5.25/5.49 thf(fact_2875_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(1)
% 5.25/5.49 thf(fact_2876_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( times_times_complex @ A @ ( plus_plus_complex @ B @ C ) )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(1)
% 5.25/5.49 thf(fact_2877_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(1)
% 5.25/5.49 thf(fact_2878_ring__class_Oring__distribs_I1_J,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(1)
% 5.25/5.49 thf(fact_2879_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(2)
% 5.25/5.49 thf(fact_2880_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(2)
% 5.25/5.49 thf(fact_2881_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(2)
% 5.25/5.49 thf(fact_2882_ring__class_Oring__distribs_I2_J,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ring_class.ring_distribs(2)
% 5.25/5.49 thf(fact_2883_dvd__mod,axiom,
% 5.25/5.49 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.25/5.49 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_2884_dvd__mod,axiom,
% 5.25/5.49 ! [K: int,M: int,N2: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_int @ K @ N2 )
% 5.25/5.49 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_2885_dvd__mod,axiom,
% 5.25/5.49 ! [K: code_integer,M: code_integer,N2: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ K @ N2 )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mod
% 5.25/5.49 thf(fact_2886_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_2887_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_2888_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_2889_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_2890_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_2891_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_2892_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_2893_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_2894_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_2895_divide__divide__eq__left_H,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.25/5.49 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_divide_eq_left'
% 5.25/5.49 thf(fact_2896_divide__divide__eq__left_H,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.25/5.49 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_divide_eq_left'
% 5.25/5.49 thf(fact_2897_divide__divide__times__eq,axiom,
% 5.25/5.49 ! [X4: real,Y: real,Z: real,W: real] :
% 5.25/5.49 ( ( divide_divide_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.25/5.49 = ( divide_divide_real @ ( times_times_real @ X4 @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_divide_times_eq
% 5.25/5.49 thf(fact_2898_divide__divide__times__eq,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 5.25/5.49 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.25/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_divide_times_eq
% 5.25/5.49 thf(fact_2899_times__divide__times__eq,axiom,
% 5.25/5.49 ! [X4: real,Y: real,Z: real,W: real] :
% 5.25/5.49 ( ( times_times_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.25/5.49 = ( divide_divide_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % times_divide_times_eq
% 5.25/5.49 thf(fact_2900_times__divide__times__eq,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,Z: complex,W: complex] :
% 5.25/5.49 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.25/5.49 = ( divide1717551699836669952omplex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % times_divide_times_eq
% 5.25/5.49 thf(fact_2901_power__commuting__commutes,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,N2: nat] :
% 5.25/5.49 ( ( ( times_times_complex @ X4 @ Y )
% 5.25/5.49 = ( times_times_complex @ Y @ X4 ) )
% 5.25/5.49 => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ Y )
% 5.25/5.49 = ( times_times_complex @ Y @ ( power_power_complex @ X4 @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commuting_commutes
% 5.25/5.49 thf(fact_2902_power__commuting__commutes,axiom,
% 5.25/5.49 ! [X4: real,Y: real,N2: nat] :
% 5.25/5.49 ( ( ( times_times_real @ X4 @ Y )
% 5.25/5.49 = ( times_times_real @ Y @ X4 ) )
% 5.25/5.49 => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ Y )
% 5.25/5.49 = ( times_times_real @ Y @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commuting_commutes
% 5.25/5.49 thf(fact_2903_power__commuting__commutes,axiom,
% 5.25/5.49 ! [X4: nat,Y: nat,N2: nat] :
% 5.25/5.49 ( ( ( times_times_nat @ X4 @ Y )
% 5.25/5.49 = ( times_times_nat @ Y @ X4 ) )
% 5.25/5.49 => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ Y )
% 5.25/5.49 = ( times_times_nat @ Y @ ( power_power_nat @ X4 @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commuting_commutes
% 5.25/5.49 thf(fact_2904_power__commuting__commutes,axiom,
% 5.25/5.49 ! [X4: int,Y: int,N2: nat] :
% 5.25/5.49 ( ( ( times_times_int @ X4 @ Y )
% 5.25/5.49 = ( times_times_int @ Y @ X4 ) )
% 5.25/5.49 => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ Y )
% 5.25/5.49 = ( times_times_int @ Y @ ( power_power_int @ X4 @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commuting_commutes
% 5.25/5.49 thf(fact_2905_power__mult__distrib,axiom,
% 5.25/5.49 ! [A: complex,B: complex,N2: nat] :
% 5.25/5.49 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N2 )
% 5.25/5.49 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ ( power_power_complex @ B @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult_distrib
% 5.25/5.49 thf(fact_2906_power__mult__distrib,axiom,
% 5.25/5.49 ! [A: real,B: real,N2: nat] :
% 5.25/5.49 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N2 )
% 5.25/5.49 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult_distrib
% 5.25/5.49 thf(fact_2907_power__mult__distrib,axiom,
% 5.25/5.49 ! [A: nat,B: nat,N2: nat] :
% 5.25/5.49 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N2 )
% 5.25/5.49 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult_distrib
% 5.25/5.49 thf(fact_2908_power__mult__distrib,axiom,
% 5.25/5.49 ! [A: int,B: int,N2: nat] :
% 5.25/5.49 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N2 )
% 5.25/5.49 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult_distrib
% 5.25/5.49 thf(fact_2909_power__commutes,axiom,
% 5.25/5.49 ! [A: complex,N2: nat] :
% 5.25/5.49 ( ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A )
% 5.25/5.49 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commutes
% 5.25/5.49 thf(fact_2910_power__commutes,axiom,
% 5.25/5.49 ! [A: real,N2: nat] :
% 5.25/5.49 ( ( times_times_real @ ( power_power_real @ A @ N2 ) @ A )
% 5.25/5.49 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commutes
% 5.25/5.49 thf(fact_2911_power__commutes,axiom,
% 5.25/5.49 ! [A: nat,N2: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A )
% 5.25/5.49 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commutes
% 5.25/5.49 thf(fact_2912_power__commutes,axiom,
% 5.25/5.49 ! [A: int,N2: nat] :
% 5.25/5.49 ( ( times_times_int @ ( power_power_int @ A @ N2 ) @ A )
% 5.25/5.49 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_commutes
% 5.25/5.49 thf(fact_2913_Suc__mult__cancel1,axiom,
% 5.25/5.49 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.49 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.25/5.49 = ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.25/5.49 = ( M = N2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % Suc_mult_cancel1
% 5.25/5.49 thf(fact_2914_power__mult,axiom,
% 5.25/5.49 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.49 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.49 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult
% 5.25/5.49 thf(fact_2915_power__mult,axiom,
% 5.25/5.49 ! [A: real,M: nat,N2: nat] :
% 5.25/5.49 ( ( power_power_real @ A @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.49 = ( power_power_real @ ( power_power_real @ A @ M ) @ N2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult
% 5.25/5.49 thf(fact_2916_power__mult,axiom,
% 5.25/5.49 ! [A: int,M: nat,N2: nat] :
% 5.25/5.49 ( ( power_power_int @ A @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.49 = ( power_power_int @ ( power_power_int @ A @ M ) @ N2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult
% 5.25/5.49 thf(fact_2917_power__mult,axiom,
% 5.25/5.49 ! [A: complex,M: nat,N2: nat] :
% 5.25/5.49 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N2 ) )
% 5.25/5.49 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N2 ) ) ).
% 5.25/5.49
% 5.25/5.49 % power_mult
% 5.25/5.49 thf(fact_2918_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.25/5.49 ! [X4: produc3368934014287244435at_num] :
% 5.25/5.49 ~ ! [F2: nat > num > num,A5: nat,B5: nat,Acc: num] :
% 5.25/5.49 ( X4
% 5.25/5.49 != ( produc851828971589881931at_num @ F2 @ ( produc1195630363706982562at_num @ A5 @ ( product_Pair_nat_num @ B5 @ Acc ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % fold_atLeastAtMost_nat.cases
% 5.25/5.49 thf(fact_2919_fold__atLeastAtMost__nat_Ocases,axiom,
% 5.25/5.49 ! [X4: produc4471711990508489141at_nat] :
% 5.25/5.49 ~ ! [F2: nat > nat > nat,A5: nat,B5: nat,Acc: nat] :
% 5.25/5.49 ( X4
% 5.25/5.49 != ( produc3209952032786966637at_nat @ F2 @ ( produc487386426758144856at_nat @ A5 @ ( product_Pair_nat_nat @ B5 @ Acc ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % fold_atLeastAtMost_nat.cases
% 5.25/5.49 thf(fact_2920_mult__0,axiom,
% 5.25/5.49 ! [N2: nat] :
% 5.25/5.49 ( ( times_times_nat @ zero_zero_nat @ N2 )
% 5.25/5.49 = zero_zero_nat ) ).
% 5.25/5.49
% 5.25/5.49 % mult_0
% 5.25/5.49 thf(fact_2921_nat__mult__eq__cancel__disj,axiom,
% 5.25/5.49 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.49 ( ( ( times_times_nat @ K @ M )
% 5.25/5.49 = ( times_times_nat @ K @ N2 ) )
% 5.25/5.49 = ( ( K = zero_zero_nat )
% 5.25/5.49 | ( M = N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nat_mult_eq_cancel_disj
% 5.25/5.49 thf(fact_2922_mult__le__mono2,axiom,
% 5.25/5.49 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_mono2
% 5.25/5.49 thf(fact_2923_mult__le__mono1,axiom,
% 5.25/5.49 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_mono1
% 5.25/5.49 thf(fact_2924_mult__le__mono,axiom,
% 5.25/5.49 ! [I2: nat,J: nat,K: nat,L: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ I2 @ J )
% 5.25/5.49 => ( ( ord_less_eq_nat @ K @ L )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_mono
% 5.25/5.49 thf(fact_2925_le__square,axiom,
% 5.25/5.49 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_square
% 5.25/5.49 thf(fact_2926_le__cube,axiom,
% 5.25/5.49 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_cube
% 5.25/5.49 thf(fact_2927_mod__mult__eq,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_eq
% 5.25/5.49 thf(fact_2928_mod__mult__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_eq
% 5.25/5.49 thf(fact_2929_mod__mult__eq,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_eq
% 5.25/5.49 thf(fact_2930_mod__mult__cong,axiom,
% 5.25/5.49 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.25/5.49 ( ( ( modulo_modulo_nat @ A @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.25/5.49 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.25/5.49 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_cong
% 5.25/5.49 thf(fact_2931_mod__mult__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 @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_cong
% 5.25/5.49 thf(fact_2932_mod__mult__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 @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_cong
% 5.25/5.49 thf(fact_2933_mod__mult__mult2,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.49 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_mult2
% 5.25/5.49 thf(fact_2934_mod__mult__mult2,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_mult2
% 5.25/5.49 thf(fact_2935_mod__mult__mult2,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.25/5.49 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_mult2
% 5.25/5.49 thf(fact_2936_mult__mod__right,axiom,
% 5.25/5.49 ! [C: nat,A: nat,B: nat] :
% 5.25/5.49 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.49 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mod_right
% 5.25/5.49 thf(fact_2937_mult__mod__right,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.49 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mod_right
% 5.25/5.49 thf(fact_2938_mult__mod__right,axiom,
% 5.25/5.49 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mod_right
% 5.25/5.49 thf(fact_2939_mod__mult__left__eq,axiom,
% 5.25/5.49 ! [A: nat,C: nat,B: nat] :
% 5.25/5.49 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_left_eq
% 5.25/5.49 thf(fact_2940_mod__mult__left__eq,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_left_eq
% 5.25/5.49 thf(fact_2941_mod__mult__left__eq,axiom,
% 5.25/5.49 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_left_eq
% 5.25/5.49 thf(fact_2942_mod__mult__right__eq,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_right_eq
% 5.25/5.49 thf(fact_2943_mod__mult__right__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_right_eq
% 5.25/5.49 thf(fact_2944_mod__mult__right__eq,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.49 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.25/5.49 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.25/5.49
% 5.25/5.49 % mod_mult_right_eq
% 5.25/5.49 thf(fact_2945_left__add__mult__distrib,axiom,
% 5.25/5.49 ! [I2: nat,U: nat,J: nat,K: nat] :
% 5.25/5.49 ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I2 @ J ) @ U ) @ K ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_add_mult_distrib
% 5.25/5.49 thf(fact_2946_add__mult__distrib2,axiom,
% 5.25/5.49 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.49 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_mult_distrib2
% 5.25/5.49 thf(fact_2947_add__mult__distrib,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,K: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( plus_plus_nat @ M @ N2 ) @ K )
% 5.25/5.49 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % add_mult_distrib
% 5.25/5.49 thf(fact_2948_nat__mult__1__right,axiom,
% 5.25/5.49 ! [N2: nat] :
% 5.25/5.49 ( ( times_times_nat @ N2 @ one_one_nat )
% 5.25/5.49 = N2 ) ).
% 5.25/5.49
% 5.25/5.49 % nat_mult_1_right
% 5.25/5.49 thf(fact_2949_nat__mult__1,axiom,
% 5.25/5.49 ! [N2: nat] :
% 5.25/5.49 ( ( times_times_nat @ one_one_nat @ N2 )
% 5.25/5.49 = N2 ) ).
% 5.25/5.49
% 5.25/5.49 % nat_mult_1
% 5.25/5.49 thf(fact_2950_div__mult2__eq,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,Q3: nat] :
% 5.25/5.49 ( ( divide_divide_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 5.25/5.49 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult2_eq
% 5.25/5.49 thf(fact_2951_div__mod__decomp__int,axiom,
% 5.25/5.49 ! [A2: int,N2: int] :
% 5.25/5.49 ( A2
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_int @ A2 @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mod_decomp_int
% 5.25/5.49 thf(fact_2952_split__zdiv,axiom,
% 5.25/5.49 ! [P: int > $o,N2: int,K: int] :
% 5.25/5.49 ( ( P @ ( divide_divide_int @ N2 @ K ) )
% 5.25/5.49 = ( ( ( K = zero_zero_int )
% 5.25/5.49 => ( P @ zero_zero_int ) )
% 5.25/5.49 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.49 => ! [I3: int,J3: int] :
% 5.25/5.49 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.49 & ( ord_less_int @ J3 @ K )
% 5.25/5.49 & ( N2
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.49 => ( P @ I3 ) ) )
% 5.25/5.49 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.49 => ! [I3: int,J3: int] :
% 5.25/5.49 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.49 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.49 & ( N2
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.49 => ( P @ I3 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_zdiv
% 5.25/5.49 thf(fact_2953_int__div__neg__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,Q3: int,R3: int] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.49 => ( ( ord_less_eq_int @ R3 @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_int @ B @ R3 )
% 5.25/5.49 => ( ( divide_divide_int @ A @ B )
% 5.25/5.49 = Q3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_div_neg_eq
% 5.25/5.49 thf(fact_2954_int__div__pos__eq,axiom,
% 5.25/5.49 ! [A: int,B: int,Q3: int,R3: int] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ B @ Q3 ) @ R3 ) )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.25/5.49 => ( ( ord_less_int @ R3 @ B )
% 5.25/5.49 => ( ( divide_divide_int @ A @ B )
% 5.25/5.49 = Q3 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % int_div_pos_eq
% 5.25/5.49 thf(fact_2955_split__neg__lemma,axiom,
% 5.25/5.49 ! [K: int,P: int > int > $o,N2: int] :
% 5.25/5.49 ( ( ord_less_int @ K @ zero_zero_int )
% 5.25/5.49 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.25/5.49 = ( ! [I3: int,J3: int] :
% 5.25/5.49 ( ( ( ord_less_int @ K @ J3 )
% 5.25/5.49 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.25/5.49 & ( N2
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.49 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_neg_lemma
% 5.25/5.49 thf(fact_2956_split__pos__lemma,axiom,
% 5.25/5.49 ! [K: int,P: int > int > $o,N2: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ K )
% 5.25/5.49 => ( ( P @ ( divide_divide_int @ N2 @ K ) @ ( modulo_modulo_int @ N2 @ K ) )
% 5.25/5.49 = ( ! [I3: int,J3: int] :
% 5.25/5.49 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.25/5.49 & ( ord_less_int @ J3 @ K )
% 5.25/5.49 & ( N2
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ K @ I3 ) @ J3 ) ) )
% 5.25/5.49 => ( P @ I3 @ J3 ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_pos_lemma
% 5.25/5.49 thf(fact_2957_zdiv__zmult2__eq,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 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 % zdiv_zmult2_eq
% 5.25/5.49 thf(fact_2958_zmod__zmult2__eq,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zmod_zmult2_eq
% 5.25/5.49 thf(fact_2959_dvd__pos__nat,axiom,
% 5.25/5.49 ! [N2: nat,M: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.49 => ( ( dvd_dvd_nat @ M @ N2 )
% 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_2960_enat__0__less__mult__iff,axiom,
% 5.25/5.49 ! [M: extended_enat,N2: extended_enat] :
% 5.25/5.49 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N2 ) )
% 5.25/5.49 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.25/5.49 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % enat_0_less_mult_iff
% 5.25/5.49 thf(fact_2961_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( A != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.25/5.49 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_right
% 5.25/5.49 thf(fact_2962_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( A != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.25/5.49 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_right
% 5.25/5.49 thf(fact_2963_is__unit__div__mult__cancel__right,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_right
% 5.25/5.49 thf(fact_2964_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( A != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.49 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.25/5.49 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_left
% 5.25/5.49 thf(fact_2965_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( A != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.49 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.25/5.49 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_left
% 5.25/5.49 thf(fact_2966_is__unit__div__mult__cancel__left,axiom,
% 5.25/5.49 ! [A: code_integer,B: code_integer] :
% 5.25/5.49 ( ( A != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unit_div_mult_cancel_left
% 5.25/5.49 thf(fact_2967_is__unitE,axiom,
% 5.25/5.49 ! [A: nat,C: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.49 => ~ ( ( A != zero_zero_nat )
% 5.25/5.49 => ! [B5: nat] :
% 5.25/5.49 ( ( B5 != zero_zero_nat )
% 5.25/5.49 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.25/5.49 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.25/5.49 = B5 )
% 5.25/5.49 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.25/5.49 = A )
% 5.25/5.49 => ( ( ( times_times_nat @ A @ B5 )
% 5.25/5.49 = one_one_nat )
% 5.25/5.49 => ( ( divide_divide_nat @ C @ A )
% 5.25/5.49 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unitE
% 5.25/5.49 thf(fact_2968_is__unitE,axiom,
% 5.25/5.49 ! [A: int,C: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.49 => ~ ( ( A != zero_zero_int )
% 5.25/5.49 => ! [B5: int] :
% 5.25/5.49 ( ( B5 != zero_zero_int )
% 5.25/5.49 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.25/5.49 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.25/5.49 = B5 )
% 5.25/5.49 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.25/5.49 = A )
% 5.25/5.49 => ( ( ( times_times_int @ A @ B5 )
% 5.25/5.49 = one_one_int )
% 5.25/5.49 => ( ( divide_divide_int @ C @ A )
% 5.25/5.49 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unitE
% 5.25/5.49 thf(fact_2969_is__unitE,axiom,
% 5.25/5.49 ! [A: code_integer,C: 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 => ! [B5: code_integer] :
% 5.25/5.49 ( ( B5 != zero_z3403309356797280102nteger )
% 5.25/5.49 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.25/5.49 = B5 )
% 5.25/5.49 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.25/5.49 = A )
% 5.25/5.49 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.25/5.49 = one_one_Code_integer )
% 5.25/5.49 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.25/5.49 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % is_unitE
% 5.25/5.49 thf(fact_2970_evenE,axiom,
% 5.25/5.49 ! [A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ~ ! [B5: code_integer] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % evenE
% 5.25/5.49 thf(fact_2971_evenE,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ~ ! [B5: nat] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % evenE
% 5.25/5.49 thf(fact_2972_evenE,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ~ ! [B5: int] :
% 5.25/5.49 ( A
% 5.25/5.49 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % evenE
% 5.25/5.49 thf(fact_2973_dvd__mult__cancel2,axiom,
% 5.25/5.49 ! [M: nat,N2: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( times_times_nat @ N2 @ M ) @ M )
% 5.25/5.49 = ( N2 = one_one_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_cancel2
% 5.25/5.49 thf(fact_2974_dvd__mult__cancel1,axiom,
% 5.25/5.49 ! [M: nat,N2: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.49 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N2 ) @ M )
% 5.25/5.49 = ( N2 = one_one_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_mult_cancel1
% 5.25/5.49 thf(fact_2975_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( zero_n2687167440665602831ol_nat
% 5.25/5.49 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.49 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_odd_eq_mod_2
% 5.25/5.49 thf(fact_2976_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( zero_n2684676970156552555ol_int
% 5.25/5.49 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.49 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_odd_eq_mod_2
% 5.25/5.49 thf(fact_2977_of__bool__odd__eq__mod__2,axiom,
% 5.25/5.49 ! [A: code_integer] :
% 5.25/5.49 ( ( zero_n356916108424825756nteger
% 5.25/5.49 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.25/5.49 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_odd_eq_mod_2
% 5.25/5.49 thf(fact_2978_even__two__times__div__two,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_two_times_div_two
% 5.25/5.49 thf(fact_2979_even__two__times__div__two,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_two_times_div_two
% 5.25/5.49 thf(fact_2980_even__two__times__div__two,axiom,
% 5.25/5.49 ! [A: code_integer] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.25/5.49 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.25/5.49 = A ) ) ).
% 5.25/5.49
% 5.25/5.49 % even_two_times_div_two
% 5.25/5.49 thf(fact_2981_zero__less__eq__of__bool,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_eq_of_bool
% 5.25/5.49 thf(fact_2982_zero__less__eq__of__bool,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_eq_of_bool
% 5.25/5.49 thf(fact_2983_zero__less__eq__of__bool,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_eq_of_bool
% 5.25/5.49 thf(fact_2984_zero__less__eq__of__bool,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_eq_of_bool
% 5.25/5.49 thf(fact_2985_zero__less__eq__of__bool,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_eq_of_bool
% 5.25/5.49 thf(fact_2986_of__bool__less__eq__one,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_less_eq_one
% 5.25/5.49 thf(fact_2987_of__bool__less__eq__one,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_less_eq_one
% 5.25/5.49 thf(fact_2988_of__bool__less__eq__one,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_less_eq_one
% 5.25/5.49 thf(fact_2989_of__bool__less__eq__one,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_less_eq_one
% 5.25/5.49 thf(fact_2990_of__bool__less__eq__one,axiom,
% 5.25/5.49 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_less_eq_one
% 5.25/5.49 thf(fact_2991_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: complex > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_complex ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2992_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: real > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_real ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2993_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: rat > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_rat ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2994_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: nat > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_nat ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2995_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: int > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_int ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2996_split__of__bool__asm,axiom,
% 5.25/5.49 ! [P: code_integer > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.25/5.49 = ( ~ ( ( P2
% 5.25/5.49 & ~ ( P @ one_one_Code_integer ) )
% 5.25/5.49 | ( ~ P2
% 5.25/5.49 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool_asm
% 5.25/5.49 thf(fact_2997_split__of__bool,axiom,
% 5.25/5.49 ! [P: complex > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n1201886186963655149omplex @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_complex ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_2998_split__of__bool,axiom,
% 5.25/5.49 ! [P: real > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n3304061248610475627l_real @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_real ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_zero_real ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_2999_split__of__bool,axiom,
% 5.25/5.49 ! [P: rat > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2052037380579107095ol_rat @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_rat ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_3000_split__of__bool,axiom,
% 5.25/5.49 ! [P: nat > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2687167440665602831ol_nat @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_nat ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_3001_split__of__bool,axiom,
% 5.25/5.49 ! [P: int > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n2684676970156552555ol_int @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_int ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_zero_int ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_3002_split__of__bool,axiom,
% 5.25/5.49 ! [P: code_integer > $o,P2: $o] :
% 5.25/5.49 ( ( P @ ( zero_n356916108424825756nteger @ P2 ) )
% 5.25/5.49 = ( ( P2
% 5.25/5.49 => ( P @ one_one_Code_integer ) )
% 5.25/5.49 & ( ~ P2
% 5.25/5.49 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_of_bool
% 5.25/5.49 thf(fact_3003_of__bool__def,axiom,
% 5.25/5.49 ( zero_n1201886186963655149omplex
% 5.25/5.49 = ( ^ [P5: $o] : ( if_complex @ P5 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3004_of__bool__def,axiom,
% 5.25/5.49 ( zero_n3304061248610475627l_real
% 5.25/5.49 = ( ^ [P5: $o] : ( if_real @ P5 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3005_of__bool__def,axiom,
% 5.25/5.49 ( zero_n2052037380579107095ol_rat
% 5.25/5.49 = ( ^ [P5: $o] : ( if_rat @ P5 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3006_of__bool__def,axiom,
% 5.25/5.49 ( zero_n2687167440665602831ol_nat
% 5.25/5.49 = ( ^ [P5: $o] : ( if_nat @ P5 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3007_of__bool__def,axiom,
% 5.25/5.49 ( zero_n2684676970156552555ol_int
% 5.25/5.49 = ( ^ [P5: $o] : ( if_int @ P5 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3008_of__bool__def,axiom,
% 5.25/5.49 ( zero_n356916108424825756nteger
% 5.25/5.49 = ( ^ [P5: $o] : ( if_Code_integer @ P5 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % of_bool_def
% 5.25/5.49 thf(fact_3009_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_3010_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_3011_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_3012_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_3013_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_3014_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_3015_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_3016_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_3017_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_3018_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_3019_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_3020_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_3021_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_3022_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_3023_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_3024_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_3025_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_3026_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_3027_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_3028_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_3029_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_3030_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_3031_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_3032_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_3033_div__power,axiom,
% 5.25/5.49 ! [B: nat,A: nat,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ B @ A )
% 5.25/5.49 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N2 )
% 5.25/5.49 = ( divide_divide_nat @ ( power_power_nat @ A @ N2 ) @ ( power_power_nat @ B @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3034_div__power,axiom,
% 5.25/5.49 ! [B: int,A: int,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ B @ A )
% 5.25/5.49 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N2 )
% 5.25/5.49 = ( divide_divide_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3035_div__power,axiom,
% 5.25/5.49 ! [B: code_integer,A: code_integer,N2: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.25/5.49 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N2 )
% 5.25/5.49 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_power
% 5.25/5.49 thf(fact_3036_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_3037_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_3038_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_3039_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_3040_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_3041_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_3042_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_3043_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_3044_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_3045_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.49 thf(fact_3046_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.49 thf(fact_3047_ordered__comm__semiring__class_Ocomm__mult__left__mono,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 @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.49 thf(fact_3048_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.25/5.49 thf(fact_3049_zero__le__mult__iff,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_mult_iff
% 5.25/5.49 thf(fact_3050_zero__le__mult__iff,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_mult_iff
% 5.25/5.49 thf(fact_3051_zero__le__mult__iff,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_mult_iff
% 5.25/5.49 thf(fact_3052_mult__nonneg__nonpos2,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos2
% 5.25/5.49 thf(fact_3053_mult__nonneg__nonpos2,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos2
% 5.25/5.49 thf(fact_3054_mult__nonneg__nonpos2,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos2
% 5.25/5.49 thf(fact_3055_mult__nonneg__nonpos2,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos2
% 5.25/5.49 thf(fact_3056_mult__nonpos__nonneg,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonneg
% 5.25/5.49 thf(fact_3057_mult__nonpos__nonneg,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonneg
% 5.25/5.49 thf(fact_3058_mult__nonpos__nonneg,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonneg
% 5.25/5.49 thf(fact_3059_mult__nonpos__nonneg,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonneg
% 5.25/5.49 thf(fact_3060_mult__nonneg__nonpos,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos
% 5.25/5.49 thf(fact_3061_mult__nonneg__nonpos,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos
% 5.25/5.49 thf(fact_3062_mult__nonneg__nonpos,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos
% 5.25/5.49 thf(fact_3063_mult__nonneg__nonpos,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonpos
% 5.25/5.49 thf(fact_3064_mult__nonneg__nonneg,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonneg
% 5.25/5.49 thf(fact_3065_mult__nonneg__nonneg,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonneg
% 5.25/5.49 thf(fact_3066_mult__nonneg__nonneg,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.49 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonneg
% 5.25/5.49 thf(fact_3067_mult__nonneg__nonneg,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonneg_nonneg
% 5.25/5.49 thf(fact_3068_split__mult__neg__le,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_neg_le
% 5.25/5.49 thf(fact_3069_split__mult__neg__le,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.25/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_neg_le
% 5.25/5.49 thf(fact_3070_split__mult__neg__le,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.49 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.25/5.49 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.25/5.49 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_neg_le
% 5.25/5.49 thf(fact_3071_split__mult__neg__le,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.25/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_neg_le
% 5.25/5.49 thf(fact_3072_mult__le__0__iff,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.25/5.49 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.25/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_0_iff
% 5.25/5.49 thf(fact_3073_mult__le__0__iff,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.49 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.25/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_0_iff
% 5.25/5.49 thf(fact_3074_mult__le__0__iff,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.25/5.49 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.25/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_le_0_iff
% 5.25/5.49 thf(fact_3075_mult__right__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono
% 5.25/5.49 thf(fact_3076_mult__right__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono
% 5.25/5.49 thf(fact_3077_mult__right__mono,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 @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono
% 5.25/5.49 thf(fact_3078_mult__right__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono
% 5.25/5.49 thf(fact_3079_mult__right__mono__neg,axiom,
% 5.25/5.49 ! [B: real,A: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono_neg
% 5.25/5.49 thf(fact_3080_mult__right__mono__neg,axiom,
% 5.25/5.49 ! [B: rat,A: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono_neg
% 5.25/5.49 thf(fact_3081_mult__right__mono__neg,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_right_mono_neg
% 5.25/5.49 thf(fact_3082_mult__left__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono
% 5.25/5.49 thf(fact_3083_mult__left__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono
% 5.25/5.49 thf(fact_3084_mult__left__mono,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 @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono
% 5.25/5.49 thf(fact_3085_mult__left__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono
% 5.25/5.49 thf(fact_3086_mult__nonpos__nonpos,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonpos
% 5.25/5.49 thf(fact_3087_mult__nonpos__nonpos,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonpos
% 5.25/5.49 thf(fact_3088_mult__nonpos__nonpos,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_nonpos_nonpos
% 5.25/5.49 thf(fact_3089_mult__left__mono__neg,axiom,
% 5.25/5.49 ! [B: real,A: real,C: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono_neg
% 5.25/5.49 thf(fact_3090_mult__left__mono__neg,axiom,
% 5.25/5.49 ! [B: rat,A: rat,C: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono_neg
% 5.25/5.49 thf(fact_3091_mult__left__mono__neg,axiom,
% 5.25/5.49 ! [B: int,A: int,C: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ B @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_left_mono_neg
% 5.25/5.49 thf(fact_3092_split__mult__pos__le,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.25/5.49 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_pos_le
% 5.25/5.49 thf(fact_3093_split__mult__pos__le,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.25/5.49 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_pos_le
% 5.25/5.49 thf(fact_3094_split__mult__pos__le,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.25/5.49 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.25/5.49 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % split_mult_pos_le
% 5.25/5.49 thf(fact_3095_zero__le__square,axiom,
% 5.25/5.49 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_square
% 5.25/5.49 thf(fact_3096_zero__le__square,axiom,
% 5.25/5.49 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_square
% 5.25/5.49 thf(fact_3097_zero__le__square,axiom,
% 5.25/5.49 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_le_square
% 5.25/5.49 thf(fact_3098_mult__mono_H,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono'
% 5.25/5.49 thf(fact_3099_mult__mono_H,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono'
% 5.25/5.49 thf(fact_3100_mult__mono_H,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono'
% 5.25/5.49 thf(fact_3101_mult__mono_H,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono'
% 5.25/5.49 thf(fact_3102_mult__mono,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.49 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.49 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono
% 5.25/5.49 thf(fact_3103_mult__mono,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.49 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.49 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono
% 5.25/5.49 thf(fact_3104_mult__mono,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono
% 5.25/5.49 thf(fact_3105_mult__mono,axiom,
% 5.25/5.49 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.49 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.49 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_mono
% 5.25/5.49 thf(fact_3106_mult__neg__neg,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_neg
% 5.25/5.49 thf(fact_3107_mult__neg__neg,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_neg
% 5.25/5.49 thf(fact_3108_mult__neg__neg,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_neg
% 5.25/5.49 thf(fact_3109_not__square__less__zero,axiom,
% 5.25/5.49 ! [A: real] :
% 5.25/5.49 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.25/5.49
% 5.25/5.49 % not_square_less_zero
% 5.25/5.49 thf(fact_3110_not__square__less__zero,axiom,
% 5.25/5.49 ! [A: rat] :
% 5.25/5.49 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.25/5.49
% 5.25/5.49 % not_square_less_zero
% 5.25/5.49 thf(fact_3111_not__square__less__zero,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.25/5.49
% 5.25/5.49 % not_square_less_zero
% 5.25/5.49 thf(fact_3112_mult__less__0__iff,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.25/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.25/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_0_iff
% 5.25/5.49 thf(fact_3113_mult__less__0__iff,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.25/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.25/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_0_iff
% 5.25/5.49 thf(fact_3114_mult__less__0__iff,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.25/5.49 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.25/5.49 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_0_iff
% 5.25/5.49 thf(fact_3115_mult__neg__pos,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_pos
% 5.25/5.49 thf(fact_3116_mult__neg__pos,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_pos
% 5.25/5.49 thf(fact_3117_mult__neg__pos,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_pos
% 5.25/5.49 thf(fact_3118_mult__neg__pos,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_neg_pos
% 5.25/5.49 thf(fact_3119_mult__pos__neg,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg
% 5.25/5.49 thf(fact_3120_mult__pos__neg,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg
% 5.25/5.49 thf(fact_3121_mult__pos__neg,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg
% 5.25/5.49 thf(fact_3122_mult__pos__neg,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg
% 5.25/5.49 thf(fact_3123_mult__pos__pos,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.49 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_pos
% 5.25/5.49 thf(fact_3124_mult__pos__pos,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.49 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_pos
% 5.25/5.49 thf(fact_3125_mult__pos__pos,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.49 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_pos
% 5.25/5.49 thf(fact_3126_mult__pos__pos,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.49 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_pos
% 5.25/5.49 thf(fact_3127_mult__pos__neg2,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg2
% 5.25/5.49 thf(fact_3128_mult__pos__neg2,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg2
% 5.25/5.49 thf(fact_3129_mult__pos__neg2,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg2
% 5.25/5.49 thf(fact_3130_mult__pos__neg2,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_pos_neg2
% 5.25/5.49 thf(fact_3131_zero__less__mult__iff,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.25/5.49 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.25/5.49 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_iff
% 5.25/5.49 thf(fact_3132_zero__less__mult__iff,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.25/5.49 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_iff
% 5.25/5.49 thf(fact_3133_zero__less__mult__iff,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.49 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.25/5.49 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.25/5.49 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_iff
% 5.25/5.49 thf(fact_3134_zero__less__mult__pos,axiom,
% 5.25/5.49 ! [A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos
% 5.25/5.49 thf(fact_3135_zero__less__mult__pos,axiom,
% 5.25/5.49 ! [A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos
% 5.25/5.49 thf(fact_3136_zero__less__mult__pos,axiom,
% 5.25/5.49 ! [A: nat,B: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos
% 5.25/5.49 thf(fact_3137_zero__less__mult__pos,axiom,
% 5.25/5.49 ! [A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.25/5.49 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos
% 5.25/5.49 thf(fact_3138_zero__less__mult__pos2,axiom,
% 5.25/5.49 ! [B: real,A: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.25/5.49 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.49 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos2
% 5.25/5.49 thf(fact_3139_zero__less__mult__pos2,axiom,
% 5.25/5.49 ! [B: rat,A: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.25/5.49 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.49 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos2
% 5.25/5.49 thf(fact_3140_zero__less__mult__pos2,axiom,
% 5.25/5.49 ! [B: nat,A: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.49 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos2
% 5.25/5.49 thf(fact_3141_zero__less__mult__pos2,axiom,
% 5.25/5.49 ! [B: int,A: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.25/5.49 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.49 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % zero_less_mult_pos2
% 5.25/5.49 thf(fact_3142_mult__less__cancel__left__neg,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.49 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.49 = ( ord_less_real @ B @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_neg
% 5.25/5.49 thf(fact_3143_mult__less__cancel__left__neg,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.49 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.49 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_neg
% 5.25/5.49 thf(fact_3144_mult__less__cancel__left__neg,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.49 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.49 = ( ord_less_int @ B @ A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_neg
% 5.25/5.49 thf(fact_3145_mult__less__cancel__left__pos,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.49 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.49 = ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_pos
% 5.25/5.49 thf(fact_3146_mult__less__cancel__left__pos,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.49 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.49 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_pos
% 5.25/5.49 thf(fact_3147_mult__less__cancel__left__pos,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.49 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.49 = ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_pos
% 5.25/5.49 thf(fact_3148_mult__strict__left__mono__neg,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 @ C @ zero_zero_real )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono_neg
% 5.25/5.49 thf(fact_3149_mult__strict__left__mono__neg,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 @ C @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono_neg
% 5.25/5.49 thf(fact_3150_mult__strict__left__mono__neg,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 @ C @ zero_zero_int )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono_neg
% 5.25/5.49 thf(fact_3151_mult__strict__left__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 @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono
% 5.25/5.49 thf(fact_3152_mult__strict__left__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 @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono
% 5.25/5.49 thf(fact_3153_mult__strict__left__mono,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono
% 5.25/5.49 thf(fact_3154_mult__strict__left__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 @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_left_mono
% 5.25/5.49 thf(fact_3155_mult__less__cancel__left__disj,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.49 & ( ord_less_real @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.49 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_disj
% 5.25/5.49 thf(fact_3156_mult__less__cancel__left__disj,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.49 & ( ord_less_rat @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_disj
% 5.25/5.49 thf(fact_3157_mult__less__cancel__left__disj,axiom,
% 5.25/5.49 ! [C: int,A: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.49 & ( ord_less_int @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.49 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_left_disj
% 5.25/5.49 thf(fact_3158_mult__strict__right__mono__neg,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 @ C @ zero_zero_real )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono_neg
% 5.25/5.49 thf(fact_3159_mult__strict__right__mono__neg,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 @ C @ zero_zero_rat )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono_neg
% 5.25/5.49 thf(fact_3160_mult__strict__right__mono__neg,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 @ C @ zero_zero_int )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono_neg
% 5.25/5.49 thf(fact_3161_mult__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 @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono
% 5.25/5.49 thf(fact_3162_mult__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 @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono
% 5.25/5.49 thf(fact_3163_mult__strict__right__mono,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono
% 5.25/5.49 thf(fact_3164_mult__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 @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_strict_right_mono
% 5.25/5.49 thf(fact_3165_mult__less__cancel__right__disj,axiom,
% 5.25/5.49 ! [A: real,C: real,B: real] :
% 5.25/5.49 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.49 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.49 & ( ord_less_real @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.49 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_right_disj
% 5.25/5.49 thf(fact_3166_mult__less__cancel__right__disj,axiom,
% 5.25/5.49 ! [A: rat,C: rat,B: rat] :
% 5.25/5.49 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.49 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.49 & ( ord_less_rat @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.49 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_right_disj
% 5.25/5.49 thf(fact_3167_mult__less__cancel__right__disj,axiom,
% 5.25/5.49 ! [A: int,C: int,B: int] :
% 5.25/5.49 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.49 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.49 & ( ord_less_int @ A @ B ) )
% 5.25/5.49 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.49 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % mult_less_cancel_right_disj
% 5.25/5.49 thf(fact_3168_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__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 @ zero_zero_real @ C )
% 5.25/5.49 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.49 thf(fact_3169_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__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 @ zero_zero_rat @ C )
% 5.25/5.49 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.49 thf(fact_3170_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.25/5.49 ! [A: nat,B: nat,C: nat] :
% 5.25/5.49 ( ( ord_less_nat @ A @ B )
% 5.25/5.49 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.49 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.49 thf(fact_3171_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__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 @ zero_zero_int @ C )
% 5.25/5.49 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.25/5.49 thf(fact_3172_dvd__power__le,axiom,
% 5.25/5.49 ! [X4: code_integer,Y: code_integer,N2: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ N2 ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3173_dvd__power__le,axiom,
% 5.25/5.49 ! [X4: nat,Y: nat,N2: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ X4 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3174_dvd__power__le,axiom,
% 5.25/5.49 ! [X4: real,Y: real,N2: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ X4 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3175_dvd__power__le,axiom,
% 5.25/5.49 ! [X4: int,Y: int,N2: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ X4 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3176_dvd__power__le,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,N2: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ X4 @ Y )
% 5.25/5.49 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % dvd_power_le
% 5.25/5.49 thf(fact_3177_power__le__dvd,axiom,
% 5.25/5.49 ! [A: code_integer,N2: nat,B: code_integer,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N2 )
% 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_3178_power__le__dvd,axiom,
% 5.25/5.49 ! [A: nat,N2: nat,B: nat,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N2 )
% 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_3179_power__le__dvd,axiom,
% 5.25/5.49 ! [A: real,N2: nat,B: real,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_real @ ( power_power_real @ A @ N2 ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N2 )
% 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_3180_power__le__dvd,axiom,
% 5.25/5.49 ! [A: int,N2: nat,B: int,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N2 )
% 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_3181_power__le__dvd,axiom,
% 5.25/5.49 ! [A: complex,N2: nat,B: complex,M: nat] :
% 5.25/5.49 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N2 ) @ B )
% 5.25/5.49 => ( ( ord_less_eq_nat @ M @ N2 )
% 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_3182_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,A: code_integer] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.49 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3183_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,A: nat] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.49 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3184_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,A: real] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.49 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3185_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,A: int] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.49 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3186_le__imp__power__dvd,axiom,
% 5.25/5.49 ! [M: nat,N2: nat,A: complex] :
% 5.25/5.49 ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.49 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % le_imp_power_dvd
% 5.25/5.49 thf(fact_3187_less__1__mult,axiom,
% 5.25/5.49 ! [M: real,N2: real] :
% 5.25/5.49 ( ( ord_less_real @ one_one_real @ M )
% 5.25/5.49 => ( ( ord_less_real @ one_one_real @ N2 )
% 5.25/5.49 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_1_mult
% 5.25/5.49 thf(fact_3188_less__1__mult,axiom,
% 5.25/5.49 ! [M: rat,N2: rat] :
% 5.25/5.49 ( ( ord_less_rat @ one_one_rat @ M )
% 5.25/5.49 => ( ( ord_less_rat @ one_one_rat @ N2 )
% 5.25/5.49 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_1_mult
% 5.25/5.49 thf(fact_3189_less__1__mult,axiom,
% 5.25/5.49 ! [M: nat,N2: nat] :
% 5.25/5.49 ( ( ord_less_nat @ one_one_nat @ M )
% 5.25/5.49 => ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.25/5.49 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_1_mult
% 5.25/5.49 thf(fact_3190_less__1__mult,axiom,
% 5.25/5.49 ! [M: int,N2: int] :
% 5.25/5.49 ( ( ord_less_int @ one_one_int @ M )
% 5.25/5.49 => ( ( ord_less_int @ one_one_int @ N2 )
% 5.25/5.49 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N2 ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % less_1_mult
% 5.25/5.49 thf(fact_3191_nonzero__eq__divide__eq,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.49 = ( ( times_times_rat @ A @ C )
% 5.25/5.49 = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_eq_divide_eq
% 5.25/5.49 thf(fact_3192_nonzero__eq__divide__eq,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide_divide_real @ B @ C ) )
% 5.25/5.49 = ( ( times_times_real @ A @ C )
% 5.25/5.49 = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_eq_divide_eq
% 5.25/5.49 thf(fact_3193_nonzero__eq__divide__eq,axiom,
% 5.25/5.49 ! [C: complex,A: complex,B: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( A
% 5.25/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.49 = ( ( times_times_complex @ A @ C )
% 5.25/5.49 = B ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_eq_divide_eq
% 5.25/5.49 thf(fact_3194_nonzero__divide__eq__eq,axiom,
% 5.25/5.49 ! [C: rat,B: rat,A: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_divide_eq_eq
% 5.25/5.49 thf(fact_3195_nonzero__divide__eq__eq,axiom,
% 5.25/5.49 ! [C: real,B: real,A: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( ( divide_divide_real @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_divide_eq_eq
% 5.25/5.49 thf(fact_3196_nonzero__divide__eq__eq,axiom,
% 5.25/5.49 ! [C: complex,B: complex,A: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( B
% 5.25/5.49 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nonzero_divide_eq_eq
% 5.25/5.49 thf(fact_3197_eq__divide__imp,axiom,
% 5.25/5.49 ! [C: rat,A: rat,B: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( ( times_times_rat @ A @ C )
% 5.25/5.49 = B )
% 5.25/5.49 => ( A
% 5.25/5.49 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_imp
% 5.25/5.49 thf(fact_3198_eq__divide__imp,axiom,
% 5.25/5.49 ! [C: real,A: real,B: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( ( times_times_real @ A @ C )
% 5.25/5.49 = B )
% 5.25/5.49 => ( A
% 5.25/5.49 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_imp
% 5.25/5.49 thf(fact_3199_eq__divide__imp,axiom,
% 5.25/5.49 ! [C: complex,A: complex,B: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( ( times_times_complex @ A @ C )
% 5.25/5.49 = B )
% 5.25/5.49 => ( A
% 5.25/5.49 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_imp
% 5.25/5.49 thf(fact_3200_divide__eq__imp,axiom,
% 5.25/5.49 ! [C: rat,B: rat,A: rat] :
% 5.25/5.49 ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( B
% 5.25/5.49 = ( times_times_rat @ A @ C ) )
% 5.25/5.49 => ( ( divide_divide_rat @ B @ C )
% 5.25/5.49 = A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_imp
% 5.25/5.49 thf(fact_3201_divide__eq__imp,axiom,
% 5.25/5.49 ! [C: real,B: real,A: real] :
% 5.25/5.49 ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( B
% 5.25/5.49 = ( times_times_real @ A @ C ) )
% 5.25/5.49 => ( ( divide_divide_real @ B @ C )
% 5.25/5.49 = A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_imp
% 5.25/5.49 thf(fact_3202_divide__eq__imp,axiom,
% 5.25/5.49 ! [C: complex,B: complex,A: complex] :
% 5.25/5.49 ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( B
% 5.25/5.49 = ( times_times_complex @ A @ C ) )
% 5.25/5.49 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.49 = A ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_imp
% 5.25/5.49 thf(fact_3203_eq__divide__eq,axiom,
% 5.25/5.49 ! [A: rat,B: rat,C: rat] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.49 = ( ( ( C != zero_zero_rat )
% 5.25/5.49 => ( ( times_times_rat @ A @ C )
% 5.25/5.49 = B ) )
% 5.25/5.49 & ( ( C = zero_zero_rat )
% 5.25/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_eq
% 5.25/5.49 thf(fact_3204_eq__divide__eq,axiom,
% 5.25/5.49 ! [A: real,B: real,C: real] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( divide_divide_real @ B @ C ) )
% 5.25/5.49 = ( ( ( C != zero_zero_real )
% 5.25/5.49 => ( ( times_times_real @ A @ C )
% 5.25/5.49 = B ) )
% 5.25/5.49 & ( ( C = zero_zero_real )
% 5.25/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_eq
% 5.25/5.49 thf(fact_3205_eq__divide__eq,axiom,
% 5.25/5.49 ! [A: complex,B: complex,C: complex] :
% 5.25/5.49 ( ( A
% 5.25/5.49 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.49 = ( ( ( C != zero_zero_complex )
% 5.25/5.49 => ( ( times_times_complex @ A @ C )
% 5.25/5.49 = B ) )
% 5.25/5.49 & ( ( C = zero_zero_complex )
% 5.25/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % eq_divide_eq
% 5.25/5.49 thf(fact_3206_divide__eq__eq,axiom,
% 5.25/5.49 ! [B: rat,C: rat,A: rat] :
% 5.25/5.49 ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( ( ( C != zero_zero_rat )
% 5.25/5.49 => ( B
% 5.25/5.49 = ( times_times_rat @ A @ C ) ) )
% 5.25/5.49 & ( ( C = zero_zero_rat )
% 5.25/5.49 => ( A = zero_zero_rat ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_eq
% 5.25/5.49 thf(fact_3207_divide__eq__eq,axiom,
% 5.25/5.49 ! [B: real,C: real,A: real] :
% 5.25/5.49 ( ( ( divide_divide_real @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( ( ( C != zero_zero_real )
% 5.25/5.49 => ( B
% 5.25/5.49 = ( times_times_real @ A @ C ) ) )
% 5.25/5.49 & ( ( C = zero_zero_real )
% 5.25/5.49 => ( A = zero_zero_real ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_eq
% 5.25/5.49 thf(fact_3208_divide__eq__eq,axiom,
% 5.25/5.49 ! [B: complex,C: complex,A: complex] :
% 5.25/5.49 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.49 = A )
% 5.25/5.49 = ( ( ( C != zero_zero_complex )
% 5.25/5.49 => ( B
% 5.25/5.49 = ( times_times_complex @ A @ C ) ) )
% 5.25/5.49 & ( ( C = zero_zero_complex )
% 5.25/5.49 => ( A = zero_zero_complex ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % divide_eq_eq
% 5.25/5.49 thf(fact_3209_frac__eq__eq,axiom,
% 5.25/5.49 ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 5.25/5.49 ( ( Y != zero_zero_rat )
% 5.25/5.49 => ( ( Z != zero_zero_rat )
% 5.25/5.49 => ( ( ( divide_divide_rat @ X4 @ Y )
% 5.25/5.49 = ( divide_divide_rat @ W @ Z ) )
% 5.25/5.49 = ( ( times_times_rat @ X4 @ Z )
% 5.25/5.49 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % frac_eq_eq
% 5.25/5.49 thf(fact_3210_frac__eq__eq,axiom,
% 5.25/5.49 ! [Y: real,Z: real,X4: real,W: real] :
% 5.25/5.49 ( ( Y != zero_zero_real )
% 5.25/5.49 => ( ( Z != zero_zero_real )
% 5.25/5.49 => ( ( ( divide_divide_real @ X4 @ Y )
% 5.25/5.49 = ( divide_divide_real @ W @ Z ) )
% 5.25/5.49 = ( ( times_times_real @ X4 @ Z )
% 5.25/5.49 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % frac_eq_eq
% 5.25/5.49 thf(fact_3211_frac__eq__eq,axiom,
% 5.25/5.49 ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 5.25/5.49 ( ( Y != zero_zero_complex )
% 5.25/5.49 => ( ( Z != zero_zero_complex )
% 5.25/5.49 => ( ( ( divide1717551699836669952omplex @ X4 @ Y )
% 5.25/5.49 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.25/5.49 = ( ( times_times_complex @ X4 @ Z )
% 5.25/5.49 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % frac_eq_eq
% 5.25/5.49 thf(fact_3212_mult__numeral__1__right,axiom,
% 5.25/5.49 ! [A: extended_enat] :
% 5.25/5.49 ( ( times_7803423173614009249d_enat @ A @ ( numera1916890842035813515d_enat @ one ) )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1_right
% 5.25/5.49 thf(fact_3213_mult__numeral__1__right,axiom,
% 5.25/5.49 ! [A: complex] :
% 5.25/5.49 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1_right
% 5.25/5.49 thf(fact_3214_mult__numeral__1__right,axiom,
% 5.25/5.49 ! [A: real] :
% 5.25/5.49 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1_right
% 5.25/5.49 thf(fact_3215_mult__numeral__1__right,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1_right
% 5.25/5.49 thf(fact_3216_mult__numeral__1__right,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1_right
% 5.25/5.49 thf(fact_3217_mult__numeral__1,axiom,
% 5.25/5.49 ! [A: extended_enat] :
% 5.25/5.49 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ one ) @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1
% 5.25/5.49 thf(fact_3218_mult__numeral__1,axiom,
% 5.25/5.49 ! [A: complex] :
% 5.25/5.49 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1
% 5.25/5.49 thf(fact_3219_mult__numeral__1,axiom,
% 5.25/5.49 ! [A: real] :
% 5.25/5.49 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1
% 5.25/5.49 thf(fact_3220_mult__numeral__1,axiom,
% 5.25/5.49 ! [A: nat] :
% 5.25/5.49 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1
% 5.25/5.49 thf(fact_3221_mult__numeral__1,axiom,
% 5.25/5.49 ! [A: int] :
% 5.25/5.49 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.25/5.49 = A ) ).
% 5.25/5.49
% 5.25/5.49 % mult_numeral_1
% 5.25/5.49 thf(fact_3222_nat__dvd__not__less,axiom,
% 5.25/5.49 ! [M: nat,N2: nat] :
% 5.25/5.49 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.25/5.49 => ( ( ord_less_nat @ M @ N2 )
% 5.25/5.49 => ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % nat_dvd_not_less
% 5.25/5.49 thf(fact_3223_div__mult2__numeral__eq,axiom,
% 5.25/5.49 ! [A: nat,K: num,L: num] :
% 5.25/5.49 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L ) )
% 5.25/5.49 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult2_numeral_eq
% 5.25/5.49 thf(fact_3224_div__mult2__numeral__eq,axiom,
% 5.25/5.49 ! [A: int,K: num,L: num] :
% 5.25/5.49 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L ) )
% 5.25/5.49 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult2_numeral_eq
% 5.25/5.49 thf(fact_3225_div__mult2__numeral__eq,axiom,
% 5.25/5.49 ! [A: code_integer,K: num,L: num] :
% 5.25/5.49 ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ K ) ) @ ( numera6620942414471956472nteger @ L ) )
% 5.25/5.49 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( times_times_num @ K @ L ) ) ) ) ).
% 5.25/5.49
% 5.25/5.49 % div_mult2_numeral_eq
% 5.25/5.49 thf(fact_3226_left__right__inverse__power,axiom,
% 5.25/5.49 ! [X4: rat,Y: rat,N2: nat] :
% 5.25/5.49 ( ( ( times_times_rat @ X4 @ Y )
% 5.25/5.49 = one_one_rat )
% 5.25/5.49 => ( ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.25/5.49 = one_one_rat ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_right_inverse_power
% 5.25/5.49 thf(fact_3227_left__right__inverse__power,axiom,
% 5.25/5.49 ! [X4: complex,Y: complex,N2: nat] :
% 5.25/5.49 ( ( ( times_times_complex @ X4 @ Y )
% 5.25/5.49 = one_one_complex )
% 5.25/5.49 => ( ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.25/5.49 = one_one_complex ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_right_inverse_power
% 5.25/5.49 thf(fact_3228_left__right__inverse__power,axiom,
% 5.25/5.49 ! [X4: real,Y: real,N2: nat] :
% 5.25/5.49 ( ( ( times_times_real @ X4 @ Y )
% 5.25/5.49 = one_one_real )
% 5.25/5.49 => ( ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.25/5.49 = one_one_real ) ) ).
% 5.25/5.49
% 5.25/5.49 % left_right_inverse_power
% 5.25/5.49 thf(fact_3229_left__right__inverse__power,axiom,
% 5.25/5.50 ! [X4: nat,Y: nat,N2: nat] :
% 5.25/5.50 ( ( ( times_times_nat @ X4 @ Y )
% 5.25/5.50 = one_one_nat )
% 5.25/5.50 => ( ( times_times_nat @ ( power_power_nat @ X4 @ N2 ) @ ( power_power_nat @ Y @ N2 ) )
% 5.25/5.50 = one_one_nat ) ) ).
% 5.25/5.50
% 5.25/5.50 % left_right_inverse_power
% 5.25/5.50 thf(fact_3230_left__right__inverse__power,axiom,
% 5.25/5.50 ! [X4: int,Y: int,N2: nat] :
% 5.25/5.50 ( ( ( times_times_int @ X4 @ Y )
% 5.25/5.50 = one_one_int )
% 5.25/5.50 => ( ( times_times_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.25/5.50 = one_one_int ) ) ).
% 5.25/5.50
% 5.25/5.50 % left_right_inverse_power
% 5.25/5.50 thf(fact_3231_power__Suc,axiom,
% 5.25/5.50 ! [A: complex,N2: nat] :
% 5.25/5.50 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_complex @ A @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc
% 5.25/5.50 thf(fact_3232_power__Suc,axiom,
% 5.25/5.50 ! [A: real,N2: nat] :
% 5.25/5.50 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc
% 5.25/5.50 thf(fact_3233_power__Suc,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc
% 5.25/5.50 thf(fact_3234_power__Suc,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc
% 5.25/5.50 thf(fact_3235_power__Suc2,axiom,
% 5.25/5.50 ! [A: complex,N2: nat] :
% 5.25/5.50 ( ( power_power_complex @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_complex @ ( power_power_complex @ A @ N2 ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc2
% 5.25/5.50 thf(fact_3236_power__Suc2,axiom,
% 5.25/5.50 ! [A: real,N2: nat] :
% 5.25/5.50 ( ( power_power_real @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_real @ ( power_power_real @ A @ N2 ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc2
% 5.25/5.50 thf(fact_3237_power__Suc2,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_nat @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_nat @ ( power_power_nat @ A @ N2 ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc2
% 5.25/5.50 thf(fact_3238_power__Suc2,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( power_power_int @ A @ ( suc @ N2 ) )
% 5.25/5.50 = ( times_times_int @ ( power_power_int @ A @ N2 ) @ A ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_Suc2
% 5.25/5.50 thf(fact_3239_mod__eqE,axiom,
% 5.25/5.50 ! [A: int,C: int,B: int] :
% 5.25/5.50 ( ( ( modulo_modulo_int @ A @ C )
% 5.25/5.50 = ( modulo_modulo_int @ B @ C ) )
% 5.25/5.50 => ~ ! [D3: int] :
% 5.25/5.50 ( B
% 5.25/5.50 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_eqE
% 5.25/5.50 thf(fact_3240_mod__eqE,axiom,
% 5.25/5.50 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.25/5.50 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.25/5.50 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.25/5.50 => ~ ! [D3: code_integer] :
% 5.25/5.50 ( B
% 5.25/5.50 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_eqE
% 5.25/5.50 thf(fact_3241_Suc__mult__less__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.25/5.50 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc_mult_less_cancel1
% 5.25/5.50 thf(fact_3242_power__add,axiom,
% 5.25/5.50 ! [A: complex,M: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.50 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_add
% 5.25/5.50 thf(fact_3243_power__add,axiom,
% 5.25/5.50 ! [A: real,M: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.50 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_add
% 5.25/5.50 thf(fact_3244_power__add,axiom,
% 5.25/5.50 ! [A: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.50 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_add
% 5.25/5.50 thf(fact_3245_power__add,axiom,
% 5.25/5.50 ! [A: int,M: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N2 ) )
% 5.25/5.50 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_add
% 5.25/5.50 thf(fact_3246_nat__mult__less__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.50 = ( ord_less_nat @ M @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mult_less_cancel1
% 5.25/5.50 thf(fact_3247_nat__mult__eq__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ( ( times_times_nat @ K @ M )
% 5.25/5.50 = ( times_times_nat @ K @ N2 ) )
% 5.25/5.50 = ( M = N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mult_eq_cancel1
% 5.25/5.50 thf(fact_3248_mult__less__mono2,axiom,
% 5.25/5.50 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.50 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ K @ I2 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_mono2
% 5.25/5.50 thf(fact_3249_mult__less__mono1,axiom,
% 5.25/5.50 ! [I2: nat,J: nat,K: nat] :
% 5.25/5.50 ( ( ord_less_nat @ I2 @ J )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ I2 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_mono1
% 5.25/5.50 thf(fact_3250_Suc__mult__le__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N2 ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.25/5.50
% 5.25/5.50 % Suc_mult_le_cancel1
% 5.25/5.50 thf(fact_3251_mult__Suc,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( times_times_nat @ ( suc @ M ) @ N2 )
% 5.25/5.50 = ( plus_plus_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_Suc
% 5.25/5.50 thf(fact_3252_mult__eq__self__implies__10,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( M
% 5.25/5.50 = ( times_times_nat @ M @ N2 ) )
% 5.25/5.50 => ( ( N2 = one_one_nat )
% 5.25/5.50 | ( M = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_eq_self_implies_10
% 5.25/5.50 thf(fact_3253_less__mult__imp__div__less,axiom,
% 5.25/5.50 ! [M: nat,I2: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ M @ ( times_times_nat @ I2 @ N2 ) )
% 5.25/5.50 => ( ord_less_nat @ ( divide_divide_nat @ M @ N2 ) @ I2 ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_mult_imp_div_less
% 5.25/5.50 thf(fact_3254_div__times__less__eq__dividend,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) @ M ) ).
% 5.25/5.50
% 5.25/5.50 % div_times_less_eq_dividend
% 5.25/5.50 thf(fact_3255_times__div__less__eq__dividend,axiom,
% 5.25/5.50 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) @ M ) ).
% 5.25/5.50
% 5.25/5.50 % times_div_less_eq_dividend
% 5.25/5.50 thf(fact_3256_mod__eq__0D,axiom,
% 5.25/5.50 ! [M: nat,D: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ M @ D )
% 5.25/5.50 = zero_zero_nat )
% 5.25/5.50 => ? [Q2: nat] :
% 5.25/5.50 ( M
% 5.25/5.50 = ( times_times_nat @ D @ Q2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_eq_0D
% 5.25/5.50 thf(fact_3257_nat__mod__eq__iff,axiom,
% 5.25/5.50 ! [X4: nat,N2: nat,Y: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 5.25/5.50 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.25/5.50 = ( ? [Q1: nat,Q22: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ X4 @ ( times_times_nat @ N2 @ Q1 ) )
% 5.25/5.50 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q22 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mod_eq_iff
% 5.25/5.50 thf(fact_3258_bits__induct,axiom,
% 5.25/5.50 ! [P: nat > $o,A: nat] :
% 5.25/5.50 ( ! [A5: nat] :
% 5.25/5.50 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ A5 ) )
% 5.25/5.50 => ( ! [A5: nat,B5: $o] :
% 5.25/5.50 ( ( P @ A5 )
% 5.25/5.50 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.50 => ( P @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bits_induct
% 5.25/5.50 thf(fact_3259_bits__induct,axiom,
% 5.25/5.50 ! [P: int > $o,A: int] :
% 5.25/5.50 ( ! [A5: int] :
% 5.25/5.50 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ A5 ) )
% 5.25/5.50 => ( ! [A5: int,B5: $o] :
% 5.25/5.50 ( ( P @ A5 )
% 5.25/5.50 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.50 => ( P @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bits_induct
% 5.25/5.50 thf(fact_3260_bits__induct,axiom,
% 5.25/5.50 ! [P: code_integer > $o,A: code_integer] :
% 5.25/5.50 ( ! [A5: code_integer] :
% 5.25/5.50 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ A5 ) )
% 5.25/5.50 => ( ! [A5: code_integer,B5: $o] :
% 5.25/5.50 ( ( P @ A5 )
% 5.25/5.50 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.25/5.50 = A5 )
% 5.25/5.50 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.25/5.50 => ( P @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % bits_induct
% 5.25/5.50 thf(fact_3261_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_3262_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_3263_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_3264_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.25/5.50 ! [X4: produc9072475918466114483BT_nat] :
% 5.25/5.50 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.25/5.50 ( X4
% 5.25/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.25/5.50 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT,Deg3: nat] :
% 5.25/5.50 ( X4
% 5.25/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Deg3 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % VEBT_internal.valid'.cases
% 5.25/5.50 thf(fact_3265_power__odd__eq,axiom,
% 5.25/5.50 ! [A: complex,N2: nat] :
% 5.25/5.50 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.50 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_odd_eq
% 5.25/5.50 thf(fact_3266_power__odd__eq,axiom,
% 5.25/5.50 ! [A: real,N2: nat] :
% 5.25/5.50 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.50 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_odd_eq
% 5.25/5.50 thf(fact_3267_power__odd__eq,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.50 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_odd_eq
% 5.25/5.50 thf(fact_3268_power__odd__eq,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.25/5.50 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_odd_eq
% 5.25/5.50 thf(fact_3269_exp__mod__exp,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.50 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % exp_mod_exp
% 5.25/5.50 thf(fact_3270_exp__mod__exp,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.50 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % exp_mod_exp
% 5.25/5.50 thf(fact_3271_exp__mod__exp,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.25/5.50 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N2 ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % exp_mod_exp
% 5.25/5.50 thf(fact_3272_unit__div__eq__0__iff,axiom,
% 5.25/5.50 ! [B: nat,A: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ( ( divide_divide_nat @ A @ B )
% 5.25/5.50 = zero_zero_nat )
% 5.25/5.50 = ( A = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_eq_0_iff
% 5.25/5.50 thf(fact_3273_unit__div__eq__0__iff,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.25/5.50 => ( ( ( divide_divide_int @ A @ B )
% 5.25/5.50 = zero_zero_int )
% 5.25/5.50 = ( A = zero_zero_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_eq_0_iff
% 5.25/5.50 thf(fact_3274_unit__div__eq__0__iff,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 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.25/5.50 = zero_z3403309356797280102nteger )
% 5.25/5.50 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % unit_div_eq_0_iff
% 5.25/5.50 thf(fact_3275_even__numeral,axiom,
% 5.25/5.50 ! [N2: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_numeral
% 5.25/5.50 thf(fact_3276_even__numeral,axiom,
% 5.25/5.50 ! [N2: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_numeral
% 5.25/5.50 thf(fact_3277_even__numeral,axiom,
% 5.25/5.50 ! [N2: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % even_numeral
% 5.25/5.50 thf(fact_3278_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_3279_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_3280_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_3281_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: code_integer,N2: nat] :
% 5.25/5.50 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) @ one_one_Code_integer )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.25/5.50 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3282_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N2 ) @ one_one_nat )
% 5.25/5.50 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.25/5.50 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3283_is__unit__power__iff,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( dvd_dvd_int @ ( power_power_int @ A @ N2 ) @ one_one_int )
% 5.25/5.50 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.25/5.50 | ( N2 = zero_zero_nat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % is_unit_power_iff
% 5.25/5.50 thf(fact_3284_mult__le__cancel__left,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left
% 5.25/5.50 thf(fact_3285_mult__le__cancel__left,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left
% 5.25/5.50 thf(fact_3286_mult__le__cancel__left,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left
% 5.25/5.50 thf(fact_3287_mult__le__cancel__right,axiom,
% 5.25/5.50 ! [A: real,C: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right
% 5.25/5.50 thf(fact_3288_mult__le__cancel__right,axiom,
% 5.25/5.50 ! [A: rat,C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right
% 5.25/5.50 thf(fact_3289_mult__le__cancel__right,axiom,
% 5.25/5.50 ! [A: int,C: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right
% 5.25/5.50 thf(fact_3290_mult__left__less__imp__less,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_less_imp_less
% 5.25/5.50 thf(fact_3291_mult__left__less__imp__less,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_less_imp_less
% 5.25/5.50 thf(fact_3292_mult__left__less__imp__less,axiom,
% 5.25/5.50 ! [C: nat,A: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_less_imp_less
% 5.25/5.50 thf(fact_3293_mult__left__less__imp__less,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_less_imp_less
% 5.25/5.50 thf(fact_3294_mult__strict__mono,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.50 ( ( ord_less_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_real @ C @ D )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono
% 5.25/5.50 thf(fact_3295_mult__strict__mono,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_rat @ C @ D )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono
% 5.25/5.50 thf(fact_3296_mult__strict__mono,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.50 ( ( ord_less_nat @ A @ B )
% 5.25/5.50 => ( ( ord_less_nat @ C @ D )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono
% 5.25/5.50 thf(fact_3297_mult__strict__mono,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.50 ( ( ord_less_int @ A @ B )
% 5.25/5.50 => ( ( ord_less_int @ C @ D )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono
% 5.25/5.50 thf(fact_3298_mult__less__cancel__left,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left
% 5.25/5.50 thf(fact_3299_mult__less__cancel__left,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left
% 5.25/5.50 thf(fact_3300_mult__less__cancel__left,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left
% 5.25/5.50 thf(fact_3301_mult__right__less__imp__less,axiom,
% 5.25/5.50 ! [A: real,C: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_less_imp_less
% 5.25/5.50 thf(fact_3302_mult__right__less__imp__less,axiom,
% 5.25/5.50 ! [A: rat,C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_less_imp_less
% 5.25/5.50 thf(fact_3303_mult__right__less__imp__less,axiom,
% 5.25/5.50 ! [A: nat,C: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_less_imp_less
% 5.25/5.50 thf(fact_3304_mult__right__less__imp__less,axiom,
% 5.25/5.50 ! [A: int,C: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_less_imp_less
% 5.25/5.50 thf(fact_3305_mult__strict__mono_H,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.50 ( ( ord_less_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_real @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono'
% 5.25/5.50 thf(fact_3306_mult__strict__mono_H,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_rat @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono'
% 5.25/5.50 thf(fact_3307_mult__strict__mono_H,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.50 ( ( ord_less_nat @ A @ B )
% 5.25/5.50 => ( ( ord_less_nat @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono'
% 5.25/5.50 thf(fact_3308_mult__strict__mono_H,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.50 ( ( ord_less_int @ A @ B )
% 5.25/5.50 => ( ( ord_less_int @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_strict_mono'
% 5.25/5.50 thf(fact_3309_mult__less__cancel__right,axiom,
% 5.25/5.50 ! [A: real,C: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right
% 5.25/5.50 thf(fact_3310_mult__less__cancel__right,axiom,
% 5.25/5.50 ! [A: rat,C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right
% 5.25/5.50 thf(fact_3311_mult__less__cancel__right,axiom,
% 5.25/5.50 ! [A: int,C: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right
% 5.25/5.50 thf(fact_3312_mult__le__cancel__left__neg,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_neg
% 5.25/5.50 thf(fact_3313_mult__le__cancel__left__neg,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_neg
% 5.25/5.50 thf(fact_3314_mult__le__cancel__left__neg,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_neg
% 5.25/5.50 thf(fact_3315_mult__le__cancel__left__pos,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_pos
% 5.25/5.50 thf(fact_3316_mult__le__cancel__left__pos,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_pos
% 5.25/5.50 thf(fact_3317_mult__le__cancel__left__pos,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left_pos
% 5.25/5.50 thf(fact_3318_mult__left__le__imp__le,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_imp_le
% 5.25/5.50 thf(fact_3319_mult__left__le__imp__le,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_imp_le
% 5.25/5.50 thf(fact_3320_mult__left__le__imp__le,axiom,
% 5.25/5.50 ! [C: nat,A: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_imp_le
% 5.25/5.50 thf(fact_3321_mult__left__le__imp__le,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_imp_le
% 5.25/5.50 thf(fact_3322_mult__right__le__imp__le,axiom,
% 5.25/5.50 ! [A: real,C: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_imp_le
% 5.25/5.50 thf(fact_3323_mult__right__le__imp__le,axiom,
% 5.25/5.50 ! [A: rat,C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_imp_le
% 5.25/5.50 thf(fact_3324_mult__right__le__imp__le,axiom,
% 5.25/5.50 ! [A: nat,C: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_imp_le
% 5.25/5.50 thf(fact_3325_mult__right__le__imp__le,axiom,
% 5.25/5.50 ! [A: int,C: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_imp_le
% 5.25/5.50 thf(fact_3326_mult__le__less__imp__less,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_real @ C @ D )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_less_imp_less
% 5.25/5.50 thf(fact_3327_mult__le__less__imp__less,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_rat @ C @ D )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_less_imp_less
% 5.25/5.50 thf(fact_3328_mult__le__less__imp__less,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ A @ B )
% 5.25/5.50 => ( ( ord_less_nat @ C @ D )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_less_imp_less
% 5.25/5.50 thf(fact_3329_mult__le__less__imp__less,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ A @ B )
% 5.25/5.50 => ( ( ord_less_int @ C @ D )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_less_imp_less
% 5.25/5.50 thf(fact_3330_mult__less__le__imp__less,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real,D: real] :
% 5.25/5.50 ( ( ord_less_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_real @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_le_imp_less
% 5.25/5.50 thf(fact_3331_mult__less__le__imp__less,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.25/5.50 ( ( ord_less_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_rat @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_le_imp_less
% 5.25/5.50 thf(fact_3332_mult__less__le__imp__less,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.25/5.50 ( ( ord_less_nat @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_nat @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.25/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_le_imp_less
% 5.25/5.50 thf(fact_3333_mult__less__le__imp__less,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int,D: int] :
% 5.25/5.50 ( ( ord_less_int @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_int @ C @ D )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.50 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_le_imp_less
% 5.25/5.50 thf(fact_3334_mult__left__le__one__le,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.50 => ( ord_less_eq_real @ ( times_times_real @ Y @ X4 ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_one_le
% 5.25/5.50 thf(fact_3335_mult__left__le__one__le,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X4 ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_one_le
% 5.25/5.50 thf(fact_3336_mult__left__le__one__le,axiom,
% 5.25/5.50 ! [X4: int,Y: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.50 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.25/5.50 => ( ord_less_eq_int @ ( times_times_int @ Y @ X4 ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le_one_le
% 5.25/5.50 thf(fact_3337_mult__right__le__one__le,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.25/5.50 => ( ord_less_eq_real @ ( times_times_real @ X4 @ Y ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_one_le
% 5.25/5.50 thf(fact_3338_mult__right__le__one__le,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Y ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_one_le
% 5.25/5.50 thf(fact_3339_mult__right__le__one__le,axiom,
% 5.25/5.50 ! [X4: int,Y: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.25/5.50 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.25/5.50 => ( ord_less_eq_int @ ( times_times_int @ X4 @ Y ) @ X4 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_right_le_one_le
% 5.25/5.50 thf(fact_3340_mult__le__one,axiom,
% 5.25/5.50 ! [A: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.25/5.50 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.25/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_one
% 5.25/5.50 thf(fact_3341_mult__le__one,axiom,
% 5.25/5.50 ! [A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.25/5.50 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_one
% 5.25/5.50 thf(fact_3342_mult__le__one,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.25/5.50 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.25/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_one
% 5.25/5.50 thf(fact_3343_mult__le__one,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.25/5.50 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.25/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_one
% 5.25/5.50 thf(fact_3344_mult__left__le,axiom,
% 5.25/5.50 ! [C: real,A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.25/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le
% 5.25/5.50 thf(fact_3345_mult__left__le,axiom,
% 5.25/5.50 ! [C: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.25/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.25/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le
% 5.25/5.50 thf(fact_3346_mult__left__le,axiom,
% 5.25/5.50 ! [C: nat,A: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.25/5.50 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.25/5.50 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le
% 5.25/5.50 thf(fact_3347_mult__left__le,axiom,
% 5.25/5.50 ! [C: int,A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.25/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.25/5.50 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_left_le
% 5.25/5.50 thf(fact_3348_sum__squares__ge__zero,axiom,
% 5.25/5.50 ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_ge_zero
% 5.25/5.50 thf(fact_3349_sum__squares__ge__zero,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_ge_zero
% 5.25/5.50 thf(fact_3350_sum__squares__ge__zero,axiom,
% 5.25/5.50 ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_ge_zero
% 5.25/5.50 thf(fact_3351_sum__squares__le__zero__iff,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.25/5.50 = ( ( X4 = zero_zero_real )
% 5.25/5.50 & ( Y = zero_zero_real ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_le_zero_iff
% 5.25/5.50 thf(fact_3352_sum__squares__le__zero__iff,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.25/5.50 = ( ( X4 = zero_zero_rat )
% 5.25/5.50 & ( Y = zero_zero_rat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_le_zero_iff
% 5.25/5.50 thf(fact_3353_sum__squares__le__zero__iff,axiom,
% 5.25/5.50 ! [X4: int,Y: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.25/5.50 = ( ( X4 = zero_zero_int )
% 5.25/5.50 & ( Y = zero_zero_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_le_zero_iff
% 5.25/5.50 thf(fact_3354_not__sum__squares__lt__zero,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.25/5.50
% 5.25/5.50 % not_sum_squares_lt_zero
% 5.25/5.50 thf(fact_3355_not__sum__squares__lt__zero,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.25/5.50
% 5.25/5.50 % not_sum_squares_lt_zero
% 5.25/5.50 thf(fact_3356_not__sum__squares__lt__zero,axiom,
% 5.25/5.50 ! [X4: int,Y: int] :
% 5.25/5.50 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.25/5.50
% 5.25/5.50 % not_sum_squares_lt_zero
% 5.25/5.50 thf(fact_3357_sum__squares__gt__zero__iff,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) )
% 5.25/5.50 = ( ( X4 != zero_zero_real )
% 5.25/5.50 | ( Y != zero_zero_real ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_gt_zero_iff
% 5.25/5.50 thf(fact_3358_sum__squares__gt__zero__iff,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.25/5.50 = ( ( X4 != zero_zero_rat )
% 5.25/5.50 | ( Y != zero_zero_rat ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_gt_zero_iff
% 5.25/5.50 thf(fact_3359_sum__squares__gt__zero__iff,axiom,
% 5.25/5.50 ! [X4: int,Y: int] :
% 5.25/5.50 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) ) )
% 5.25/5.50 = ( ( X4 != zero_zero_int )
% 5.25/5.50 | ( Y != zero_zero_int ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % sum_squares_gt_zero_iff
% 5.25/5.50 thf(fact_3360_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.25/5.50 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 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 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.25/5.50 thf(fact_3361_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.25/5.50 ! [C: nat,A: nat,B: nat] :
% 5.25/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 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 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.25/5.50 thf(fact_3362_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.25/5.50 ! [C: int,A: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 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 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.25/5.50 thf(fact_3363_divide__strict__left__mono__neg,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.50 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_strict_left_mono_neg
% 5.25/5.50 thf(fact_3364_divide__strict__left__mono__neg,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real] :
% 5.25/5.50 ( ( ord_less_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.50 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_strict_left_mono_neg
% 5.25/5.50 thf(fact_3365_divide__strict__left__mono,axiom,
% 5.25/5.50 ! [B: rat,A: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_rat @ B @ A )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.50 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_strict_left_mono
% 5.25/5.50 thf(fact_3366_divide__strict__left__mono,axiom,
% 5.25/5.50 ! [B: real,A: real,C: real] :
% 5.25/5.50 ( ( ord_less_real @ B @ A )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.50 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_strict_left_mono
% 5.25/5.50 thf(fact_3367_mult__imp__less__div__pos,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X4: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 5.25/5.50 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_less_div_pos
% 5.25/5.50 thf(fact_3368_mult__imp__less__div__pos,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X4: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 5.25/5.50 => ( ord_less_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_less_div_pos
% 5.25/5.50 thf(fact_3369_mult__imp__div__pos__less,axiom,
% 5.25/5.50 ! [Y: rat,X4: rat,Z: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 5.25/5.50 => ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_div_pos_less
% 5.25/5.50 thf(fact_3370_mult__imp__div__pos__less,axiom,
% 5.25/5.50 ! [Y: real,X4: real,Z: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 5.25/5.50 => ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_div_pos_less
% 5.25/5.50 thf(fact_3371_pos__less__divide__eq,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_less_divide_eq
% 5.25/5.50 thf(fact_3372_pos__less__divide__eq,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_less_divide_eq
% 5.25/5.50 thf(fact_3373_pos__divide__less__eq,axiom,
% 5.25/5.50 ! [C: rat,B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_divide_less_eq
% 5.25/5.50 thf(fact_3374_pos__divide__less__eq,axiom,
% 5.25/5.50 ! [C: real,B: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_divide_less_eq
% 5.25/5.50 thf(fact_3375_neg__less__divide__eq,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_divide_eq
% 5.25/5.50 thf(fact_3376_neg__less__divide__eq,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_less_divide_eq
% 5.25/5.50 thf(fact_3377_neg__divide__less__eq,axiom,
% 5.25/5.50 ! [C: rat,B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_divide_less_eq
% 5.25/5.50 thf(fact_3378_neg__divide__less__eq,axiom,
% 5.25/5.50 ! [C: real,B: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_divide_less_eq
% 5.25/5.50 thf(fact_3379_less__divide__eq,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_divide_eq
% 5.25/5.50 thf(fact_3380_less__divide__eq,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real] :
% 5.25/5.50 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % less_divide_eq
% 5.25/5.50 thf(fact_3381_divide__less__eq,axiom,
% 5.25/5.50 ! [B: rat,C: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.25/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.25/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_less_eq
% 5.25/5.50 thf(fact_3382_divide__less__eq,axiom,
% 5.25/5.50 ! [B: real,C: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.25/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.25/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_less_eq
% 5.25/5.50 thf(fact_3383_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [W: num,B: rat,C: rat] :
% 5.25/5.50 ( ( ( numeral_numeral_rat @ W )
% 5.25/5.50 = ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( C != zero_zero_rat )
% 5.25/5.50 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( C = zero_zero_rat )
% 5.25/5.50 => ( ( numeral_numeral_rat @ W )
% 5.25/5.50 = zero_zero_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % eq_divide_eq_numeral(1)
% 5.25/5.50 thf(fact_3384_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [W: num,B: real,C: real] :
% 5.25/5.50 ( ( ( numeral_numeral_real @ W )
% 5.25/5.50 = ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ( ( C != zero_zero_real )
% 5.25/5.50 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( C = zero_zero_real )
% 5.25/5.50 => ( ( numeral_numeral_real @ W )
% 5.25/5.50 = zero_zero_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % eq_divide_eq_numeral(1)
% 5.25/5.50 thf(fact_3385_eq__divide__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [W: num,B: complex,C: complex] :
% 5.25/5.50 ( ( ( numera6690914467698888265omplex @ W )
% 5.25/5.50 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.25/5.50 = ( ( ( C != zero_zero_complex )
% 5.25/5.50 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( C = zero_zero_complex )
% 5.25/5.50 => ( ( numera6690914467698888265omplex @ W )
% 5.25/5.50 = zero_zero_complex ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % eq_divide_eq_numeral(1)
% 5.25/5.50 thf(fact_3386_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [B: rat,C: rat,W: num] :
% 5.25/5.50 ( ( ( divide_divide_rat @ B @ C )
% 5.25/5.50 = ( numeral_numeral_rat @ W ) )
% 5.25/5.50 = ( ( ( C != zero_zero_rat )
% 5.25/5.50 => ( B
% 5.25/5.50 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.25/5.50 & ( ( C = zero_zero_rat )
% 5.25/5.50 => ( ( numeral_numeral_rat @ W )
% 5.25/5.50 = zero_zero_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_eq_eq_numeral(1)
% 5.25/5.50 thf(fact_3387_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [B: real,C: real,W: num] :
% 5.25/5.50 ( ( ( divide_divide_real @ B @ C )
% 5.25/5.50 = ( numeral_numeral_real @ W ) )
% 5.25/5.50 = ( ( ( C != zero_zero_real )
% 5.25/5.50 => ( B
% 5.25/5.50 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.25/5.50 & ( ( C = zero_zero_real )
% 5.25/5.50 => ( ( numeral_numeral_real @ W )
% 5.25/5.50 = zero_zero_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_eq_eq_numeral(1)
% 5.25/5.50 thf(fact_3388_divide__eq__eq__numeral_I1_J,axiom,
% 5.25/5.50 ! [B: complex,C: complex,W: num] :
% 5.25/5.50 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.25/5.50 = ( numera6690914467698888265omplex @ W ) )
% 5.25/5.50 = ( ( ( C != zero_zero_complex )
% 5.25/5.50 => ( B
% 5.25/5.50 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.25/5.50 & ( ( C = zero_zero_complex )
% 5.25/5.50 => ( ( numera6690914467698888265omplex @ W )
% 5.25/5.50 = zero_zero_complex ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_eq_eq_numeral(1)
% 5.25/5.50 thf(fact_3389_divide__add__eq__iff,axiom,
% 5.25/5.50 ! [Z: rat,X4: rat,Y: rat] :
% 5.25/5.50 ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_add_eq_iff
% 5.25/5.50 thf(fact_3390_divide__add__eq__iff,axiom,
% 5.25/5.50 ! [Z: real,X4: real,Y: real] :
% 5.25/5.50 ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_add_eq_iff
% 5.25/5.50 thf(fact_3391_divide__add__eq__iff,axiom,
% 5.25/5.50 ! [Z: complex,X4: complex,Y: complex] :
% 5.25/5.50 ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_add_eq_iff
% 5.25/5.50 thf(fact_3392_add__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: rat,X4: rat,Y: rat] :
% 5.25/5.50 ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_iff
% 5.25/5.50 thf(fact_3393_add__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: real,X4: real,Y: real] :
% 5.25/5.50 ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_iff
% 5.25/5.50 thf(fact_3394_add__divide__eq__iff,axiom,
% 5.25/5.50 ! [Z: complex,X4: complex,Y: complex] :
% 5.25/5.50 ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_iff
% 5.25/5.50 thf(fact_3395_add__num__frac,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X4: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_num_frac
% 5.25/5.50 thf(fact_3396_add__num__frac,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X4: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X4 @ Y ) )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_num_frac
% 5.25/5.50 thf(fact_3397_add__num__frac,axiom,
% 5.25/5.50 ! [Y: complex,Z: complex,X4: complex] :
% 5.25/5.50 ( ( Y != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_num_frac
% 5.25/5.50 thf(fact_3398_add__frac__num,axiom,
% 5.25/5.50 ! [Y: rat,X4: rat,Z: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ X4 @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_num
% 5.25/5.50 thf(fact_3399_add__frac__num,axiom,
% 5.25/5.50 ! [Y: real,X4: real,Z: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ Z )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_num
% 5.25/5.50 thf(fact_3400_add__frac__num,axiom,
% 5.25/5.50 ! [Y: complex,X4: complex,Z: complex] :
% 5.25/5.50 ( ( Y != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ Z )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X4 @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_num
% 5.25/5.50 thf(fact_3401_add__frac__eq,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 5.25/5.50 ( ( Y != zero_zero_rat )
% 5.25/5.50 => ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_eq
% 5.25/5.50 thf(fact_3402_add__frac__eq,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X4: real,W: real] :
% 5.25/5.50 ( ( Y != zero_zero_real )
% 5.25/5.50 => ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_eq
% 5.25/5.50 thf(fact_3403_add__frac__eq,axiom,
% 5.25/5.50 ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 5.25/5.50 ( ( Y != zero_zero_complex )
% 5.25/5.50 => ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_frac_eq
% 5.25/5.50 thf(fact_3404_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.50 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ( Z = zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(1)
% 5.25/5.50 thf(fact_3405_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.50 ! [Z: real,A: real,B: real] :
% 5.25/5.50 ( ( ( Z = zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(1)
% 5.25/5.50 thf(fact_3406_add__divide__eq__if__simps_I1_J,axiom,
% 5.25/5.50 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.50 ( ( ( Z = zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.50 = A ) )
% 5.25/5.50 & ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(1)
% 5.25/5.50 thf(fact_3407_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.50 ! [Z: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ( Z = zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( Z != zero_zero_rat )
% 5.25/5.50 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.25/5.50 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(2)
% 5.25/5.50 thf(fact_3408_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.50 ! [Z: real,A: real,B: real] :
% 5.25/5.50 ( ( ( Z = zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( Z != zero_zero_real )
% 5.25/5.50 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.25/5.50 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(2)
% 5.25/5.50 thf(fact_3409_add__divide__eq__if__simps_I2_J,axiom,
% 5.25/5.50 ! [Z: complex,A: complex,B: complex] :
% 5.25/5.50 ( ( ( Z = zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.50 = B ) )
% 5.25/5.50 & ( ( Z != zero_zero_complex )
% 5.25/5.50 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.25/5.50 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % add_divide_eq_if_simps(2)
% 5.25/5.50 thf(fact_3410_power__less__power__Suc,axiom,
% 5.25/5.50 ! [A: real,N2: nat] :
% 5.25/5.50 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.50 => ( ord_less_real @ ( power_power_real @ A @ N2 ) @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_less_power_Suc
% 5.25/5.50 thf(fact_3411_power__less__power__Suc,axiom,
% 5.25/5.50 ! [A: rat,N2: nat] :
% 5.25/5.50 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.50 => ( ord_less_rat @ ( power_power_rat @ A @ N2 ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_less_power_Suc
% 5.25/5.50 thf(fact_3412_power__less__power__Suc,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.50 => ( ord_less_nat @ ( power_power_nat @ A @ N2 ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_less_power_Suc
% 5.25/5.50 thf(fact_3413_power__less__power__Suc,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.50 => ( ord_less_int @ ( power_power_int @ A @ N2 ) @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_less_power_Suc
% 5.25/5.50 thf(fact_3414_power__gt1__lemma,axiom,
% 5.25/5.50 ! [A: real,N2: nat] :
% 5.25/5.50 ( ( ord_less_real @ one_one_real @ A )
% 5.25/5.50 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_gt1_lemma
% 5.25/5.50 thf(fact_3415_power__gt1__lemma,axiom,
% 5.25/5.50 ! [A: rat,N2: nat] :
% 5.25/5.50 ( ( ord_less_rat @ one_one_rat @ A )
% 5.25/5.50 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_gt1_lemma
% 5.25/5.50 thf(fact_3416_power__gt1__lemma,axiom,
% 5.25/5.50 ! [A: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ one_one_nat @ A )
% 5.25/5.50 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_gt1_lemma
% 5.25/5.50 thf(fact_3417_power__gt1__lemma,axiom,
% 5.25/5.50 ! [A: int,N2: nat] :
% 5.25/5.50 ( ( ord_less_int @ one_one_int @ A )
% 5.25/5.50 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % power_gt1_lemma
% 5.25/5.50 thf(fact_3418_dvd__imp__le,axiom,
% 5.25/5.50 ! [K: nat,N2: nat] :
% 5.25/5.50 ( ( dvd_dvd_nat @ K @ N2 )
% 5.25/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 => ( ord_less_eq_nat @ K @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_imp_le
% 5.25/5.50 thf(fact_3419_mult__div__mod__eq,axiom,
% 5.25/5.50 ! [B: nat,A: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mult_div_mod_eq
% 5.25/5.50 thf(fact_3420_mult__div__mod__eq,axiom,
% 5.25/5.50 ! [B: int,A: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mult_div_mod_eq
% 5.25/5.50 thf(fact_3421_mult__div__mod__eq,axiom,
% 5.25/5.50 ! [B: code_integer,A: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mult_div_mod_eq
% 5.25/5.50 thf(fact_3422_mod__mult__div__eq,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_mult_div_eq
% 5.25/5.50 thf(fact_3423_mod__mult__div__eq,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_mult_div_eq
% 5.25/5.50 thf(fact_3424_mod__mult__div__eq,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_mult_div_eq
% 5.25/5.50 thf(fact_3425_mod__div__mult__eq,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_mult_eq
% 5.25/5.50 thf(fact_3426_mod__div__mult__eq,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_mult_eq
% 5.25/5.50 thf(fact_3427_mod__div__mult__eq,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_mult_eq
% 5.25/5.50 thf(fact_3428_div__mult__mod__eq,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult_mod_eq
% 5.25/5.50 thf(fact_3429_div__mult__mod__eq,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult_mod_eq
% 5.25/5.50 thf(fact_3430_div__mult__mod__eq,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.25/5.50 = A ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult_mod_eq
% 5.25/5.50 thf(fact_3431_mod__div__decomp,axiom,
% 5.25/5.50 ! [A: nat,B: nat] :
% 5.25/5.50 ( A
% 5.25/5.50 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_decomp
% 5.25/5.50 thf(fact_3432_mod__div__decomp,axiom,
% 5.25/5.50 ! [A: int,B: int] :
% 5.25/5.50 ( A
% 5.25/5.50 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_decomp
% 5.25/5.50 thf(fact_3433_mod__div__decomp,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer] :
% 5.25/5.50 ( A
% 5.25/5.50 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_div_decomp
% 5.25/5.50 thf(fact_3434_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_plus_nat @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(1)
% 5.25/5.50 thf(fact_3435_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_plus_int @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(1)
% 5.25/5.50 thf(fact_3436_cancel__div__mod__rules_I1_J,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(1)
% 5.25/5.50 thf(fact_3437_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.50 ! [B: nat,A: nat,C: nat] :
% 5.25/5.50 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_plus_nat @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(2)
% 5.25/5.50 thf(fact_3438_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.50 ! [B: int,A: int,C: int] :
% 5.25/5.50 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_plus_int @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(2)
% 5.25/5.50 thf(fact_3439_cancel__div__mod__rules_I2_J,axiom,
% 5.25/5.50 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.25/5.50 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.25/5.50 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.25/5.50
% 5.25/5.50 % cancel_div_mod_rules(2)
% 5.25/5.50 thf(fact_3440_div__mult1__eq,axiom,
% 5.25/5.50 ! [A: nat,B: nat,C: nat] :
% 5.25/5.50 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.25/5.50 = ( 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 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult1_eq
% 5.25/5.50 thf(fact_3441_div__mult1__eq,axiom,
% 5.25/5.50 ! [A: int,B: int,C: int] :
% 5.25/5.50 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.25/5.50 = ( 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 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult1_eq
% 5.25/5.50 thf(fact_3442_div__mult1__eq,axiom,
% 5.25/5.50 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.25/5.50 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.25/5.50 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_mult1_eq
% 5.25/5.50 thf(fact_3443_pos__zmod__mult__2,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 => ( ( 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 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_zmod_mult_2
% 5.25/5.50 thf(fact_3444_one__less__mult,axiom,
% 5.25/5.50 ! [N2: nat,M: nat] :
% 5.25/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.25/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.50 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % one_less_mult
% 5.25/5.50 thf(fact_3445_n__less__m__mult__n,axiom,
% 5.25/5.50 ! [N2: nat,M: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.50 => ( ord_less_nat @ N2 @ ( times_times_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % n_less_m_mult_n
% 5.25/5.50 thf(fact_3446_n__less__n__mult__m,axiom,
% 5.25/5.50 ! [N2: nat,M: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.25/5.50 => ( ord_less_nat @ N2 @ ( times_times_nat @ N2 @ M ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % n_less_n_mult_m
% 5.25/5.50 thf(fact_3447_mod__greater__zero__iff__not__dvd,axiom,
% 5.25/5.50 ! [M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.25/5.50 = ( ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_greater_zero_iff_not_dvd
% 5.25/5.50 thf(fact_3448_nat__mult__le__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.50 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mult_le_cancel1
% 5.25/5.50 thf(fact_3449_div__less__iff__less__mult,axiom,
% 5.25/5.50 ! [Q3: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.25/5.50 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q3 ) @ N2 )
% 5.25/5.50 = ( ord_less_nat @ M @ ( times_times_nat @ N2 @ Q3 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_less_iff_less_mult
% 5.25/5.50 thf(fact_3450_nat__mult__div__cancel1,axiom,
% 5.25/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.25/5.50 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) )
% 5.25/5.50 = ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mult_div_cancel1
% 5.25/5.50 thf(fact_3451_mod__eq__nat1E,axiom,
% 5.25/5.50 ! [M: nat,Q3: nat,N2: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.25/5.50 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.25/5.50 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.25/5.50 => ~ ! [S3: nat] :
% 5.25/5.50 ( M
% 5.25/5.50 != ( plus_plus_nat @ N2 @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_eq_nat1E
% 5.25/5.50 thf(fact_3452_mod__eq__nat2E,axiom,
% 5.25/5.50 ! [M: nat,Q3: nat,N2: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.25/5.50 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.25/5.50 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.25/5.50 => ~ ! [S3: nat] :
% 5.25/5.50 ( N2
% 5.25/5.50 != ( plus_plus_nat @ M @ ( times_times_nat @ Q3 @ S3 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_eq_nat2E
% 5.25/5.50 thf(fact_3453_nat__mod__eq__lemma,axiom,
% 5.25/5.50 ! [X4: nat,N2: nat,Y: nat] :
% 5.25/5.50 ( ( ( modulo_modulo_nat @ X4 @ N2 )
% 5.25/5.50 = ( modulo_modulo_nat @ Y @ N2 ) )
% 5.25/5.50 => ( ( ord_less_eq_nat @ Y @ X4 )
% 5.25/5.50 => ? [Q2: nat] :
% 5.25/5.50 ( X4
% 5.25/5.50 = ( plus_plus_nat @ Y @ ( times_times_nat @ N2 @ Q2 ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % nat_mod_eq_lemma
% 5.25/5.50 thf(fact_3454_div__mod__decomp,axiom,
% 5.25/5.50 ! [A2: nat,N2: nat] :
% 5.25/5.50 ( A2
% 5.25/5.50 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N2 ) @ N2 ) @ ( modulo_modulo_nat @ A2 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % div_mod_decomp
% 5.25/5.50 thf(fact_3455_mod__mult2__eq,axiom,
% 5.25/5.50 ! [M: nat,N2: nat,Q3: nat] :
% 5.25/5.50 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N2 @ Q3 ) )
% 5.25/5.50 = ( plus_plus_nat @ ( times_times_nat @ N2 @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N2 ) @ Q3 ) ) @ ( modulo_modulo_nat @ M @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mod_mult2_eq
% 5.25/5.50 thf(fact_3456_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_3457_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_3458_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_3459_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_3460_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_3461_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_3462_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_3463_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_3464_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_3465_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y6: nat,Z4: nat] : ( Y6 = Z4 ) )
% 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_3466_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 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_3467_bit__eq__rec,axiom,
% 5.25/5.50 ( ( ^ [Y6: code_integer,Z4: code_integer] : ( Y6 = Z4 ) )
% 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_3468_dvd__power__iff,axiom,
% 5.25/5.50 ! [X4: code_integer,M: nat,N2: nat] :
% 5.25/5.50 ( ( X4 != zero_z3403309356797280102nteger )
% 5.25/5.50 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X4 @ M ) @ ( power_8256067586552552935nteger @ X4 @ N2 ) )
% 5.25/5.50 = ( ( dvd_dvd_Code_integer @ X4 @ one_one_Code_integer )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3469_dvd__power__iff,axiom,
% 5.25/5.50 ! [X4: nat,M: nat,N2: nat] :
% 5.25/5.50 ( ( X4 != zero_zero_nat )
% 5.25/5.50 => ( ( dvd_dvd_nat @ ( power_power_nat @ X4 @ M ) @ ( power_power_nat @ X4 @ N2 ) )
% 5.25/5.50 = ( ( dvd_dvd_nat @ X4 @ one_one_nat )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3470_dvd__power__iff,axiom,
% 5.25/5.50 ! [X4: int,M: nat,N2: nat] :
% 5.25/5.50 ( ( X4 != zero_zero_int )
% 5.25/5.50 => ( ( dvd_dvd_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ N2 ) )
% 5.25/5.50 = ( ( dvd_dvd_int @ X4 @ one_one_int )
% 5.25/5.50 | ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power_iff
% 5.25/5.50 thf(fact_3471_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: code_integer] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_Code_integer ) )
% 5.25/5.50 => ( dvd_dvd_Code_integer @ X4 @ ( power_8256067586552552935nteger @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3472_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: rat] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_rat ) )
% 5.25/5.50 => ( dvd_dvd_rat @ X4 @ ( power_power_rat @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3473_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: nat] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_nat ) )
% 5.25/5.50 => ( dvd_dvd_nat @ X4 @ ( power_power_nat @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3474_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: real] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_real ) )
% 5.25/5.50 => ( dvd_dvd_real @ X4 @ ( power_power_real @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3475_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: int] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_int ) )
% 5.25/5.50 => ( dvd_dvd_int @ X4 @ ( power_power_int @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3476_dvd__power,axiom,
% 5.25/5.50 ! [N2: nat,X4: complex] :
% 5.25/5.50 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.25/5.50 | ( X4 = one_one_complex ) )
% 5.25/5.50 => ( dvd_dvd_complex @ X4 @ ( power_power_complex @ X4 @ N2 ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % dvd_power
% 5.25/5.50 thf(fact_3477_field__le__mult__one__interval,axiom,
% 5.25/5.50 ! [X4: real,Y: real] :
% 5.25/5.50 ( ! [Z2: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ Z2 )
% 5.25/5.50 => ( ( ord_less_real @ Z2 @ one_one_real )
% 5.25/5.50 => ( ord_less_eq_real @ ( times_times_real @ Z2 @ X4 ) @ Y ) ) )
% 5.25/5.50 => ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % field_le_mult_one_interval
% 5.25/5.50 thf(fact_3478_field__le__mult__one__interval,axiom,
% 5.25/5.50 ! [X4: rat,Y: rat] :
% 5.25/5.50 ( ! [Z2: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ Z2 )
% 5.25/5.50 => ( ( ord_less_rat @ Z2 @ one_one_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ Z2 @ X4 ) @ Y ) ) )
% 5.25/5.50 => ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.25/5.50
% 5.25/5.50 % field_le_mult_one_interval
% 5.25/5.50 thf(fact_3479_mult__less__cancel__right2,axiom,
% 5.25/5.50 ! [A: real,C: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ one_one_real ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right2
% 5.25/5.50 thf(fact_3480_mult__less__cancel__right2,axiom,
% 5.25/5.50 ! [A: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right2
% 5.25/5.50 thf(fact_3481_mult__less__cancel__right2,axiom,
% 5.25/5.50 ! [A: int,C: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ one_one_int ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right2
% 5.25/5.50 thf(fact_3482_mult__less__cancel__right1,axiom,
% 5.25/5.50 ! [C: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ one_one_real @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right1
% 5.25/5.50 thf(fact_3483_mult__less__cancel__right1,axiom,
% 5.25/5.50 ! [C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right1
% 5.25/5.50 thf(fact_3484_mult__less__cancel__right1,axiom,
% 5.25/5.50 ! [C: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ one_one_int @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_right1
% 5.25/5.50 thf(fact_3485_mult__less__cancel__left2,axiom,
% 5.25/5.50 ! [C: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ A @ one_one_real ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left2
% 5.25/5.50 thf(fact_3486_mult__less__cancel__left2,axiom,
% 5.25/5.50 ! [C: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left2
% 5.25/5.50 thf(fact_3487_mult__less__cancel__left2,axiom,
% 5.25/5.50 ! [C: int,A: int] :
% 5.25/5.50 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ A @ one_one_int ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left2
% 5.25/5.50 thf(fact_3488_mult__less__cancel__left1,axiom,
% 5.25/5.50 ! [C: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_real @ one_one_real @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left1
% 5.25/5.50 thf(fact_3489_mult__less__cancel__left1,axiom,
% 5.25/5.50 ! [C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left1
% 5.25/5.50 thf(fact_3490_mult__less__cancel__left1,axiom,
% 5.25/5.50 ! [C: int,B: int] :
% 5.25/5.50 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_int @ one_one_int @ B ) )
% 5.25/5.50 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_less_cancel_left1
% 5.25/5.50 thf(fact_3491_mult__le__cancel__right2,axiom,
% 5.25/5.50 ! [A: real,C: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right2
% 5.25/5.50 thf(fact_3492_mult__le__cancel__right2,axiom,
% 5.25/5.50 ! [A: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right2
% 5.25/5.50 thf(fact_3493_mult__le__cancel__right2,axiom,
% 5.25/5.50 ! [A: int,C: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right2
% 5.25/5.50 thf(fact_3494_mult__le__cancel__right1,axiom,
% 5.25/5.50 ! [C: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right1
% 5.25/5.50 thf(fact_3495_mult__le__cancel__right1,axiom,
% 5.25/5.50 ! [C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right1
% 5.25/5.50 thf(fact_3496_mult__le__cancel__right1,axiom,
% 5.25/5.50 ! [C: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_right1
% 5.25/5.50 thf(fact_3497_mult__le__cancel__left2,axiom,
% 5.25/5.50 ! [C: real,A: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left2
% 5.25/5.50 thf(fact_3498_mult__le__cancel__left2,axiom,
% 5.25/5.50 ! [C: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left2
% 5.25/5.50 thf(fact_3499_mult__le__cancel__left2,axiom,
% 5.25/5.50 ! [C: int,A: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left2
% 5.25/5.50 thf(fact_3500_mult__le__cancel__left1,axiom,
% 5.25/5.50 ! [C: real,B: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.25/5.50 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left1
% 5.25/5.50 thf(fact_3501_mult__le__cancel__left1,axiom,
% 5.25/5.50 ! [C: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.25/5.50 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left1
% 5.25/5.50 thf(fact_3502_mult__le__cancel__left1,axiom,
% 5.25/5.50 ! [C: int,B: int] :
% 5.25/5.50 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.25/5.50 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.25/5.50 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.25/5.50 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.25/5.50 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_le_cancel_left1
% 5.25/5.50 thf(fact_3503_divide__left__mono__neg,axiom,
% 5.25/5.50 ! [A: real,B: real,C: real] :
% 5.25/5.50 ( ( ord_less_eq_real @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.25/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_left_mono_neg
% 5.25/5.50 thf(fact_3504_divide__left__mono__neg,axiom,
% 5.25/5.50 ! [A: rat,B: rat,C: rat] :
% 5.25/5.50 ( ( ord_less_eq_rat @ A @ B )
% 5.25/5.50 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.25/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % divide_left_mono_neg
% 5.25/5.50 thf(fact_3505_mult__imp__le__div__pos,axiom,
% 5.25/5.50 ! [Y: real,Z: real,X4: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X4 )
% 5.25/5.50 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_le_div_pos
% 5.25/5.50 thf(fact_3506_mult__imp__le__div__pos,axiom,
% 5.25/5.50 ! [Y: rat,Z: rat,X4: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X4 )
% 5.25/5.50 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_le_div_pos
% 5.25/5.50 thf(fact_3507_mult__imp__div__pos__le,axiom,
% 5.25/5.50 ! [Y: real,X4: real,Z: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.25/5.50 => ( ( ord_less_eq_real @ X4 @ ( times_times_real @ Z @ Y ) )
% 5.25/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_div_pos_le
% 5.25/5.50 thf(fact_3508_mult__imp__div__pos__le,axiom,
% 5.25/5.50 ! [Y: rat,X4: rat,Z: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.25/5.50 => ( ( ord_less_eq_rat @ X4 @ ( times_times_rat @ Z @ Y ) )
% 5.25/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ Z ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % mult_imp_div_pos_le
% 5.25/5.50 thf(fact_3509_pos__le__divide__eq,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_le_divide_eq
% 5.25/5.50 thf(fact_3510_pos__le__divide__eq,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_le_divide_eq
% 5.25/5.50 thf(fact_3511_pos__divide__le__eq,axiom,
% 5.25/5.50 ! [C: real,B: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ zero_zero_real @ C )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_divide_le_eq
% 5.25/5.50 thf(fact_3512_pos__divide__le__eq,axiom,
% 5.25/5.50 ! [C: rat,B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.25/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % pos_divide_le_eq
% 5.25/5.50 thf(fact_3513_neg__le__divide__eq,axiom,
% 5.25/5.50 ! [C: real,A: real,B: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.25/5.50 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_divide_eq
% 5.25/5.50 thf(fact_3514_neg__le__divide__eq,axiom,
% 5.25/5.50 ! [C: rat,A: rat,B: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.25/5.50 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.25/5.50 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_le_divide_eq
% 5.25/5.50 thf(fact_3515_neg__divide__le__eq,axiom,
% 5.25/5.50 ! [C: real,B: real,A: real] :
% 5.25/5.50 ( ( ord_less_real @ C @ zero_zero_real )
% 5.25/5.50 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.25/5.50 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.25/5.50
% 5.25/5.50 % neg_divide_le_eq
% 5.25/5.50 thf(fact_3516_neg__divide__le__eq,axiom,
% 5.25/5.50 ! [C: rat,B: rat,A: rat] :
% 5.25/5.50 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.27/5.50 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % neg_divide_le_eq
% 5.27/5.50 thf(fact_3517_divide__left__mono,axiom,
% 5.27/5.50 ! [B: real,A: real,C: real] :
% 5.27/5.50 ( ( ord_less_eq_real @ B @ A )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.27/5.50 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_left_mono
% 5.27/5.50 thf(fact_3518_divide__left__mono,axiom,
% 5.27/5.50 ! [B: rat,A: rat,C: rat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ B @ A )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.50 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_left_mono
% 5.27/5.50 thf(fact_3519_le__divide__eq,axiom,
% 5.27/5.50 ! [A: real,B: real,C: real] :
% 5.27/5.50 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % le_divide_eq
% 5.27/5.50 thf(fact_3520_le__divide__eq,axiom,
% 5.27/5.50 ! [A: rat,B: rat,C: rat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % le_divide_eq
% 5.27/5.50 thf(fact_3521_divide__le__eq,axiom,
% 5.27/5.50 ! [B: real,C: real,A: real] :
% 5.27/5.50 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_le_eq
% 5.27/5.50 thf(fact_3522_divide__le__eq,axiom,
% 5.27/5.50 ! [B: rat,C: rat,A: rat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_le_eq
% 5.27/5.50 thf(fact_3523_convex__bound__le,axiom,
% 5.27/5.50 ! [X4: real,A: real,Y: real,U: real,V: real] :
% 5.27/5.50 ( ( ord_less_eq_real @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_eq_real @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.27/5.50 => ( ( ( plus_plus_real @ U @ V )
% 5.27/5.50 = one_one_real )
% 5.27/5.50 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_le
% 5.27/5.50 thf(fact_3524_convex__bound__le,axiom,
% 5.27/5.50 ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_eq_rat @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.27/5.50 => ( ( ( plus_plus_rat @ U @ V )
% 5.27/5.50 = one_one_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_le
% 5.27/5.50 thf(fact_3525_convex__bound__le,axiom,
% 5.27/5.50 ! [X4: int,A: int,Y: int,U: int,V: int] :
% 5.27/5.50 ( ( ord_less_eq_int @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_eq_int @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.27/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.27/5.50 => ( ( ( plus_plus_int @ U @ V )
% 5.27/5.50 = one_one_int )
% 5.27/5.50 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_le
% 5.27/5.50 thf(fact_3526_less__divide__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [W: num,B: rat,C: rat] :
% 5.27/5.50 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % less_divide_eq_numeral(1)
% 5.27/5.50 thf(fact_3527_less__divide__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [W: num,B: real,C: real] :
% 5.27/5.50 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % less_divide_eq_numeral(1)
% 5.27/5.50 thf(fact_3528_divide__less__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [B: rat,C: rat,W: num] :
% 5.27/5.50 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_less_eq_numeral(1)
% 5.27/5.50 thf(fact_3529_divide__less__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [B: real,C: real,W: num] :
% 5.27/5.50 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_less_eq_numeral(1)
% 5.27/5.50 thf(fact_3530_power__Suc__less,axiom,
% 5.27/5.50 ! [A: real,N2: nat] :
% 5.27/5.50 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.50 => ( ( ord_less_real @ A @ one_one_real )
% 5.27/5.50 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N2 ) ) @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_Suc_less
% 5.27/5.50 thf(fact_3531_power__Suc__less,axiom,
% 5.27/5.50 ! [A: rat,N2: nat] :
% 5.27/5.50 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.50 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.27/5.50 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N2 ) ) @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_Suc_less
% 5.27/5.50 thf(fact_3532_power__Suc__less,axiom,
% 5.27/5.50 ! [A: nat,N2: nat] :
% 5.27/5.50 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.27/5.50 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.27/5.50 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N2 ) ) @ ( power_power_nat @ A @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_Suc_less
% 5.27/5.50 thf(fact_3533_power__Suc__less,axiom,
% 5.27/5.50 ! [A: int,N2: nat] :
% 5.27/5.50 ( ( ord_less_int @ zero_zero_int @ A )
% 5.27/5.50 => ( ( ord_less_int @ A @ one_one_int )
% 5.27/5.50 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N2 ) ) @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_Suc_less
% 5.27/5.50 thf(fact_3534_left__add__twice,axiom,
% 5.27/5.50 ! [A: rat,B: rat] :
% 5.27/5.50 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.50 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3535_left__add__twice,axiom,
% 5.27/5.50 ! [A: extended_enat,B: extended_enat] :
% 5.27/5.50 ( ( plus_p3455044024723400733d_enat @ A @ ( plus_p3455044024723400733d_enat @ A @ B ) )
% 5.27/5.50 = ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3536_left__add__twice,axiom,
% 5.27/5.50 ! [A: complex,B: complex] :
% 5.27/5.50 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.27/5.50 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3537_left__add__twice,axiom,
% 5.27/5.50 ! [A: real,B: real] :
% 5.27/5.50 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.27/5.50 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3538_left__add__twice,axiom,
% 5.27/5.50 ! [A: nat,B: nat] :
% 5.27/5.50 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.27/5.50 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3539_left__add__twice,axiom,
% 5.27/5.50 ! [A: int,B: int] :
% 5.27/5.50 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.27/5.50 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.27/5.50
% 5.27/5.50 % left_add_twice
% 5.27/5.50 thf(fact_3540_mult__2__right,axiom,
% 5.27/5.50 ! [Z: rat] :
% 5.27/5.50 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3541_mult__2__right,axiom,
% 5.27/5.50 ! [Z: extended_enat] :
% 5.27/5.50 ( ( times_7803423173614009249d_enat @ Z @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3542_mult__2__right,axiom,
% 5.27/5.50 ! [Z: complex] :
% 5.27/5.50 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3543_mult__2__right,axiom,
% 5.27/5.50 ! [Z: real] :
% 5.27/5.50 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3544_mult__2__right,axiom,
% 5.27/5.50 ! [Z: nat] :
% 5.27/5.50 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3545_mult__2__right,axiom,
% 5.27/5.50 ! [Z: int] :
% 5.27/5.50 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2_right
% 5.27/5.50 thf(fact_3546_mult__2,axiom,
% 5.27/5.50 ! [Z: rat] :
% 5.27/5.50 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3547_mult__2,axiom,
% 5.27/5.50 ! [Z: extended_enat] :
% 5.27/5.50 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_p3455044024723400733d_enat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3548_mult__2,axiom,
% 5.27/5.50 ! [Z: complex] :
% 5.27/5.50 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3549_mult__2,axiom,
% 5.27/5.50 ! [Z: real] :
% 5.27/5.50 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3550_mult__2,axiom,
% 5.27/5.50 ! [Z: nat] :
% 5.27/5.50 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3551_mult__2,axiom,
% 5.27/5.50 ! [Z: int] :
% 5.27/5.50 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.27/5.50 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.27/5.50
% 5.27/5.50 % mult_2
% 5.27/5.50 thf(fact_3552_power2__eq__square,axiom,
% 5.27/5.50 ! [A: complex] :
% 5.27/5.50 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( times_times_complex @ A @ A ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_eq_square
% 5.27/5.50 thf(fact_3553_power2__eq__square,axiom,
% 5.27/5.50 ! [A: real] :
% 5.27/5.50 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( times_times_real @ A @ A ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_eq_square
% 5.27/5.50 thf(fact_3554_power2__eq__square,axiom,
% 5.27/5.50 ! [A: nat] :
% 5.27/5.50 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( times_times_nat @ A @ A ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_eq_square
% 5.27/5.50 thf(fact_3555_power2__eq__square,axiom,
% 5.27/5.50 ! [A: int] :
% 5.27/5.50 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( times_times_int @ A @ A ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_eq_square
% 5.27/5.50 thf(fact_3556_power4__eq__xxxx,axiom,
% 5.27/5.50 ! [X4: complex] :
% 5.27/5.50 ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.50 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.27/5.50
% 5.27/5.50 % power4_eq_xxxx
% 5.27/5.50 thf(fact_3557_power4__eq__xxxx,axiom,
% 5.27/5.50 ! [X4: real] :
% 5.27/5.50 ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.50 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.27/5.50
% 5.27/5.50 % power4_eq_xxxx
% 5.27/5.50 thf(fact_3558_power4__eq__xxxx,axiom,
% 5.27/5.50 ! [X4: nat] :
% 5.27/5.50 ( ( power_power_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.50 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.27/5.50
% 5.27/5.50 % power4_eq_xxxx
% 5.27/5.50 thf(fact_3559_power4__eq__xxxx,axiom,
% 5.27/5.50 ! [X4: int] :
% 5.27/5.50 ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.50 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X4 @ X4 ) @ X4 ) @ X4 ) ) ).
% 5.27/5.50
% 5.27/5.50 % power4_eq_xxxx
% 5.27/5.50 thf(fact_3560_double__not__eq__Suc__double,axiom,
% 5.27/5.50 ! [M: nat,N2: nat] :
% 5.27/5.50 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.27/5.50 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % double_not_eq_Suc_double
% 5.27/5.50 thf(fact_3561_Suc__double__not__eq__double,axiom,
% 5.27/5.50 ! [M: nat,N2: nat] :
% 5.27/5.50 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.50 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.50
% 5.27/5.50 % Suc_double_not_eq_double
% 5.27/5.50 thf(fact_3562_power__even__eq,axiom,
% 5.27/5.50 ! [A: nat,N2: nat] :
% 5.27/5.50 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.50 = ( power_power_nat @ ( power_power_nat @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_even_eq
% 5.27/5.50 thf(fact_3563_power__even__eq,axiom,
% 5.27/5.50 ! [A: real,N2: nat] :
% 5.27/5.50 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.50 = ( power_power_real @ ( power_power_real @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_even_eq
% 5.27/5.50 thf(fact_3564_power__even__eq,axiom,
% 5.27/5.50 ! [A: int,N2: nat] :
% 5.27/5.50 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.50 = ( power_power_int @ ( power_power_int @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_even_eq
% 5.27/5.50 thf(fact_3565_power__even__eq,axiom,
% 5.27/5.50 ! [A: complex,N2: nat] :
% 5.27/5.50 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.50 = ( power_power_complex @ ( power_power_complex @ A @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_even_eq
% 5.27/5.50 thf(fact_3566_power__dvd__imp__le,axiom,
% 5.27/5.50 ! [I2: nat,M: nat,N2: nat] :
% 5.27/5.50 ( ( dvd_dvd_nat @ ( power_power_nat @ I2 @ M ) @ ( power_power_nat @ I2 @ N2 ) )
% 5.27/5.50 => ( ( ord_less_nat @ one_one_nat @ I2 )
% 5.27/5.50 => ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_dvd_imp_le
% 5.27/5.50 thf(fact_3567_neg__zdiv__mult__2,axiom,
% 5.27/5.50 ! [A: int,B: int] :
% 5.27/5.50 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.27/5.50 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.50 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % neg_zdiv_mult_2
% 5.27/5.50 thf(fact_3568_pos__zdiv__mult__2,axiom,
% 5.27/5.50 ! [A: int,B: int] :
% 5.27/5.50 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.27/5.50 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.50 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % pos_zdiv_mult_2
% 5.27/5.50 thf(fact_3569_div__nat__eqI,axiom,
% 5.27/5.50 ! [N2: nat,Q3: nat,M: nat] :
% 5.27/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q3 ) @ M )
% 5.27/5.50 => ( ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q3 ) ) )
% 5.27/5.50 => ( ( divide_divide_nat @ M @ N2 )
% 5.27/5.50 = Q3 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % div_nat_eqI
% 5.27/5.50 thf(fact_3570_less__eq__div__iff__mult__less__eq,axiom,
% 5.27/5.50 ! [Q3: nat,M: nat,N2: nat] :
% 5.27/5.50 ( ( ord_less_nat @ zero_zero_nat @ Q3 )
% 5.27/5.50 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N2 @ Q3 ) )
% 5.27/5.50 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q3 ) @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % less_eq_div_iff_mult_less_eq
% 5.27/5.50 thf(fact_3571_dividend__less__times__div,axiom,
% 5.27/5.50 ! [N2: nat,M: nat] :
% 5.27/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.50 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ N2 @ ( divide_divide_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % dividend_less_times_div
% 5.27/5.50 thf(fact_3572_dividend__less__div__times,axiom,
% 5.27/5.50 ! [N2: nat,M: nat] :
% 5.27/5.50 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.50 => ( ord_less_nat @ M @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( divide_divide_nat @ M @ N2 ) @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % dividend_less_div_times
% 5.27/5.50 thf(fact_3573_split__div,axiom,
% 5.27/5.50 ! [P: nat > $o,M: nat,N2: nat] :
% 5.27/5.50 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.50 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.50 => ( P @ zero_zero_nat ) )
% 5.27/5.50 & ( ( N2 != zero_zero_nat )
% 5.27/5.50 => ! [I3: nat,J3: nat] :
% 5.27/5.50 ( ( ord_less_nat @ J3 @ N2 )
% 5.27/5.50 => ( ( M
% 5.27/5.50 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 5.27/5.50 => ( P @ I3 ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % split_div
% 5.27/5.50 thf(fact_3574_split__mod,axiom,
% 5.27/5.50 ! [P: nat > $o,M: nat,N2: nat] :
% 5.27/5.50 ( ( P @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.27/5.50 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.50 => ( P @ M ) )
% 5.27/5.50 & ( ( N2 != zero_zero_nat )
% 5.27/5.50 => ! [I3: nat,J3: nat] :
% 5.27/5.50 ( ( ord_less_nat @ J3 @ N2 )
% 5.27/5.50 => ( ( M
% 5.27/5.50 = ( plus_plus_nat @ ( times_times_nat @ N2 @ I3 ) @ J3 ) )
% 5.27/5.50 => ( P @ J3 ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % split_mod
% 5.27/5.50 thf(fact_3575_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.27/5.50 ! [X4: produc9072475918466114483BT_nat] :
% 5.27/5.50 ( ! [A5: $o,B5: $o,X5: nat] :
% 5.27/5.50 ( X4
% 5.27/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X5 ) )
% 5.27/5.50 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.27/5.50 ( X4
% 5.27/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.27/5.50 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X5: nat] :
% 5.27/5.50 ( X4
% 5.27/5.50 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X5 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % VEBT_internal.naive_member.cases
% 5.27/5.50 thf(fact_3576_even__iff__mod__2__eq__zero,axiom,
% 5.27/5.50 ! [A: nat] :
% 5.27/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_zero_nat ) ) ).
% 5.27/5.50
% 5.27/5.50 % even_iff_mod_2_eq_zero
% 5.27/5.50 thf(fact_3577_even__iff__mod__2__eq__zero,axiom,
% 5.27/5.50 ! [A: int] :
% 5.27/5.50 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_zero_int ) ) ).
% 5.27/5.50
% 5.27/5.50 % even_iff_mod_2_eq_zero
% 5.27/5.50 thf(fact_3578_even__iff__mod__2__eq__zero,axiom,
% 5.27/5.50 ! [A: code_integer] :
% 5.27/5.50 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.50
% 5.27/5.50 % even_iff_mod_2_eq_zero
% 5.27/5.50 thf(fact_3579_odd__iff__mod__2__eq__one,axiom,
% 5.27/5.50 ! [A: nat] :
% 5.27/5.50 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.50 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_nat ) ) ).
% 5.27/5.50
% 5.27/5.50 % odd_iff_mod_2_eq_one
% 5.27/5.50 thf(fact_3580_odd__iff__mod__2__eq__one,axiom,
% 5.27/5.50 ! [A: int] :
% 5.27/5.50 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.50 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_int ) ) ).
% 5.27/5.50
% 5.27/5.50 % odd_iff_mod_2_eq_one
% 5.27/5.50 thf(fact_3581_odd__iff__mod__2__eq__one,axiom,
% 5.27/5.50 ! [A: code_integer] :
% 5.27/5.50 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.50 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_Code_integer ) ) ).
% 5.27/5.50
% 5.27/5.50 % odd_iff_mod_2_eq_one
% 5.27/5.50 thf(fact_3582_power__mono__odd,axiom,
% 5.27/5.50 ! [N2: nat,A: real,B: real] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_real @ A @ B )
% 5.27/5.50 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_mono_odd
% 5.27/5.50 thf(fact_3583_power__mono__odd,axiom,
% 5.27/5.50 ! [N2: nat,A: rat,B: rat] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.50 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_mono_odd
% 5.27/5.50 thf(fact_3584_power__mono__odd,axiom,
% 5.27/5.50 ! [N2: nat,A: int,B: int] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_int @ A @ B )
% 5.27/5.50 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power_mono_odd
% 5.27/5.50 thf(fact_3585_convex__bound__lt,axiom,
% 5.27/5.50 ! [X4: real,A: real,Y: real,U: real,V: real] :
% 5.27/5.50 ( ( ord_less_real @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_real @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.27/5.50 => ( ( ( plus_plus_real @ U @ V )
% 5.27/5.50 = one_one_real )
% 5.27/5.50 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X4 ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_lt
% 5.27/5.50 thf(fact_3586_convex__bound__lt,axiom,
% 5.27/5.50 ! [X4: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.27/5.50 ( ( ord_less_rat @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_rat @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.27/5.50 => ( ( ( plus_plus_rat @ U @ V )
% 5.27/5.50 = one_one_rat )
% 5.27/5.50 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X4 ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_lt
% 5.27/5.50 thf(fact_3587_convex__bound__lt,axiom,
% 5.27/5.50 ! [X4: int,A: int,Y: int,U: int,V: int] :
% 5.27/5.50 ( ( ord_less_int @ X4 @ A )
% 5.27/5.50 => ( ( ord_less_int @ Y @ A )
% 5.27/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.27/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.27/5.50 => ( ( ( plus_plus_int @ U @ V )
% 5.27/5.50 = one_one_int )
% 5.27/5.50 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X4 ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % convex_bound_lt
% 5.27/5.50 thf(fact_3588_le__divide__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [W: num,B: real,C: real] :
% 5.27/5.50 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % le_divide_eq_numeral(1)
% 5.27/5.50 thf(fact_3589_le__divide__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [W: num,B: rat,C: rat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % le_divide_eq_numeral(1)
% 5.27/5.50 thf(fact_3590_divide__le__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [B: real,C: real,W: num] :
% 5.27/5.50 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.27/5.50 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.50 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_le_eq_numeral(1)
% 5.27/5.50 thf(fact_3591_divide__le__eq__numeral_I1_J,axiom,
% 5.27/5.50 ! [B: rat,C: rat,W: num] :
% 5.27/5.50 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.27/5.50 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.50 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.27/5.50 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divide_le_eq_numeral(1)
% 5.27/5.50 thf(fact_3592_odd__pos,axiom,
% 5.27/5.50 ! [N2: nat] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.50
% 5.27/5.50 % odd_pos
% 5.27/5.50 thf(fact_3593_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.27/5.50 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.27/5.50 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.27/5.50 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.27/5.50 thf(fact_3594_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.27/5.50 ! [C: nat,A: nat,B: nat] :
% 5.27/5.50 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.27/5.50 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.27/5.50 thf(fact_3595_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.27/5.50 ! [C: int,A: int,B: int] :
% 5.27/5.50 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.27/5.50 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.27/5.50 thf(fact_3596_dvd__power__iff__le,axiom,
% 5.27/5.50 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.50 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.27/5.50 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) )
% 5.27/5.50 = ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % dvd_power_iff_le
% 5.27/5.50 thf(fact_3597_num_Osize__gen_I1_J,axiom,
% 5.27/5.50 ( ( size_num @ one )
% 5.27/5.50 = zero_zero_nat ) ).
% 5.27/5.50
% 5.27/5.50 % num.size_gen(1)
% 5.27/5.50 thf(fact_3598_four__x__squared,axiom,
% 5.27/5.50 ! [X4: real] :
% 5.27/5.50 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.50 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % four_x_squared
% 5.27/5.50 thf(fact_3599_split__div_H,axiom,
% 5.27/5.50 ! [P: nat > $o,M: nat,N2: nat] :
% 5.27/5.50 ( ( P @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.50 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.50 & ( P @ zero_zero_nat ) )
% 5.27/5.50 | ? [Q5: nat] :
% 5.27/5.50 ( ( ord_less_eq_nat @ ( times_times_nat @ N2 @ Q5 ) @ M )
% 5.27/5.50 & ( ord_less_nat @ M @ ( times_times_nat @ N2 @ ( suc @ Q5 ) ) )
% 5.27/5.50 & ( P @ Q5 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % split_div'
% 5.27/5.50 thf(fact_3600_Suc__times__mod__eq,axiom,
% 5.27/5.50 ! [M: nat,N2: nat] :
% 5.27/5.50 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.27/5.50 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N2 ) ) @ M )
% 5.27/5.50 = one_one_nat ) ) ).
% 5.27/5.50
% 5.27/5.50 % Suc_times_mod_eq
% 5.27/5.50 thf(fact_3601_parity__cases,axiom,
% 5.27/5.50 ! [A: nat] :
% 5.27/5.50 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 != zero_zero_nat ) )
% 5.27/5.50 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 != one_one_nat ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % parity_cases
% 5.27/5.50 thf(fact_3602_parity__cases,axiom,
% 5.27/5.50 ! [A: int] :
% 5.27/5.50 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 != zero_zero_int ) )
% 5.27/5.50 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 != one_one_int ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % parity_cases
% 5.27/5.50 thf(fact_3603_parity__cases,axiom,
% 5.27/5.50 ! [A: code_integer] :
% 5.27/5.50 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 != zero_z3403309356797280102nteger ) )
% 5.27/5.50 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 != one_one_Code_integer ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % parity_cases
% 5.27/5.50 thf(fact_3604_mod2__eq__if,axiom,
% 5.27/5.50 ! [A: nat] :
% 5.27/5.50 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_zero_nat ) )
% 5.27/5.50 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_nat ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % mod2_eq_if
% 5.27/5.50 thf(fact_3605_mod2__eq__if,axiom,
% 5.27/5.50 ! [A: int] :
% 5.27/5.50 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_zero_int ) )
% 5.27/5.50 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_int ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % mod2_eq_if
% 5.27/5.50 thf(fact_3606_mod2__eq__if,axiom,
% 5.27/5.50 ! [A: code_integer] :
% 5.27/5.50 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 = zero_z3403309356797280102nteger ) )
% 5.27/5.50 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.50 = one_one_Code_integer ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % mod2_eq_if
% 5.27/5.50 thf(fact_3607_zero__le__even__power,axiom,
% 5.27/5.50 ! [N2: nat,A: real] :
% 5.27/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power
% 5.27/5.50 thf(fact_3608_zero__le__even__power,axiom,
% 5.27/5.50 ! [N2: nat,A: rat] :
% 5.27/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power
% 5.27/5.50 thf(fact_3609_zero__le__even__power,axiom,
% 5.27/5.50 ! [N2: nat,A: int] :
% 5.27/5.50 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power
% 5.27/5.50 thf(fact_3610_zero__le__odd__power,axiom,
% 5.27/5.50 ! [N2: nat,A: real] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.27/5.50 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_odd_power
% 5.27/5.50 thf(fact_3611_zero__le__odd__power,axiom,
% 5.27/5.50 ! [N2: nat,A: rat] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.27/5.50 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_odd_power
% 5.27/5.50 thf(fact_3612_zero__le__odd__power,axiom,
% 5.27/5.50 ! [N2: nat,A: int] :
% 5.27/5.50 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.27/5.50 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_odd_power
% 5.27/5.50 thf(fact_3613_zero__le__power__eq,axiom,
% 5.27/5.50 ! [A: real,N2: nat] :
% 5.27/5.50 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.27/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_power_eq
% 5.27/5.50 thf(fact_3614_zero__le__power__eq,axiom,
% 5.27/5.50 ! [A: rat,N2: nat] :
% 5.27/5.50 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.27/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_power_eq
% 5.27/5.50 thf(fact_3615_zero__le__power__eq,axiom,
% 5.27/5.50 ! [A: int,N2: nat] :
% 5.27/5.50 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.27/5.50 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.50 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_power_eq
% 5.27/5.50 thf(fact_3616_divmod__digit__0_I2_J,axiom,
% 5.27/5.50 ! [B: nat,A: nat] :
% 5.27/5.50 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.27/5.50 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.50 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.27/5.50 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divmod_digit_0(2)
% 5.27/5.50 thf(fact_3617_divmod__digit__0_I2_J,axiom,
% 5.27/5.50 ! [B: int,A: int] :
% 5.27/5.50 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.50 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.50 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.27/5.50 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divmod_digit_0(2)
% 5.27/5.50 thf(fact_3618_divmod__digit__0_I2_J,axiom,
% 5.27/5.50 ! [B: code_integer,A: code_integer] :
% 5.27/5.50 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.27/5.50 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.50 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.27/5.50 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % divmod_digit_0(2)
% 5.27/5.50 thf(fact_3619_power2__sum,axiom,
% 5.27/5.50 ! [X4: rat,Y: rat] :
% 5.27/5.50 ( ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3620_power2__sum,axiom,
% 5.27/5.50 ! [X4: extended_enat,Y: extended_enat] :
% 5.27/5.50 ( ( power_8040749407984259932d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( power_8040749407984259932d_enat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8040749407984259932d_enat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_7803423173614009249d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3621_power2__sum,axiom,
% 5.27/5.50 ! [X4: complex,Y: complex] :
% 5.27/5.50 ( ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3622_power2__sum,axiom,
% 5.27/5.50 ! [X4: real,Y: real] :
% 5.27/5.50 ( ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3623_power2__sum,axiom,
% 5.27/5.50 ! [X4: nat,Y: nat] :
% 5.27/5.50 ( ( power_power_nat @ ( plus_plus_nat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3624_power2__sum,axiom,
% 5.27/5.50 ! [X4: int,Y: int] :
% 5.27/5.50 ( ( power_power_int @ ( plus_plus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.50 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % power2_sum
% 5.27/5.50 thf(fact_3625_zero__le__even__power_H,axiom,
% 5.27/5.50 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power'
% 5.27/5.50 thf(fact_3626_zero__le__even__power_H,axiom,
% 5.27/5.50 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power'
% 5.27/5.50 thf(fact_3627_zero__le__even__power_H,axiom,
% 5.27/5.50 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % zero_le_even_power'
% 5.27/5.50 thf(fact_3628_nat__bit__induct,axiom,
% 5.27/5.50 ! [P: nat > $o,N2: nat] :
% 5.27/5.50 ( ( P @ zero_zero_nat )
% 5.27/5.50 => ( ! [N3: nat] :
% 5.27/5.50 ( ( P @ N3 )
% 5.27/5.50 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.50 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.27/5.50 => ( ! [N3: nat] :
% 5.27/5.50 ( ( P @ N3 )
% 5.27/5.50 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.27/5.50 => ( P @ N2 ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % nat_bit_induct
% 5.27/5.50 thf(fact_3629_L2__set__mult__ineq__lemma,axiom,
% 5.27/5.50 ! [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 ) ) ) ) ) ) ).
% 5.27/5.50
% 5.27/5.50 % L2_set_mult_ineq_lemma
% 5.27/5.50 thf(fact_3630_zero__less__power__eq,axiom,
% 5.27/5.50 ! [A: real,N2: nat] :
% 5.27/5.50 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N2 ) )
% 5.27/5.51 = ( ( N2 = zero_zero_nat )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A != zero_zero_real ) )
% 5.27/5.51 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % zero_less_power_eq
% 5.27/5.51 thf(fact_3631_zero__less__power__eq,axiom,
% 5.27/5.51 ! [A: rat,N2: nat] :
% 5.27/5.51 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N2 ) )
% 5.27/5.51 = ( ( N2 = zero_zero_nat )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A != zero_zero_rat ) )
% 5.27/5.51 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % zero_less_power_eq
% 5.27/5.51 thf(fact_3632_zero__less__power__eq,axiom,
% 5.27/5.51 ! [A: int,N2: nat] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N2 ) )
% 5.27/5.51 = ( ( N2 = zero_zero_nat )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A != zero_zero_int ) )
% 5.27/5.51 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % zero_less_power_eq
% 5.27/5.51 thf(fact_3633_Euclid__induct,axiom,
% 5.27/5.51 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.27/5.51 ( ! [A5: nat,B5: nat] :
% 5.27/5.51 ( ( P @ A5 @ B5 )
% 5.27/5.51 = ( P @ B5 @ A5 ) )
% 5.27/5.51 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.27/5.51 => ( ! [A5: nat,B5: nat] :
% 5.27/5.51 ( ( P @ A5 @ B5 )
% 5.27/5.51 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.27/5.51 => ( P @ A @ B ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % Euclid_induct
% 5.27/5.51 thf(fact_3634_sum__squares__bound,axiom,
% 5.27/5.51 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % sum_squares_bound
% 5.27/5.51 thf(fact_3635_sum__squares__bound,axiom,
% 5.27/5.51 ! [X4: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % sum_squares_bound
% 5.27/5.51 thf(fact_3636_divmod__digit__0_I1_J,axiom,
% 5.27/5.51 ! [B: nat,A: nat] :
% 5.27/5.51 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.27/5.51 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.51 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.51 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % divmod_digit_0(1)
% 5.27/5.51 thf(fact_3637_divmod__digit__0_I1_J,axiom,
% 5.27/5.51 ! [B: int,A: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.51 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.51 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.51 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % divmod_digit_0(1)
% 5.27/5.51 thf(fact_3638_divmod__digit__0_I1_J,axiom,
% 5.27/5.51 ! [B: code_integer,A: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.27/5.51 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.51 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.51 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % divmod_digit_0(1)
% 5.27/5.51 thf(fact_3639_odd__0__le__power__imp__0__le,axiom,
% 5.27/5.51 ! [A: real,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.51 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_0_le_power_imp_0_le
% 5.27/5.51 thf(fact_3640_odd__0__le__power__imp__0__le,axiom,
% 5.27/5.51 ! [A: rat,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.51 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_0_le_power_imp_0_le
% 5.27/5.51 thf(fact_3641_odd__0__le__power__imp__0__le,axiom,
% 5.27/5.51 ! [A: int,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.51 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_0_le_power_imp_0_le
% 5.27/5.51 thf(fact_3642_odd__power__less__zero,axiom,
% 5.27/5.51 ! [A: real,N2: nat] :
% 5.27/5.51 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.51 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_real ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_power_less_zero
% 5.27/5.51 thf(fact_3643_odd__power__less__zero,axiom,
% 5.27/5.51 ! [A: rat,N2: nat] :
% 5.27/5.51 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.51 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_rat ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_power_less_zero
% 5.27/5.51 thf(fact_3644_odd__power__less__zero,axiom,
% 5.27/5.51 ! [A: int,N2: nat] :
% 5.27/5.51 ( ( ord_less_int @ A @ zero_zero_int )
% 5.27/5.51 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ zero_zero_int ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_power_less_zero
% 5.27/5.51 thf(fact_3645_VEBT__internal_Omembermima_Ocases,axiom,
% 5.27/5.51 ! [X4: produc9072475918466114483BT_nat] :
% 5.27/5.51 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.27/5.51 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.27/5.51 => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X5: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X5 ) )
% 5.27/5.51 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT,X5: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ X5 ) )
% 5.27/5.51 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT,X5: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ X5 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % VEBT_internal.membermima.cases
% 5.27/5.51 thf(fact_3646_power__le__zero__eq,axiom,
% 5.27/5.51 ! [A: real,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ zero_zero_real )
% 5.27/5.51 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % power_le_zero_eq
% 5.27/5.51 thf(fact_3647_power__le__zero__eq,axiom,
% 5.27/5.51 ! [A: rat,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ zero_zero_rat )
% 5.27/5.51 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % power_le_zero_eq
% 5.27/5.51 thf(fact_3648_power__le__zero__eq,axiom,
% 5.27/5.51 ! [A: int,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ zero_zero_int )
% 5.27/5.51 = ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.27/5.51 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % power_le_zero_eq
% 5.27/5.51 thf(fact_3649_mod__double__modulus,axiom,
% 5.27/5.51 ! [M: code_integer,X4: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.27/5.51 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.27/5.51 => ( ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( modulo364778990260209775nteger @ X4 @ M ) )
% 5.27/5.51 | ( ( modulo364778990260209775nteger @ X4 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mod_double_modulus
% 5.27/5.51 thf(fact_3650_mod__double__modulus,axiom,
% 5.27/5.51 ! [M: nat,X4: nat] :
% 5.27/5.51 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.51 => ( ( ord_less_eq_nat @ zero_zero_nat @ X4 )
% 5.27/5.51 => ( ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( modulo_modulo_nat @ X4 @ M ) )
% 5.27/5.51 | ( ( modulo_modulo_nat @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( plus_plus_nat @ ( modulo_modulo_nat @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mod_double_modulus
% 5.27/5.51 thf(fact_3651_mod__double__modulus,axiom,
% 5.27/5.51 ! [M: int,X4: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ M )
% 5.27/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.51 => ( ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( modulo_modulo_int @ X4 @ M ) )
% 5.27/5.51 | ( ( modulo_modulo_int @ X4 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ X4 @ M ) @ M ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mod_double_modulus
% 5.27/5.51 thf(fact_3652_option_Osize__gen_I1_J,axiom,
% 5.27/5.51 ! [X4: product_prod_nat_nat > nat] :
% 5.27/5.51 ( ( size_o8335143837870341156at_nat @ X4 @ none_P5556105721700978146at_nat )
% 5.27/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % option.size_gen(1)
% 5.27/5.51 thf(fact_3653_option_Osize__gen_I1_J,axiom,
% 5.27/5.51 ! [X4: num > nat] :
% 5.27/5.51 ( ( size_option_num @ X4 @ none_num )
% 5.27/5.51 = ( suc @ zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % option.size_gen(1)
% 5.27/5.51 thf(fact_3654_flip__bit__0,axiom,
% 5.27/5.51 ! [A: code_integer] :
% 5.27/5.51 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_0
% 5.27/5.51 thf(fact_3655_flip__bit__0,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.27/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_0
% 5.27/5.51 thf(fact_3656_flip__bit__0,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.27/5.51 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_0
% 5.27/5.51 thf(fact_3657_set__bit__0,axiom,
% 5.27/5.51 ! [A: code_integer] :
% 5.27/5.51 ( ( bit_se2793503036327961859nteger @ zero_zero_nat @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_0
% 5.27/5.51 thf(fact_3658_set__bit__0,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.27/5.51 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_0
% 5.27/5.51 thf(fact_3659_set__bit__0,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.27/5.51 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_0
% 5.27/5.51 thf(fact_3660_even__even__mod__4__iff,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_even_mod_4_iff
% 5.27/5.51 thf(fact_3661_div2__even__ext__nat,axiom,
% 5.27/5.51 ! [X4: nat,Y: nat] :
% 5.27/5.51 ( ( ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.51 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.51 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.51 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.27/5.51 => ( X4 = Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % div2_even_ext_nat
% 5.27/5.51 thf(fact_3662_unset__bit__0,axiom,
% 5.27/5.51 ! [A: code_integer] :
% 5.27/5.51 ( ( bit_se8260200283734997820nteger @ zero_zero_nat @ A )
% 5.27/5.51 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_0
% 5.27/5.51 thf(fact_3663_unset__bit__0,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.27/5.51 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_0
% 5.27/5.51 thf(fact_3664_unset__bit__0,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.27/5.51 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_0
% 5.27/5.51 thf(fact_3665_incr__mult__lemma,axiom,
% 5.27/5.51 ! [D: int,P: int > $o,K: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.51 => ( ! [X5: int] :
% 5.27/5.51 ( ( P @ X5 )
% 5.27/5.51 => ( P @ ( plus_plus_int @ X5 @ D ) ) )
% 5.27/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.51 => ! [X2: int] :
% 5.27/5.51 ( ( P @ X2 )
% 5.27/5.51 => ( P @ ( plus_plus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % incr_mult_lemma
% 5.27/5.51 thf(fact_3666_unset__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: code_integer] :
% 5.27/5.51 ( ( bit_se8260200283734997820nteger @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_Suc
% 5.27/5.51 thf(fact_3667_unset__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: int] :
% 5.27/5.51 ( ( bit_se4203085406695923979it_int @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_Suc
% 5.27/5.51 thf(fact_3668_unset__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: nat] :
% 5.27/5.51 ( ( bit_se4205575877204974255it_nat @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_Suc
% 5.27/5.51 thf(fact_3669_flip__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: code_integer] :
% 5.27/5.51 ( ( bit_se1345352211410354436nteger @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_Suc
% 5.27/5.51 thf(fact_3670_flip__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: int] :
% 5.27/5.51 ( ( bit_se2159334234014336723it_int @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_Suc
% 5.27/5.51 thf(fact_3671_flip__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: nat] :
% 5.27/5.51 ( ( bit_se2161824704523386999it_nat @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_Suc
% 5.27/5.51 thf(fact_3672_set__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: code_integer] :
% 5.27/5.51 ( ( bit_se2793503036327961859nteger @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_Suc
% 5.27/5.51 thf(fact_3673_set__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: int] :
% 5.27/5.51 ( ( bit_se7879613467334960850it_int @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_Suc
% 5.27/5.51 thf(fact_3674_set__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: nat] :
% 5.27/5.51 ( ( bit_se7882103937844011126it_nat @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_Suc
% 5.27/5.51 thf(fact_3675_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: code_integer > $o,L: code_integer] :
% 5.27/5.51 ( ( ? [X: code_integer] : ( P @ ( times_3573771949741848930nteger @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ L @ ( plus_p5714425477246183910nteger @ X @ zero_z3403309356797280102nteger ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3676_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: rat > $o,L: rat] :
% 5.27/5.51 ( ( ? [X: rat] : ( P @ ( times_times_rat @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: rat] :
% 5.27/5.51 ( ( dvd_dvd_rat @ L @ ( plus_plus_rat @ X @ zero_zero_rat ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3677_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: complex > $o,L: complex] :
% 5.27/5.51 ( ( ? [X: complex] : ( P @ ( times_times_complex @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: complex] :
% 5.27/5.51 ( ( dvd_dvd_complex @ L @ ( plus_plus_complex @ X @ zero_zero_complex ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3678_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: real > $o,L: real] :
% 5.27/5.51 ( ( ? [X: real] : ( P @ ( times_times_real @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: real] :
% 5.27/5.51 ( ( dvd_dvd_real @ L @ ( plus_plus_real @ X @ zero_zero_real ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3679_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: nat > $o,L: nat] :
% 5.27/5.51 ( ( ? [X: nat] : ( P @ ( times_times_nat @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ L @ ( plus_plus_nat @ X @ zero_zero_nat ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3680_unity__coeff__ex,axiom,
% 5.27/5.51 ! [P: int > $o,L: int] :
% 5.27/5.51 ( ( ? [X: int] : ( P @ ( times_times_int @ L @ X ) ) )
% 5.27/5.51 = ( ? [X: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ L @ ( plus_plus_int @ X @ zero_zero_int ) )
% 5.27/5.51 & ( P @ X ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unity_coeff_ex
% 5.27/5.51 thf(fact_3681_unset__bit__nonnegative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) )
% 5.27/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_nonnegative_int_iff
% 5.27/5.51 thf(fact_3682_set__bit__nonnegative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) )
% 5.27/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_nonnegative_int_iff
% 5.27/5.51 thf(fact_3683_flip__bit__nonnegative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) )
% 5.27/5.51 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_nonnegative_int_iff
% 5.27/5.51 thf(fact_3684_unset__bit__negative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_negative_int_iff
% 5.27/5.51 thf(fact_3685_set__bit__negative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_negative_int_iff
% 5.27/5.51 thf(fact_3686_flip__bit__negative__int__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int] :
% 5.27/5.51 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.51 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.51
% 5.27/5.51 % flip_bit_negative_int_iff
% 5.27/5.51 thf(fact_3687_unset__bit__less__eq,axiom,
% 5.27/5.51 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N2 @ K ) @ K ) ).
% 5.27/5.51
% 5.27/5.51 % unset_bit_less_eq
% 5.27/5.51 thf(fact_3688_set__bit__greater__eq,axiom,
% 5.27/5.51 ! [K: int,N2: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N2 @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_bit_greater_eq
% 5.27/5.51 thf(fact_3689_minf_I7_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_real @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(7)
% 5.27/5.51 thf(fact_3690_minf_I7_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_rat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(7)
% 5.27/5.51 thf(fact_3691_minf_I7_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_num @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(7)
% 5.27/5.51 thf(fact_3692_minf_I7_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_nat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(7)
% 5.27/5.51 thf(fact_3693_minf_I7_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_int @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(7)
% 5.27/5.51 thf(fact_3694_minf_I5_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_real @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(5)
% 5.27/5.51 thf(fact_3695_minf_I5_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_rat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(5)
% 5.27/5.51 thf(fact_3696_minf_I5_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_num @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(5)
% 5.27/5.51 thf(fact_3697_minf_I5_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_nat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(5)
% 5.27/5.51 thf(fact_3698_minf_I5_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_int @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(5)
% 5.27/5.51 thf(fact_3699_minf_I4_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(4)
% 5.27/5.51 thf(fact_3700_minf_I4_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(4)
% 5.27/5.51 thf(fact_3701_minf_I4_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(4)
% 5.27/5.51 thf(fact_3702_minf_I4_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(4)
% 5.27/5.51 thf(fact_3703_minf_I4_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(4)
% 5.27/5.51 thf(fact_3704_minf_I3_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(3)
% 5.27/5.51 thf(fact_3705_minf_I3_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(3)
% 5.27/5.51 thf(fact_3706_minf_I3_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(3)
% 5.27/5.51 thf(fact_3707_minf_I3_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(3)
% 5.27/5.51 thf(fact_3708_minf_I3_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(3)
% 5.27/5.51 thf(fact_3709_minf_I2_J,axiom,
% 5.27/5.51 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.27/5.51 ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(2)
% 5.27/5.51 thf(fact_3710_minf_I2_J,axiom,
% 5.27/5.51 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.27/5.51 ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(2)
% 5.27/5.51 thf(fact_3711_minf_I2_J,axiom,
% 5.27/5.51 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.27/5.51 ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(2)
% 5.27/5.51 thf(fact_3712_minf_I2_J,axiom,
% 5.27/5.51 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.27/5.51 ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(2)
% 5.27/5.51 thf(fact_3713_minf_I2_J,axiom,
% 5.27/5.51 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.27/5.51 ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(2)
% 5.27/5.51 thf(fact_3714_minf_I1_J,axiom,
% 5.27/5.51 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.27/5.51 ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(1)
% 5.27/5.51 thf(fact_3715_minf_I1_J,axiom,
% 5.27/5.51 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.27/5.51 ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(1)
% 5.27/5.51 thf(fact_3716_minf_I1_J,axiom,
% 5.27/5.51 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.27/5.51 ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(1)
% 5.27/5.51 thf(fact_3717_minf_I1_J,axiom,
% 5.27/5.51 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.27/5.51 ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(1)
% 5.27/5.51 thf(fact_3718_minf_I1_J,axiom,
% 5.27/5.51 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.27/5.51 ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(1)
% 5.27/5.51 thf(fact_3719_pinf_I7_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_real @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(7)
% 5.27/5.51 thf(fact_3720_pinf_I7_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_rat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(7)
% 5.27/5.51 thf(fact_3721_pinf_I7_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_num @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(7)
% 5.27/5.51 thf(fact_3722_pinf_I7_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_nat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(7)
% 5.27/5.51 thf(fact_3723_pinf_I7_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_int @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(7)
% 5.27/5.51 thf(fact_3724_pinf_I5_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_real @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(5)
% 5.27/5.51 thf(fact_3725_pinf_I5_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_rat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(5)
% 5.27/5.51 thf(fact_3726_pinf_I5_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_num @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(5)
% 5.27/5.51 thf(fact_3727_pinf_I5_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_nat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(5)
% 5.27/5.51 thf(fact_3728_pinf_I5_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_int @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(5)
% 5.27/5.51 thf(fact_3729_pinf_I4_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(4)
% 5.27/5.51 thf(fact_3730_pinf_I4_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(4)
% 5.27/5.51 thf(fact_3731_pinf_I4_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(4)
% 5.27/5.51 thf(fact_3732_pinf_I4_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(4)
% 5.27/5.51 thf(fact_3733_pinf_I4_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(4)
% 5.27/5.51 thf(fact_3734_pinf_I3_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(3)
% 5.27/5.51 thf(fact_3735_pinf_I3_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(3)
% 5.27/5.51 thf(fact_3736_pinf_I3_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(3)
% 5.27/5.51 thf(fact_3737_pinf_I3_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(3)
% 5.27/5.51 thf(fact_3738_pinf_I3_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( X2 != T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(3)
% 5.27/5.51 thf(fact_3739_pinf_I2_J,axiom,
% 5.27/5.51 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.27/5.51 ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(2)
% 5.27/5.51 thf(fact_3740_pinf_I2_J,axiom,
% 5.27/5.51 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.27/5.51 ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(2)
% 5.27/5.51 thf(fact_3741_pinf_I2_J,axiom,
% 5.27/5.51 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.27/5.51 ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(2)
% 5.27/5.51 thf(fact_3742_pinf_I2_J,axiom,
% 5.27/5.51 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.27/5.51 ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(2)
% 5.27/5.51 thf(fact_3743_pinf_I2_J,axiom,
% 5.27/5.51 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.27/5.51 ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 | ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 | ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(2)
% 5.27/5.51 thf(fact_3744_pinf_I1_J,axiom,
% 5.27/5.51 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.27/5.51 ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: real] :
% 5.27/5.51 ! [X5: real] :
% 5.27/5.51 ( ( ord_less_real @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(1)
% 5.27/5.51 thf(fact_3745_pinf_I1_J,axiom,
% 5.27/5.51 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.27/5.51 ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: rat] :
% 5.27/5.51 ! [X5: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(1)
% 5.27/5.51 thf(fact_3746_pinf_I1_J,axiom,
% 5.27/5.51 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.27/5.51 ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: num] :
% 5.27/5.51 ! [X5: num] :
% 5.27/5.51 ( ( ord_less_num @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(1)
% 5.27/5.51 thf(fact_3747_pinf_I1_J,axiom,
% 5.27/5.51 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.27/5.51 ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: nat] :
% 5.27/5.51 ! [X5: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(1)
% 5.27/5.51 thf(fact_3748_pinf_I1_J,axiom,
% 5.27/5.51 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.27/5.51 ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.51 => ( ( P @ X5 )
% 5.27/5.51 = ( P6 @ X5 ) ) )
% 5.27/5.51 => ( ? [Z3: int] :
% 5.27/5.51 ! [X5: int] :
% 5.27/5.51 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.51 => ( ( Q @ X5 )
% 5.27/5.51 = ( Q6 @ X5 ) ) )
% 5.27/5.51 => ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ( ( P @ X2 )
% 5.27/5.51 & ( Q @ X2 ) )
% 5.27/5.51 = ( ( P6 @ X2 )
% 5.27/5.51 & ( Q6 @ X2 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(1)
% 5.27/5.51 thf(fact_3749_minf_I8_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(8)
% 5.27/5.51 thf(fact_3750_minf_I8_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(8)
% 5.27/5.51 thf(fact_3751_minf_I8_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(8)
% 5.27/5.51 thf(fact_3752_minf_I8_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(8)
% 5.27/5.51 thf(fact_3753_minf_I8_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ~ ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(8)
% 5.27/5.51 thf(fact_3754_minf_I6_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(6)
% 5.27/5.51 thf(fact_3755_minf_I6_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(6)
% 5.27/5.51 thf(fact_3756_minf_I6_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(6)
% 5.27/5.51 thf(fact_3757_minf_I6_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(6)
% 5.27/5.51 thf(fact_3758_minf_I6_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(6)
% 5.27/5.51 thf(fact_3759_pinf_I8_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_eq_real @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(8)
% 5.27/5.51 thf(fact_3760_pinf_I8_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_eq_rat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(8)
% 5.27/5.51 thf(fact_3761_pinf_I8_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_eq_num @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(8)
% 5.27/5.51 thf(fact_3762_pinf_I8_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_eq_nat @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(8)
% 5.27/5.51 thf(fact_3763_pinf_I8_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ord_less_eq_int @ T2 @ X2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(8)
% 5.27/5.51 thf(fact_3764_pinf_I6_J,axiom,
% 5.27/5.51 ! [T2: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_eq_real @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(6)
% 5.27/5.51 thf(fact_3765_pinf_I6_J,axiom,
% 5.27/5.51 ! [T2: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_eq_rat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(6)
% 5.27/5.51 thf(fact_3766_pinf_I6_J,axiom,
% 5.27/5.51 ! [T2: num] :
% 5.27/5.51 ? [Z2: num] :
% 5.27/5.51 ! [X2: num] :
% 5.27/5.51 ( ( ord_less_num @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_eq_num @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(6)
% 5.27/5.51 thf(fact_3767_pinf_I6_J,axiom,
% 5.27/5.51 ! [T2: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_eq_nat @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(6)
% 5.27/5.51 thf(fact_3768_pinf_I6_J,axiom,
% 5.27/5.51 ! [T2: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ~ ( ord_less_eq_int @ X2 @ T2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(6)
% 5.27/5.51 thf(fact_3769_list__decode_Ocases,axiom,
% 5.27/5.51 ! [X4: nat] :
% 5.27/5.51 ( ( X4 != zero_zero_nat )
% 5.27/5.51 => ~ ! [N3: nat] :
% 5.27/5.51 ( X4
% 5.27/5.51 != ( suc @ N3 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % list_decode.cases
% 5.27/5.51 thf(fact_3770_imp__le__cong,axiom,
% 5.27/5.51 ! [X4: int,X7: int,P: $o,P6: $o] :
% 5.27/5.51 ( ( X4 = X7 )
% 5.27/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.27/5.51 => ( P = P6 ) )
% 5.27/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.51 => P )
% 5.27/5.51 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.27/5.51 => P6 ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % imp_le_cong
% 5.27/5.51 thf(fact_3771_conj__le__cong,axiom,
% 5.27/5.51 ! [X4: int,X7: int,P: $o,P6: $o] :
% 5.27/5.51 ( ( X4 = X7 )
% 5.27/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.27/5.51 => ( P = P6 ) )
% 5.27/5.51 => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.51 & P )
% 5.27/5.51 = ( ( ord_less_eq_int @ zero_zero_int @ X7 )
% 5.27/5.51 & P6 ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % conj_le_cong
% 5.27/5.51 thf(fact_3772_even__set__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 & ( M != zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_set_bit_iff
% 5.27/5.51 thf(fact_3773_even__set__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 & ( M != zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_set_bit_iff
% 5.27/5.51 thf(fact_3774_even__set__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 & ( M != zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_set_bit_iff
% 5.27/5.51 thf(fact_3775_even__flip__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 != ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_flip_bit_iff
% 5.27/5.51 thf(fact_3776_even__flip__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 != ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_flip_bit_iff
% 5.27/5.51 thf(fact_3777_even__flip__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 != ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_flip_bit_iff
% 5.27/5.51 thf(fact_3778_even__unset__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 | ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_unset_bit_iff
% 5.27/5.51 thf(fact_3779_even__unset__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 | ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_unset_bit_iff
% 5.27/5.51 thf(fact_3780_even__unset__bit__iff,axiom,
% 5.27/5.51 ! [M: nat,A: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.27/5.51 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.51 | ( M = zero_zero_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_unset_bit_iff
% 5.27/5.51 thf(fact_3781_minf_I10_J,axiom,
% 5.27/5.51 ! [D: code_integer,S: code_integer] :
% 5.27/5.51 ? [Z2: code_integer] :
% 5.27/5.51 ! [X2: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(10)
% 5.27/5.51 thf(fact_3782_minf_I10_J,axiom,
% 5.27/5.51 ! [D: real,S: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(10)
% 5.27/5.51 thf(fact_3783_minf_I10_J,axiom,
% 5.27/5.51 ! [D: rat,S: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(10)
% 5.27/5.51 thf(fact_3784_minf_I10_J,axiom,
% 5.27/5.51 ! [D: nat,S: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(10)
% 5.27/5.51 thf(fact_3785_minf_I10_J,axiom,
% 5.27/5.51 ! [D: int,S: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(10)
% 5.27/5.51 thf(fact_3786_minf_I9_J,axiom,
% 5.27/5.51 ! [D: code_integer,S: code_integer] :
% 5.27/5.51 ? [Z2: code_integer] :
% 5.27/5.51 ! [X2: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ X2 @ Z2 )
% 5.27/5.51 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(9)
% 5.27/5.51 thf(fact_3787_minf_I9_J,axiom,
% 5.27/5.51 ! [D: real,S: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ X2 @ Z2 )
% 5.27/5.51 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(9)
% 5.27/5.51 thf(fact_3788_minf_I9_J,axiom,
% 5.27/5.51 ! [D: rat,S: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ X2 @ Z2 )
% 5.27/5.51 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(9)
% 5.27/5.51 thf(fact_3789_minf_I9_J,axiom,
% 5.27/5.51 ! [D: nat,S: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ X2 @ Z2 )
% 5.27/5.51 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(9)
% 5.27/5.51 thf(fact_3790_minf_I9_J,axiom,
% 5.27/5.51 ! [D: int,S: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ X2 @ Z2 )
% 5.27/5.51 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % minf(9)
% 5.27/5.51 thf(fact_3791_pinf_I10_J,axiom,
% 5.27/5.51 ! [D: code_integer,S: code_integer] :
% 5.27/5.51 ? [Z2: code_integer] :
% 5.27/5.51 ! [X2: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(10)
% 5.27/5.51 thf(fact_3792_pinf_I10_J,axiom,
% 5.27/5.51 ! [D: real,S: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(10)
% 5.27/5.51 thf(fact_3793_pinf_I10_J,axiom,
% 5.27/5.51 ! [D: rat,S: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(10)
% 5.27/5.51 thf(fact_3794_pinf_I10_J,axiom,
% 5.27/5.51 ! [D: nat,S: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(10)
% 5.27/5.51 thf(fact_3795_pinf_I10_J,axiom,
% 5.27/5.51 ! [D: int,S: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(10)
% 5.27/5.51 thf(fact_3796_pinf_I9_J,axiom,
% 5.27/5.51 ! [D: code_integer,S: code_integer] :
% 5.27/5.51 ? [Z2: code_integer] :
% 5.27/5.51 ! [X2: code_integer] :
% 5.27/5.51 ( ( ord_le6747313008572928689nteger @ Z2 @ X2 )
% 5.27/5.51 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(9)
% 5.27/5.51 thf(fact_3797_pinf_I9_J,axiom,
% 5.27/5.51 ! [D: real,S: real] :
% 5.27/5.51 ? [Z2: real] :
% 5.27/5.51 ! [X2: real] :
% 5.27/5.51 ( ( ord_less_real @ Z2 @ X2 )
% 5.27/5.51 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(9)
% 5.27/5.51 thf(fact_3798_pinf_I9_J,axiom,
% 5.27/5.51 ! [D: rat,S: rat] :
% 5.27/5.51 ? [Z2: rat] :
% 5.27/5.51 ! [X2: rat] :
% 5.27/5.51 ( ( ord_less_rat @ Z2 @ X2 )
% 5.27/5.51 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(9)
% 5.27/5.51 thf(fact_3799_pinf_I9_J,axiom,
% 5.27/5.51 ! [D: nat,S: nat] :
% 5.27/5.51 ? [Z2: nat] :
% 5.27/5.51 ! [X2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ Z2 @ X2 )
% 5.27/5.51 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(9)
% 5.27/5.51 thf(fact_3800_pinf_I9_J,axiom,
% 5.27/5.51 ! [D: int,S: int] :
% 5.27/5.51 ? [Z2: int] :
% 5.27/5.51 ! [X2: int] :
% 5.27/5.51 ( ( ord_less_int @ Z2 @ X2 )
% 5.27/5.51 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) )
% 5.27/5.51 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ S ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pinf(9)
% 5.27/5.51 thf(fact_3801_length__mul__elem,axiom,
% 5.27/5.51 ! [Xs: list_list_VEBT_VEBT,N2: nat] :
% 5.27/5.51 ( ! [X5: list_VEBT_VEBT] :
% 5.27/5.51 ( ( member2936631157270082147T_VEBT @ X5 @ ( set_list_VEBT_VEBT2 @ Xs ) )
% 5.27/5.51 => ( ( size_s6755466524823107622T_VEBT @ X5 )
% 5.27/5.51 = N2 ) )
% 5.27/5.51 => ( ( size_s6755466524823107622T_VEBT @ ( concat_VEBT_VEBT @ Xs ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s8217280938318005548T_VEBT @ Xs ) @ N2 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_mul_elem
% 5.27/5.51 thf(fact_3802_length__mul__elem,axiom,
% 5.27/5.51 ! [Xs: list_list_o,N2: nat] :
% 5.27/5.51 ( ! [X5: list_o] :
% 5.27/5.51 ( ( member_list_o @ X5 @ ( set_list_o2 @ Xs ) )
% 5.27/5.51 => ( ( size_size_list_o @ X5 )
% 5.27/5.51 = N2 ) )
% 5.27/5.51 => ( ( size_size_list_o @ ( concat_o @ Xs ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s2710708370519433104list_o @ Xs ) @ N2 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_mul_elem
% 5.27/5.51 thf(fact_3803_length__mul__elem,axiom,
% 5.27/5.51 ! [Xs: list_list_nat,N2: nat] :
% 5.27/5.51 ( ! [X5: list_nat] :
% 5.27/5.51 ( ( member_list_nat @ X5 @ ( set_list_nat2 @ Xs ) )
% 5.27/5.51 => ( ( size_size_list_nat @ X5 )
% 5.27/5.51 = N2 ) )
% 5.27/5.51 => ( ( size_size_list_nat @ ( concat_nat @ Xs ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s3023201423986296836st_nat @ Xs ) @ N2 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_mul_elem
% 5.27/5.51 thf(fact_3804_length__mul__elem,axiom,
% 5.27/5.51 ! [Xs: list_list_int,N2: nat] :
% 5.27/5.51 ( ! [X5: list_int] :
% 5.27/5.51 ( ( member_list_int @ X5 @ ( set_list_int2 @ Xs ) )
% 5.27/5.51 => ( ( size_size_list_int @ X5 )
% 5.27/5.51 = N2 ) )
% 5.27/5.51 => ( ( size_size_list_int @ ( concat_int @ Xs ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s533118279054570080st_int @ Xs ) @ N2 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_mul_elem
% 5.27/5.51 thf(fact_3805_mult__le__cancel__iff2,axiom,
% 5.27/5.51 ! [Z: real,X4: real,Y: real] :
% 5.27/5.51 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.27/5.51 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X4 ) @ ( times_times_real @ Z @ Y ) )
% 5.27/5.51 = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff2
% 5.27/5.51 thf(fact_3806_mult__le__cancel__iff2,axiom,
% 5.27/5.51 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.27/5.51 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X4 ) @ ( times_times_rat @ Z @ Y ) )
% 5.27/5.51 = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff2
% 5.27/5.51 thf(fact_3807_mult__le__cancel__iff2,axiom,
% 5.27/5.51 ! [Z: int,X4: int,Y: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.51 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X4 ) @ ( times_times_int @ Z @ Y ) )
% 5.27/5.51 = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff2
% 5.27/5.51 thf(fact_3808_mult__le__cancel__iff1,axiom,
% 5.27/5.51 ! [Z: real,X4: real,Y: real] :
% 5.27/5.51 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.27/5.51 => ( ( ord_less_eq_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff1
% 5.27/5.51 thf(fact_3809_mult__le__cancel__iff1,axiom,
% 5.27/5.51 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.27/5.51 => ( ( ord_less_eq_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_eq_rat @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff1
% 5.27/5.51 thf(fact_3810_mult__le__cancel__iff1,axiom,
% 5.27/5.51 ! [Z: int,X4: int,Y: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.51 => ( ( ord_less_eq_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_eq_int @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_le_cancel_iff1
% 5.27/5.51 thf(fact_3811_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_num,Ys: list_num] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_num @ Xs ) @ ( size_size_list_num @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr6456567536196504476um_num @ ( product_num_num @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( product_Pair_num_num @ ( nth_num @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) @ ( nth_num @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_num @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3812_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_Code_integer,Ys: list_o] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s3445333598471063425nteger @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr8522763379788166057eger_o @ ( produc3607205314601156340eger_o @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc6677183202524767010eger_o @ ( nth_Code_integer @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3813_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3814_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3815_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3816_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3817_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3818_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_o,Ys: list_o] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3819_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_o,Ys: list_nat] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3820_product__nth,axiom,
% 5.27/5.51 ! [N2: nat,Xs: list_o,Ys: list_int] :
% 5.27/5.51 ( ( ord_less_nat @ N2 @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.27/5.51 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N2 )
% 5.27/5.51 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N2 @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % product_nth
% 5.27/5.51 thf(fact_3821_triangle__def,axiom,
% 5.27/5.51 ( nat_triangle
% 5.27/5.51 = ( ^ [N: nat] : ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % triangle_def
% 5.27/5.51 thf(fact_3822_pos__eucl__rel__int__mult__2,axiom,
% 5.27/5.51 ! [B: int,A: int,Q3: int,R3: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.27/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % pos_eucl_rel_int_mult_2
% 5.27/5.51 thf(fact_3823_length__product,axiom,
% 5.27/5.51 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.27/5.51 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3824_length__product,axiom,
% 5.27/5.51 ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.27/5.51 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3825_length__product,axiom,
% 5.27/5.51 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.27/5.51 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3826_length__product,axiom,
% 5.27/5.51 ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.27/5.51 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3827_length__product,axiom,
% 5.27/5.51 ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.27/5.51 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3828_length__product,axiom,
% 5.27/5.51 ! [Xs: list_o,Ys: list_o] :
% 5.27/5.51 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3829_length__product,axiom,
% 5.27/5.51 ! [Xs: list_o,Ys: list_nat] :
% 5.27/5.51 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3830_length__product,axiom,
% 5.27/5.51 ! [Xs: list_o,Ys: list_int] :
% 5.27/5.51 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3831_length__product,axiom,
% 5.27/5.51 ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 5.27/5.51 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3832_length__product,axiom,
% 5.27/5.51 ! [Xs: list_nat,Ys: list_o] :
% 5.27/5.51 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 5.27/5.51 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % length_product
% 5.27/5.51 thf(fact_3833_triangle__Suc,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( nat_triangle @ ( suc @ N2 ) )
% 5.27/5.51 = ( plus_plus_nat @ ( nat_triangle @ N2 ) @ ( suc @ N2 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % triangle_Suc
% 5.27/5.51 thf(fact_3834_unique__remainder,axiom,
% 5.27/5.51 ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 5.27/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 5.27/5.51 => ( R3 = R4 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unique_remainder
% 5.27/5.51 thf(fact_3835_unique__quotient,axiom,
% 5.27/5.51 ! [A: int,B: int,Q3: int,R3: int,Q4: int,R4: int] :
% 5.27/5.51 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R4 ) )
% 5.27/5.51 => ( Q3 = Q4 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % unique_quotient
% 5.27/5.51 thf(fact_3836_eucl__rel__int__by0,axiom,
% 5.27/5.51 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % eucl_rel_int_by0
% 5.27/5.51 thf(fact_3837_div__int__unique,axiom,
% 5.27/5.51 ! [K: int,L: int,Q3: int,R3: int] :
% 5.27/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( ( divide_divide_int @ K @ L )
% 5.27/5.51 = Q3 ) ) ).
% 5.27/5.51
% 5.27/5.51 % div_int_unique
% 5.27/5.51 thf(fact_3838_mod__int__unique,axiom,
% 5.27/5.51 ! [K: int,L: int,Q3: int,R3: int] :
% 5.27/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( ( modulo_modulo_int @ K @ L )
% 5.27/5.51 = R3 ) ) ).
% 5.27/5.51
% 5.27/5.51 % mod_int_unique
% 5.27/5.51 thf(fact_3839_eucl__rel__int__dividesI,axiom,
% 5.27/5.51 ! [L: int,K: int,Q3: int] :
% 5.27/5.51 ( ( L != zero_zero_int )
% 5.27/5.51 => ( ( K
% 5.27/5.51 = ( times_times_int @ Q3 @ L ) )
% 5.27/5.51 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ zero_zero_int ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eucl_rel_int_dividesI
% 5.27/5.51 thf(fact_3840_eucl__rel__int,axiom,
% 5.27/5.51 ! [K: int,L: int] : ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L ) @ ( modulo_modulo_int @ K @ L ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eucl_rel_int
% 5.27/5.51 thf(fact_3841_eucl__rel__int__iff,axiom,
% 5.27/5.51 ! [K: int,L: int,Q3: int,R3: int] :
% 5.27/5.51 ( ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 = ( ( K
% 5.27/5.51 = ( plus_plus_int @ ( times_times_int @ L @ Q3 ) @ R3 ) )
% 5.27/5.51 & ( ( ord_less_int @ zero_zero_int @ L )
% 5.27/5.51 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.27/5.51 & ( ord_less_int @ R3 @ L ) ) )
% 5.27/5.51 & ( ~ ( ord_less_int @ zero_zero_int @ L )
% 5.27/5.51 => ( ( ( ord_less_int @ L @ zero_zero_int )
% 5.27/5.51 => ( ( ord_less_int @ L @ R3 )
% 5.27/5.51 & ( ord_less_eq_int @ R3 @ zero_zero_int ) ) )
% 5.27/5.51 & ( ~ ( ord_less_int @ L @ zero_zero_int )
% 5.27/5.51 => ( Q3 = zero_zero_int ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eucl_rel_int_iff
% 5.27/5.51 thf(fact_3842_mult__less__iff1,axiom,
% 5.27/5.51 ! [Z: real,X4: real,Y: real] :
% 5.27/5.51 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.27/5.51 => ( ( ord_less_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_real @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_less_iff1
% 5.27/5.51 thf(fact_3843_mult__less__iff1,axiom,
% 5.27/5.51 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.51 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.27/5.51 => ( ( ord_less_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_rat @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_less_iff1
% 5.27/5.51 thf(fact_3844_mult__less__iff1,axiom,
% 5.27/5.51 ! [Z: int,X4: int,Y: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.51 => ( ( ord_less_int @ ( times_times_int @ X4 @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.27/5.51 = ( ord_less_int @ X4 @ Y ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % mult_less_iff1
% 5.27/5.51 thf(fact_3845_Divides_Oadjust__div__eq,axiom,
% 5.27/5.51 ! [Q3: int,R3: int] :
% 5.27/5.51 ( ( adjust_div @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 = ( plus_plus_int @ Q3 @ ( zero_n2684676970156552555ol_int @ ( R3 != zero_zero_int ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % Divides.adjust_div_eq
% 5.27/5.51 thf(fact_3846_concat__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,K: int,L: int] :
% 5.27/5.51 ( ( bit_concat_bit @ ( suc @ N2 ) @ K @ L )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N2 @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % concat_bit_Suc
% 5.27/5.51 thf(fact_3847_neg__eucl__rel__int__mult__2,axiom,
% 5.27/5.51 ! [B: int,A: int,Q3: int,R3: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.27/5.51 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.51 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q3 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R3 ) @ one_one_int ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % neg_eucl_rel_int_mult_2
% 5.27/5.51 thf(fact_3848_signed__take__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: code_integer] :
% 5.27/5.51 ( ( bit_ri6519982836138164636nteger @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_Suc
% 5.27/5.51 thf(fact_3849_signed__take__bit__Suc,axiom,
% 5.27/5.51 ! [N2: nat,A: int] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ A )
% 5.27/5.51 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_Suc
% 5.27/5.51 thf(fact_3850_set__decode__Suc,axiom,
% 5.27/5.51 ! [N2: nat,X4: nat] :
% 5.27/5.51 ( ( member_nat @ ( suc @ N2 ) @ ( nat_set_decode @ X4 ) )
% 5.27/5.51 = ( member_nat @ N2 @ ( nat_set_decode @ ( divide_divide_nat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_decode_Suc
% 5.27/5.51 thf(fact_3851_set__decode__0,axiom,
% 5.27/5.51 ! [X4: nat] :
% 5.27/5.51 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X4 ) )
% 5.27/5.51 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X4 ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % set_decode_0
% 5.27/5.51 thf(fact_3852_add__scale__eq__noteq,axiom,
% 5.27/5.51 ! [R3: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.51 ( ( R3 != zero_zero_rat )
% 5.27/5.51 => ( ( ( A = B )
% 5.27/5.51 & ( C != D ) )
% 5.27/5.51 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R3 @ C ) )
% 5.27/5.51 != ( plus_plus_rat @ B @ ( times_times_rat @ R3 @ D ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_scale_eq_noteq
% 5.27/5.51 thf(fact_3853_add__scale__eq__noteq,axiom,
% 5.27/5.51 ! [R3: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.27/5.51 ( ( R3 != zero_zero_complex )
% 5.27/5.51 => ( ( ( A = B )
% 5.27/5.51 & ( C != D ) )
% 5.27/5.51 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R3 @ C ) )
% 5.27/5.51 != ( plus_plus_complex @ B @ ( times_times_complex @ R3 @ D ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_scale_eq_noteq
% 5.27/5.51 thf(fact_3854_add__scale__eq__noteq,axiom,
% 5.27/5.51 ! [R3: real,A: real,B: real,C: real,D: real] :
% 5.27/5.51 ( ( R3 != zero_zero_real )
% 5.27/5.51 => ( ( ( A = B )
% 5.27/5.51 & ( C != D ) )
% 5.27/5.51 => ( ( plus_plus_real @ A @ ( times_times_real @ R3 @ C ) )
% 5.27/5.51 != ( plus_plus_real @ B @ ( times_times_real @ R3 @ D ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_scale_eq_noteq
% 5.27/5.51 thf(fact_3855_add__scale__eq__noteq,axiom,
% 5.27/5.51 ! [R3: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.27/5.51 ( ( R3 != zero_zero_nat )
% 5.27/5.51 => ( ( ( A = B )
% 5.27/5.51 & ( C != D ) )
% 5.27/5.51 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R3 @ C ) )
% 5.27/5.51 != ( plus_plus_nat @ B @ ( times_times_nat @ R3 @ D ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_scale_eq_noteq
% 5.27/5.51 thf(fact_3856_add__scale__eq__noteq,axiom,
% 5.27/5.51 ! [R3: int,A: int,B: int,C: int,D: int] :
% 5.27/5.51 ( ( R3 != zero_zero_int )
% 5.27/5.51 => ( ( ( A = B )
% 5.27/5.51 & ( C != D ) )
% 5.27/5.51 => ( ( plus_plus_int @ A @ ( times_times_int @ R3 @ C ) )
% 5.27/5.51 != ( plus_plus_int @ B @ ( times_times_int @ R3 @ D ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_scale_eq_noteq
% 5.27/5.51 thf(fact_3857_even__mult__exp__div__exp__iff,axiom,
% 5.27/5.51 ! [A: nat,M: nat,N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.51 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.51 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 = zero_zero_nat )
% 5.27/5.51 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.51 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_mult_exp_div_exp_iff
% 5.27/5.51 thf(fact_3858_even__mult__exp__div__exp__iff,axiom,
% 5.27/5.51 ! [A: int,M: nat,N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.51 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.51 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 = zero_zero_int )
% 5.27/5.51 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.51 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_mult_exp_div_exp_iff
% 5.27/5.51 thf(fact_3859_even__mult__exp__div__exp__iff,axiom,
% 5.27/5.51 ! [A: code_integer,M: nat,N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.51 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.51 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 = zero_z3403309356797280102nteger )
% 5.27/5.51 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.51 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_mult_exp_div_exp_iff
% 5.27/5.51 thf(fact_3860_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.27/5.51 ! [A: complex] :
% 5.27/5.51 ( ( minus_minus_complex @ A @ A )
% 5.27/5.51 = zero_zero_complex ) ).
% 5.27/5.51
% 5.27/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.27/5.51 thf(fact_3861_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.27/5.51 ! [A: real] :
% 5.27/5.51 ( ( minus_minus_real @ A @ A )
% 5.27/5.51 = zero_zero_real ) ).
% 5.27/5.51
% 5.27/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.27/5.51 thf(fact_3862_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.27/5.51 ! [A: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ A @ A )
% 5.27/5.51 = zero_zero_rat ) ).
% 5.27/5.51
% 5.27/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.27/5.51 thf(fact_3863_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ A @ A )
% 5.27/5.51 = zero_zero_nat ) ).
% 5.27/5.51
% 5.27/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.27/5.51 thf(fact_3864_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( minus_minus_int @ A @ A )
% 5.27/5.51 = zero_zero_int ) ).
% 5.27/5.51
% 5.27/5.51 % cancel_comm_monoid_add_class.diff_cancel
% 5.27/5.51 thf(fact_3865_diff__zero,axiom,
% 5.27/5.51 ! [A: complex] :
% 5.27/5.51 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_zero
% 5.27/5.51 thf(fact_3866_diff__zero,axiom,
% 5.27/5.51 ! [A: real] :
% 5.27/5.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_zero
% 5.27/5.51 thf(fact_3867_diff__zero,axiom,
% 5.27/5.51 ! [A: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_zero
% 5.27/5.51 thf(fact_3868_diff__zero,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_zero
% 5.27/5.51 thf(fact_3869_diff__zero,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_zero
% 5.27/5.51 thf(fact_3870_zero__diff,axiom,
% 5.27/5.51 ! [A: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.27/5.51 = zero_zero_nat ) ).
% 5.27/5.51
% 5.27/5.51 % zero_diff
% 5.27/5.51 thf(fact_3871_diff__0__right,axiom,
% 5.27/5.51 ! [A: complex] :
% 5.27/5.51 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_0_right
% 5.27/5.51 thf(fact_3872_diff__0__right,axiom,
% 5.27/5.51 ! [A: real] :
% 5.27/5.51 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_0_right
% 5.27/5.51 thf(fact_3873_diff__0__right,axiom,
% 5.27/5.51 ! [A: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_0_right
% 5.27/5.51 thf(fact_3874_diff__0__right,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_0_right
% 5.27/5.51 thf(fact_3875_diff__self,axiom,
% 5.27/5.51 ! [A: complex] :
% 5.27/5.51 ( ( minus_minus_complex @ A @ A )
% 5.27/5.51 = zero_zero_complex ) ).
% 5.27/5.51
% 5.27/5.51 % diff_self
% 5.27/5.51 thf(fact_3876_diff__self,axiom,
% 5.27/5.51 ! [A: real] :
% 5.27/5.51 ( ( minus_minus_real @ A @ A )
% 5.27/5.51 = zero_zero_real ) ).
% 5.27/5.51
% 5.27/5.51 % diff_self
% 5.27/5.51 thf(fact_3877_diff__self,axiom,
% 5.27/5.51 ! [A: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ A @ A )
% 5.27/5.51 = zero_zero_rat ) ).
% 5.27/5.51
% 5.27/5.51 % diff_self
% 5.27/5.51 thf(fact_3878_diff__self,axiom,
% 5.27/5.51 ! [A: int] :
% 5.27/5.51 ( ( minus_minus_int @ A @ A )
% 5.27/5.51 = zero_zero_int ) ).
% 5.27/5.51
% 5.27/5.51 % diff_self
% 5.27/5.51 thf(fact_3879_add__diff__cancel,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel
% 5.27/5.51 thf(fact_3880_add__diff__cancel,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel
% 5.27/5.51 thf(fact_3881_add__diff__cancel,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel
% 5.27/5.51 thf(fact_3882_diff__add__cancel,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_add_cancel
% 5.27/5.51 thf(fact_3883_diff__add__cancel,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_add_cancel
% 5.27/5.51 thf(fact_3884_diff__add__cancel,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % diff_add_cancel
% 5.27/5.51 thf(fact_3885_add__diff__cancel__left,axiom,
% 5.27/5.51 ! [C: real,A: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.27/5.51 = ( minus_minus_real @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left
% 5.27/5.51 thf(fact_3886_add__diff__cancel__left,axiom,
% 5.27/5.51 ! [C: rat,A: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.27/5.51 = ( minus_minus_rat @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left
% 5.27/5.51 thf(fact_3887_add__diff__cancel__left,axiom,
% 5.27/5.51 ! [C: nat,A: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.27/5.51 = ( minus_minus_nat @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left
% 5.27/5.51 thf(fact_3888_add__diff__cancel__left,axiom,
% 5.27/5.51 ! [C: int,A: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.27/5.51 = ( minus_minus_int @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left
% 5.27/5.51 thf(fact_3889_add__diff__cancel__left_H,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.27/5.51 = B ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left'
% 5.27/5.51 thf(fact_3890_add__diff__cancel__left_H,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.27/5.51 = B ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left'
% 5.27/5.51 thf(fact_3891_add__diff__cancel__left_H,axiom,
% 5.27/5.51 ! [A: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.27/5.51 = B ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left'
% 5.27/5.51 thf(fact_3892_add__diff__cancel__left_H,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.27/5.51 = B ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_left'
% 5.27/5.51 thf(fact_3893_add__diff__cancel__right,axiom,
% 5.27/5.51 ! [A: real,C: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.27/5.51 = ( minus_minus_real @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right
% 5.27/5.51 thf(fact_3894_add__diff__cancel__right,axiom,
% 5.27/5.51 ! [A: rat,C: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_rat @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right
% 5.27/5.51 thf(fact_3895_add__diff__cancel__right,axiom,
% 5.27/5.51 ! [A: nat,C: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_nat @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right
% 5.27/5.51 thf(fact_3896_add__diff__cancel__right,axiom,
% 5.27/5.51 ! [A: int,C: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.27/5.51 = ( minus_minus_int @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right
% 5.27/5.51 thf(fact_3897_add__diff__cancel__right_H,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right'
% 5.27/5.51 thf(fact_3898_add__diff__cancel__right_H,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right'
% 5.27/5.51 thf(fact_3899_add__diff__cancel__right_H,axiom,
% 5.27/5.51 ! [A: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right'
% 5.27/5.51 thf(fact_3900_add__diff__cancel__right_H,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.27/5.51 = A ) ).
% 5.27/5.51
% 5.27/5.51 % add_diff_cancel_right'
% 5.27/5.51 thf(fact_3901_minus__mod__self2,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.27/5.51 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % minus_mod_self2
% 5.27/5.51 thf(fact_3902_minus__mod__self2,axiom,
% 5.27/5.51 ! [A: code_integer,B: code_integer] :
% 5.27/5.51 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.27/5.51 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.27/5.51
% 5.27/5.51 % minus_mod_self2
% 5.27/5.51 thf(fact_3903_diff__Suc__Suc,axiom,
% 5.27/5.51 ! [M: nat,N2: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.27/5.51 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_Suc_Suc
% 5.27/5.51 thf(fact_3904_Suc__diff__diff,axiom,
% 5.27/5.51 ! [M: nat,N2: nat,K: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( suc @ K ) )
% 5.27/5.51 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N2 ) @ K ) ) ).
% 5.27/5.51
% 5.27/5.51 % Suc_diff_diff
% 5.27/5.51 thf(fact_3905_diff__self__eq__0,axiom,
% 5.27/5.51 ! [M: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ M @ M )
% 5.27/5.51 = zero_zero_nat ) ).
% 5.27/5.51
% 5.27/5.51 % diff_self_eq_0
% 5.27/5.51 thf(fact_3906_diff__0__eq__0,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 = zero_zero_nat ) ).
% 5.27/5.51
% 5.27/5.51 % diff_0_eq_0
% 5.27/5.51 thf(fact_3907_diff__diff__cancel,axiom,
% 5.27/5.51 ! [I2: nat,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ I2 @ N2 )
% 5.27/5.51 => ( ( minus_minus_nat @ N2 @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.27/5.51 = I2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_diff_cancel
% 5.27/5.51 thf(fact_3908_diff__diff__left,axiom,
% 5.27/5.51 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.27/5.51 = ( minus_minus_nat @ I2 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_diff_left
% 5.27/5.51 thf(fact_3909_signed__take__bit__of__0,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ N2 @ zero_zero_int )
% 5.27/5.51 = zero_zero_int ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_of_0
% 5.27/5.51 thf(fact_3910_concat__bit__0,axiom,
% 5.27/5.51 ! [K: int,L: int] :
% 5.27/5.51 ( ( bit_concat_bit @ zero_zero_nat @ K @ L )
% 5.27/5.51 = L ) ).
% 5.27/5.51
% 5.27/5.51 % concat_bit_0
% 5.27/5.51 thf(fact_3911_diff__ge__0__iff__ge,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.27/5.51 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_ge_0_iff_ge
% 5.27/5.51 thf(fact_3912_diff__ge__0__iff__ge,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.51 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_ge_0_iff_ge
% 5.27/5.51 thf(fact_3913_diff__ge__0__iff__ge,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.27/5.51 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_ge_0_iff_ge
% 5.27/5.51 thf(fact_3914_diff__gt__0__iff__gt,axiom,
% 5.27/5.51 ! [A: real,B: real] :
% 5.27/5.51 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.27/5.51 = ( ord_less_real @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_gt_0_iff_gt
% 5.27/5.51 thf(fact_3915_diff__gt__0__iff__gt,axiom,
% 5.27/5.51 ! [A: rat,B: rat] :
% 5.27/5.51 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.51 = ( ord_less_rat @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_gt_0_iff_gt
% 5.27/5.51 thf(fact_3916_diff__gt__0__iff__gt,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.27/5.51 = ( ord_less_int @ B @ A ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_gt_0_iff_gt
% 5.27/5.51 thf(fact_3917_le__add__diff__inverse2,axiom,
% 5.27/5.51 ! [B: real,A: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ B @ A )
% 5.27/5.51 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse2
% 5.27/5.51 thf(fact_3918_le__add__diff__inverse2,axiom,
% 5.27/5.51 ! [B: rat,A: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.27/5.51 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse2
% 5.27/5.51 thf(fact_3919_le__add__diff__inverse2,axiom,
% 5.27/5.51 ! [B: nat,A: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ B @ A )
% 5.27/5.51 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse2
% 5.27/5.51 thf(fact_3920_le__add__diff__inverse2,axiom,
% 5.27/5.51 ! [B: int,A: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.27/5.51 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse2
% 5.27/5.51 thf(fact_3921_le__add__diff__inverse,axiom,
% 5.27/5.51 ! [B: real,A: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ B @ A )
% 5.27/5.51 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse
% 5.27/5.51 thf(fact_3922_le__add__diff__inverse,axiom,
% 5.27/5.51 ! [B: rat,A: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.27/5.51 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse
% 5.27/5.51 thf(fact_3923_le__add__diff__inverse,axiom,
% 5.27/5.51 ! [B: nat,A: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ B @ A )
% 5.27/5.51 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse
% 5.27/5.51 thf(fact_3924_le__add__diff__inverse,axiom,
% 5.27/5.51 ! [B: int,A: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.27/5.51 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.27/5.51 = A ) ) ).
% 5.27/5.51
% 5.27/5.51 % le_add_diff_inverse
% 5.27/5.51 thf(fact_3925_diff__numeral__special_I9_J,axiom,
% 5.27/5.51 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.27/5.51 = zero_zero_complex ) ).
% 5.27/5.51
% 5.27/5.51 % diff_numeral_special(9)
% 5.27/5.51 thf(fact_3926_diff__numeral__special_I9_J,axiom,
% 5.27/5.51 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.27/5.51 = zero_zero_real ) ).
% 5.27/5.51
% 5.27/5.51 % diff_numeral_special(9)
% 5.27/5.51 thf(fact_3927_diff__numeral__special_I9_J,axiom,
% 5.27/5.51 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.27/5.51 = zero_zero_rat ) ).
% 5.27/5.51
% 5.27/5.51 % diff_numeral_special(9)
% 5.27/5.51 thf(fact_3928_diff__numeral__special_I9_J,axiom,
% 5.27/5.51 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.27/5.51 = zero_zero_int ) ).
% 5.27/5.51
% 5.27/5.51 % diff_numeral_special(9)
% 5.27/5.51 thf(fact_3929_diff__add__zero,axiom,
% 5.27/5.51 ! [A: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.27/5.51 = zero_zero_nat ) ).
% 5.27/5.51
% 5.27/5.51 % diff_add_zero
% 5.27/5.51 thf(fact_3930_right__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [V: num,B: rat,C: rat] :
% 5.27/5.51 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib_numeral
% 5.27/5.51 thf(fact_3931_right__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [V: num,B: complex,C: complex] :
% 5.27/5.51 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib_numeral
% 5.27/5.51 thf(fact_3932_right__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [V: num,B: real,C: real] :
% 5.27/5.51 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib_numeral
% 5.27/5.51 thf(fact_3933_right__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [V: num,B: int,C: int] :
% 5.27/5.51 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib_numeral
% 5.27/5.51 thf(fact_3934_left__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [A: rat,B: rat,V: num] :
% 5.27/5.51 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib_numeral
% 5.27/5.51 thf(fact_3935_left__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [A: complex,B: complex,V: num] :
% 5.27/5.51 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib_numeral
% 5.27/5.51 thf(fact_3936_left__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [A: real,B: real,V: num] :
% 5.27/5.51 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib_numeral
% 5.27/5.51 thf(fact_3937_left__diff__distrib__numeral,axiom,
% 5.27/5.51 ! [A: int,B: int,V: num] :
% 5.27/5.51 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib_numeral
% 5.27/5.51 thf(fact_3938_div__diff,axiom,
% 5.27/5.51 ! [C: int,A: int,B: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ C @ A )
% 5.27/5.51 => ( ( dvd_dvd_int @ C @ B )
% 5.27/5.51 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.51 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % div_diff
% 5.27/5.51 thf(fact_3939_div__diff,axiom,
% 5.27/5.51 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.27/5.51 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.27/5.51 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.27/5.51 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % div_diff
% 5.27/5.51 thf(fact_3940_zero__less__diff,axiom,
% 5.27/5.51 ! [N2: nat,M: nat] :
% 5.27/5.51 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.51 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % zero_less_diff
% 5.27/5.51 thf(fact_3941_diff__is__0__eq_H,axiom,
% 5.27/5.51 ! [M: nat,N2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.51 => ( ( minus_minus_nat @ M @ N2 )
% 5.27/5.51 = zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_is_0_eq'
% 5.27/5.51 thf(fact_3942_diff__is__0__eq,axiom,
% 5.27/5.51 ! [M: nat,N2: nat] :
% 5.27/5.51 ( ( ( minus_minus_nat @ M @ N2 )
% 5.27/5.51 = zero_zero_nat )
% 5.27/5.51 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_is_0_eq
% 5.27/5.51 thf(fact_3943_of__bool__not__iff,axiom,
% 5.27/5.51 ! [P: $o] :
% 5.27/5.51 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.27/5.51 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % of_bool_not_iff
% 5.27/5.51 thf(fact_3944_of__bool__not__iff,axiom,
% 5.27/5.51 ! [P: $o] :
% 5.27/5.51 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.27/5.51 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % of_bool_not_iff
% 5.27/5.51 thf(fact_3945_of__bool__not__iff,axiom,
% 5.27/5.51 ! [P: $o] :
% 5.27/5.51 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.27/5.51 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % of_bool_not_iff
% 5.27/5.51 thf(fact_3946_of__bool__not__iff,axiom,
% 5.27/5.51 ! [P: $o] :
% 5.27/5.51 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.27/5.51 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % of_bool_not_iff
% 5.27/5.51 thf(fact_3947_of__bool__not__iff,axiom,
% 5.27/5.51 ! [P: $o] :
% 5.27/5.51 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.27/5.51 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % of_bool_not_iff
% 5.27/5.51 thf(fact_3948_Nat_Odiff__diff__right,axiom,
% 5.27/5.51 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.51 => ( ( minus_minus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.27/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % Nat.diff_diff_right
% 5.27/5.51 thf(fact_3949_Nat_Oadd__diff__assoc2,axiom,
% 5.27/5.51 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.51 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.27/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % Nat.add_diff_assoc2
% 5.27/5.51 thf(fact_3950_Nat_Oadd__diff__assoc,axiom,
% 5.27/5.51 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.51 => ( ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.27/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % Nat.add_diff_assoc
% 5.27/5.51 thf(fact_3951_diff__Suc__1,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.27/5.51 = N2 ) ).
% 5.27/5.51
% 5.27/5.51 % diff_Suc_1
% 5.27/5.51 thf(fact_3952_signed__take__bit__Suc__1,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ one_one_int )
% 5.27/5.51 = one_one_int ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_Suc_1
% 5.27/5.51 thf(fact_3953_signed__take__bit__numeral__of__1,axiom,
% 5.27/5.51 ! [K: num] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.27/5.51 = one_one_int ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_numeral_of_1
% 5.27/5.51 thf(fact_3954_concat__bit__nonnegative__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int,L: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N2 @ K @ L ) )
% 5.27/5.51 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ).
% 5.27/5.51
% 5.27/5.51 % concat_bit_nonnegative_iff
% 5.27/5.51 thf(fact_3955_concat__bit__negative__iff,axiom,
% 5.27/5.51 ! [N2: nat,K: int,L: int] :
% 5.27/5.51 ( ( ord_less_int @ ( bit_concat_bit @ N2 @ K @ L ) @ zero_zero_int )
% 5.27/5.51 = ( ord_less_int @ L @ zero_zero_int ) ) ).
% 5.27/5.51
% 5.27/5.51 % concat_bit_negative_iff
% 5.27/5.51 thf(fact_3956_Suc__pred,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.27/5.51 = N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % Suc_pred
% 5.27/5.51 thf(fact_3957_diff__Suc__diff__eq2,axiom,
% 5.27/5.51 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.51 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I2 )
% 5.27/5.51 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_Suc_diff_eq2
% 5.27/5.51 thf(fact_3958_diff__Suc__diff__eq1,axiom,
% 5.27/5.51 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.51 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.51 => ( ( minus_minus_nat @ I2 @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.27/5.51 = ( minus_minus_nat @ ( plus_plus_nat @ I2 @ K ) @ ( suc @ J ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_Suc_diff_eq1
% 5.27/5.51 thf(fact_3959_zle__diff1__eq,axiom,
% 5.27/5.51 ! [W: int,Z: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.27/5.51 = ( ord_less_int @ W @ Z ) ) ).
% 5.27/5.51
% 5.27/5.51 % zle_diff1_eq
% 5.27/5.51 thf(fact_3960_signed__take__bit__Suc__bit0,axiom,
% 5.27/5.51 ! [N2: nat,K: num] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.27/5.51 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_Suc_bit0
% 5.27/5.51 thf(fact_3961_Suc__diff__1,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.51 => ( ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) )
% 5.27/5.51 = N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % Suc_diff_1
% 5.27/5.51 thf(fact_3962_even__diff,axiom,
% 5.27/5.51 ! [A: code_integer,B: code_integer] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.27/5.51 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_diff
% 5.27/5.51 thf(fact_3963_even__diff,axiom,
% 5.27/5.51 ! [A: int,B: int] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.27/5.51 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_diff
% 5.27/5.51 thf(fact_3964_odd__Suc__minus__one,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 => ( ( suc @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) )
% 5.27/5.51 = N2 ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_Suc_minus_one
% 5.27/5.51 thf(fact_3965_even__diff__nat,axiom,
% 5.27/5.51 ! [M: nat,N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.51 = ( ( ord_less_nat @ M @ N2 )
% 5.27/5.51 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % even_diff_nat
% 5.27/5.51 thf(fact_3966_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) )
% 5.27/5.51 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % semiring_parity_class.even_mask_iff
% 5.27/5.51 thf(fact_3967_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) )
% 5.27/5.51 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % semiring_parity_class.even_mask_iff
% 5.27/5.51 thf(fact_3968_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.27/5.51 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.51
% 5.27/5.51 % semiring_parity_class.even_mask_iff
% 5.27/5.51 thf(fact_3969_odd__two__times__div__two__nat,axiom,
% 5.27/5.51 ! [N2: nat] :
% 5.27/5.51 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.51 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.51 = ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % odd_two_times_div_two_nat
% 5.27/5.51 thf(fact_3970_diff__right__commute,axiom,
% 5.27/5.51 ! [A: real,C: real,B: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.27/5.51 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_commute
% 5.27/5.51 thf(fact_3971_diff__right__commute,axiom,
% 5.27/5.51 ! [A: rat,C: rat,B: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.27/5.51 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_commute
% 5.27/5.51 thf(fact_3972_diff__right__commute,axiom,
% 5.27/5.51 ! [A: nat,C: nat,B: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.27/5.51 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_commute
% 5.27/5.51 thf(fact_3973_diff__right__commute,axiom,
% 5.27/5.51 ! [A: int,C: int,B: int] :
% 5.27/5.51 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.27/5.51 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_commute
% 5.27/5.51 thf(fact_3974_diff__eq__diff__eq,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.51 ( ( ( minus_minus_real @ A @ B )
% 5.27/5.51 = ( minus_minus_real @ C @ D ) )
% 5.27/5.51 => ( ( A = B )
% 5.27/5.51 = ( C = D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_eq
% 5.27/5.51 thf(fact_3975_diff__eq__diff__eq,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.27/5.51 = ( minus_minus_rat @ C @ D ) )
% 5.27/5.51 => ( ( A = B )
% 5.27/5.51 = ( C = D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_eq
% 5.27/5.51 thf(fact_3976_diff__eq__diff__eq,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.27/5.51 = ( minus_minus_int @ C @ D ) )
% 5.27/5.51 => ( ( A = B )
% 5.27/5.51 = ( C = D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_eq
% 5.27/5.51 thf(fact_3977_signed__take__bit__diff,axiom,
% 5.27/5.51 ! [N2: nat,K: int,L: int] :
% 5.27/5.51 ( ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.27/5.51 = ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % signed_take_bit_diff
% 5.27/5.51 thf(fact_3978_diff__commute,axiom,
% 5.27/5.51 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.51 ( ( minus_minus_nat @ ( minus_minus_nat @ I2 @ J ) @ K )
% 5.27/5.51 = ( minus_minus_nat @ ( minus_minus_nat @ I2 @ K ) @ J ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_commute
% 5.27/5.51 thf(fact_3979_diff__mono,axiom,
% 5.27/5.51 ! [A: real,B: real,D: real,C: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.51 => ( ( ord_less_eq_real @ D @ C )
% 5.27/5.51 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_mono
% 5.27/5.51 thf(fact_3980_diff__mono,axiom,
% 5.27/5.51 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.51 => ( ( ord_less_eq_rat @ D @ C )
% 5.27/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_mono
% 5.27/5.51 thf(fact_3981_diff__mono,axiom,
% 5.27/5.51 ! [A: int,B: int,D: int,C: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.27/5.51 => ( ( ord_less_eq_int @ D @ C )
% 5.27/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_mono
% 5.27/5.51 thf(fact_3982_diff__left__mono,axiom,
% 5.27/5.51 ! [B: real,A: real,C: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ B @ A )
% 5.27/5.51 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_left_mono
% 5.27/5.51 thf(fact_3983_diff__left__mono,axiom,
% 5.27/5.51 ! [B: rat,A: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ B @ A )
% 5.27/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_left_mono
% 5.27/5.51 thf(fact_3984_diff__left__mono,axiom,
% 5.27/5.51 ! [B: int,A: int,C: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ B @ A )
% 5.27/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_left_mono
% 5.27/5.51 thf(fact_3985_diff__right__mono,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real] :
% 5.27/5.51 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.51 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_mono
% 5.27/5.51 thf(fact_3986_diff__right__mono,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.51 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_mono
% 5.27/5.51 thf(fact_3987_diff__right__mono,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int] :
% 5.27/5.51 ( ( ord_less_eq_int @ A @ B )
% 5.27/5.51 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_right_mono
% 5.27/5.51 thf(fact_3988_diff__eq__diff__less__eq,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.51 ( ( ( minus_minus_real @ A @ B )
% 5.27/5.51 = ( minus_minus_real @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_eq_real @ A @ B )
% 5.27/5.51 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less_eq
% 5.27/5.51 thf(fact_3989_diff__eq__diff__less__eq,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.27/5.51 = ( minus_minus_rat @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.51 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less_eq
% 5.27/5.51 thf(fact_3990_diff__eq__diff__less__eq,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.27/5.51 = ( minus_minus_int @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_eq_int @ A @ B )
% 5.27/5.51 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less_eq
% 5.27/5.51 thf(fact_3991_eq__iff__diff__eq__0,axiom,
% 5.27/5.51 ( ( ^ [Y6: complex,Z4: complex] : ( Y6 = Z4 ) )
% 5.27/5.51 = ( ^ [A3: complex,B2: complex] :
% 5.27/5.51 ( ( minus_minus_complex @ A3 @ B2 )
% 5.27/5.51 = zero_zero_complex ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eq_iff_diff_eq_0
% 5.27/5.51 thf(fact_3992_eq__iff__diff__eq__0,axiom,
% 5.27/5.51 ( ( ^ [Y6: real,Z4: real] : ( Y6 = Z4 ) )
% 5.27/5.51 = ( ^ [A3: real,B2: real] :
% 5.27/5.51 ( ( minus_minus_real @ A3 @ B2 )
% 5.27/5.51 = zero_zero_real ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eq_iff_diff_eq_0
% 5.27/5.51 thf(fact_3993_eq__iff__diff__eq__0,axiom,
% 5.27/5.51 ( ( ^ [Y6: rat,Z4: rat] : ( Y6 = Z4 ) )
% 5.27/5.51 = ( ^ [A3: rat,B2: rat] :
% 5.27/5.51 ( ( minus_minus_rat @ A3 @ B2 )
% 5.27/5.51 = zero_zero_rat ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eq_iff_diff_eq_0
% 5.27/5.51 thf(fact_3994_eq__iff__diff__eq__0,axiom,
% 5.27/5.51 ( ( ^ [Y6: int,Z4: int] : ( Y6 = Z4 ) )
% 5.27/5.51 = ( ^ [A3: int,B2: int] :
% 5.27/5.51 ( ( minus_minus_int @ A3 @ B2 )
% 5.27/5.51 = zero_zero_int ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % eq_iff_diff_eq_0
% 5.27/5.51 thf(fact_3995_diff__strict__mono,axiom,
% 5.27/5.51 ! [A: real,B: real,D: real,C: real] :
% 5.27/5.51 ( ( ord_less_real @ A @ B )
% 5.27/5.51 => ( ( ord_less_real @ D @ C )
% 5.27/5.51 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_mono
% 5.27/5.51 thf(fact_3996_diff__strict__mono,axiom,
% 5.27/5.51 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_rat @ A @ B )
% 5.27/5.51 => ( ( ord_less_rat @ D @ C )
% 5.27/5.51 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_mono
% 5.27/5.51 thf(fact_3997_diff__strict__mono,axiom,
% 5.27/5.51 ! [A: int,B: int,D: int,C: int] :
% 5.27/5.51 ( ( ord_less_int @ A @ B )
% 5.27/5.51 => ( ( ord_less_int @ D @ C )
% 5.27/5.51 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_mono
% 5.27/5.51 thf(fact_3998_diff__eq__diff__less,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.51 ( ( ( minus_minus_real @ A @ B )
% 5.27/5.51 = ( minus_minus_real @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_real @ A @ B )
% 5.27/5.51 = ( ord_less_real @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less
% 5.27/5.51 thf(fact_3999_diff__eq__diff__less,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.51 ( ( ( minus_minus_rat @ A @ B )
% 5.27/5.51 = ( minus_minus_rat @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_rat @ A @ B )
% 5.27/5.51 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less
% 5.27/5.51 thf(fact_4000_diff__eq__diff__less,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.51 ( ( ( minus_minus_int @ A @ B )
% 5.27/5.51 = ( minus_minus_int @ C @ D ) )
% 5.27/5.51 => ( ( ord_less_int @ A @ B )
% 5.27/5.51 = ( ord_less_int @ C @ D ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_eq_diff_less
% 5.27/5.51 thf(fact_4001_diff__strict__left__mono,axiom,
% 5.27/5.51 ! [B: real,A: real,C: real] :
% 5.27/5.51 ( ( ord_less_real @ B @ A )
% 5.27/5.51 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_left_mono
% 5.27/5.51 thf(fact_4002_diff__strict__left__mono,axiom,
% 5.27/5.51 ! [B: rat,A: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_rat @ B @ A )
% 5.27/5.51 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_left_mono
% 5.27/5.51 thf(fact_4003_diff__strict__left__mono,axiom,
% 5.27/5.51 ! [B: int,A: int,C: int] :
% 5.27/5.51 ( ( ord_less_int @ B @ A )
% 5.27/5.51 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_left_mono
% 5.27/5.51 thf(fact_4004_diff__strict__right__mono,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real] :
% 5.27/5.51 ( ( ord_less_real @ A @ B )
% 5.27/5.51 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_right_mono
% 5.27/5.51 thf(fact_4005_diff__strict__right__mono,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat] :
% 5.27/5.51 ( ( ord_less_rat @ A @ B )
% 5.27/5.51 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_right_mono
% 5.27/5.51 thf(fact_4006_diff__strict__right__mono,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int] :
% 5.27/5.51 ( ( ord_less_int @ A @ B )
% 5.27/5.51 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % diff_strict_right_mono
% 5.27/5.51 thf(fact_4007_right__diff__distrib_H,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat] :
% 5.27/5.51 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib'
% 5.27/5.51 thf(fact_4008_right__diff__distrib_H,axiom,
% 5.27/5.51 ! [A: complex,B: complex,C: complex] :
% 5.27/5.51 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib'
% 5.27/5.51 thf(fact_4009_right__diff__distrib_H,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real] :
% 5.27/5.51 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib'
% 5.27/5.51 thf(fact_4010_right__diff__distrib_H,axiom,
% 5.27/5.51 ! [A: nat,B: nat,C: nat] :
% 5.27/5.51 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib'
% 5.27/5.51 thf(fact_4011_right__diff__distrib_H,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int] :
% 5.27/5.51 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib'
% 5.27/5.51 thf(fact_4012_left__diff__distrib_H,axiom,
% 5.27/5.51 ! [B: rat,C: rat,A: rat] :
% 5.27/5.51 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib'
% 5.27/5.51 thf(fact_4013_left__diff__distrib_H,axiom,
% 5.27/5.51 ! [B: complex,C: complex,A: complex] :
% 5.27/5.51 ( ( times_times_complex @ ( minus_minus_complex @ B @ C ) @ A )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ B @ A ) @ ( times_times_complex @ C @ A ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib'
% 5.27/5.51 thf(fact_4014_left__diff__distrib_H,axiom,
% 5.27/5.51 ! [B: real,C: real,A: real] :
% 5.27/5.51 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib'
% 5.27/5.51 thf(fact_4015_left__diff__distrib_H,axiom,
% 5.27/5.51 ! [B: nat,C: nat,A: nat] :
% 5.27/5.51 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.27/5.51 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib'
% 5.27/5.51 thf(fact_4016_left__diff__distrib_H,axiom,
% 5.27/5.51 ! [B: int,C: int,A: int] :
% 5.27/5.51 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib'
% 5.27/5.51 thf(fact_4017_right__diff__distrib,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat] :
% 5.27/5.51 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib
% 5.27/5.51 thf(fact_4018_right__diff__distrib,axiom,
% 5.27/5.51 ! [A: complex,B: complex,C: complex] :
% 5.27/5.51 ( ( times_times_complex @ A @ ( minus_minus_complex @ B @ C ) )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ A @ B ) @ ( times_times_complex @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib
% 5.27/5.51 thf(fact_4019_right__diff__distrib,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real] :
% 5.27/5.51 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib
% 5.27/5.51 thf(fact_4020_right__diff__distrib,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int] :
% 5.27/5.51 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % right_diff_distrib
% 5.27/5.51 thf(fact_4021_left__diff__distrib,axiom,
% 5.27/5.51 ! [A: rat,B: rat,C: rat] :
% 5.27/5.51 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.51 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib
% 5.27/5.51 thf(fact_4022_left__diff__distrib,axiom,
% 5.27/5.51 ! [A: complex,B: complex,C: complex] :
% 5.27/5.51 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.27/5.51 = ( minus_minus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib
% 5.27/5.51 thf(fact_4023_left__diff__distrib,axiom,
% 5.27/5.51 ! [A: real,B: real,C: real] :
% 5.27/5.51 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.51 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib
% 5.27/5.51 thf(fact_4024_left__diff__distrib,axiom,
% 5.27/5.51 ! [A: int,B: int,C: int] :
% 5.27/5.51 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.51 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.27/5.51
% 5.27/5.51 % left_diff_distrib
% 5.27/5.51 thf(fact_4025_add__diff__add,axiom,
% 5.27/5.51 ! [A: real,C: real,B: real,D: real] :
% 5.27/5.51 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.27/5.52 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_add
% 5.27/5.52 thf(fact_4026_add__diff__add,axiom,
% 5.27/5.52 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.27/5.52 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_add
% 5.27/5.52 thf(fact_4027_add__diff__add,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.27/5.52 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_add
% 5.27/5.52 thf(fact_4028_group__cancel_Osub1,axiom,
% 5.27/5.52 ! [A2: real,K: real,A: real,B: real] :
% 5.27/5.52 ( ( A2
% 5.27/5.52 = ( plus_plus_real @ K @ A ) )
% 5.27/5.52 => ( ( minus_minus_real @ A2 @ B )
% 5.27/5.52 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % group_cancel.sub1
% 5.27/5.52 thf(fact_4029_group__cancel_Osub1,axiom,
% 5.27/5.52 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.27/5.52 ( ( A2
% 5.27/5.52 = ( plus_plus_rat @ K @ A ) )
% 5.27/5.52 => ( ( minus_minus_rat @ A2 @ B )
% 5.27/5.52 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % group_cancel.sub1
% 5.27/5.52 thf(fact_4030_group__cancel_Osub1,axiom,
% 5.27/5.52 ! [A2: int,K: int,A: int,B: int] :
% 5.27/5.52 ( ( A2
% 5.27/5.52 = ( plus_plus_int @ K @ A ) )
% 5.27/5.52 => ( ( minus_minus_int @ A2 @ B )
% 5.27/5.52 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % group_cancel.sub1
% 5.27/5.52 thf(fact_4031_diff__eq__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( ( minus_minus_real @ A @ B )
% 5.27/5.52 = C )
% 5.27/5.52 = ( A
% 5.27/5.52 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_eq_eq
% 5.27/5.52 thf(fact_4032_diff__eq__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( ( minus_minus_rat @ A @ B )
% 5.27/5.52 = C )
% 5.27/5.52 = ( A
% 5.27/5.52 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_eq_eq
% 5.27/5.52 thf(fact_4033_diff__eq__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( ( minus_minus_int @ A @ B )
% 5.27/5.52 = C )
% 5.27/5.52 = ( A
% 5.27/5.52 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_eq_eq
% 5.27/5.52 thf(fact_4034_eq__diff__eq,axiom,
% 5.27/5.52 ! [A: real,C: real,B: real] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( minus_minus_real @ C @ B ) )
% 5.27/5.52 = ( ( plus_plus_real @ A @ B )
% 5.27/5.52 = C ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_diff_eq
% 5.27/5.52 thf(fact_4035_eq__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,C: rat,B: rat] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( minus_minus_rat @ C @ B ) )
% 5.27/5.52 = ( ( plus_plus_rat @ A @ B )
% 5.27/5.52 = C ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_diff_eq
% 5.27/5.52 thf(fact_4036_eq__diff__eq,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( minus_minus_int @ C @ B ) )
% 5.27/5.52 = ( ( plus_plus_int @ A @ B )
% 5.27/5.52 = C ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_diff_eq
% 5.27/5.52 thf(fact_4037_add__diff__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.27/5.52 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_eq
% 5.27/5.52 thf(fact_4038_add__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.27/5.52 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_eq
% 5.27/5.52 thf(fact_4039_add__diff__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.27/5.52 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_eq
% 5.27/5.52 thf(fact_4040_diff__diff__eq2,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.27/5.52 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq2
% 5.27/5.52 thf(fact_4041_diff__diff__eq2,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.27/5.52 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq2
% 5.27/5.52 thf(fact_4042_diff__diff__eq2,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.27/5.52 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq2
% 5.27/5.52 thf(fact_4043_diff__add__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq
% 5.27/5.52 thf(fact_4044_diff__add__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq
% 5.27/5.52 thf(fact_4045_diff__add__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq
% 5.27/5.52 thf(fact_4046_diff__add__eq__diff__diff__swap,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.27/5.52 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq_diff_diff_swap
% 5.27/5.52 thf(fact_4047_diff__add__eq__diff__diff__swap,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.27/5.52 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq_diff_diff_swap
% 5.27/5.52 thf(fact_4048_diff__add__eq__diff__diff__swap,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.27/5.52 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_eq_diff_diff_swap
% 5.27/5.52 thf(fact_4049_add__implies__diff,axiom,
% 5.27/5.52 ! [C: real,B: real,A: real] :
% 5.27/5.52 ( ( ( plus_plus_real @ C @ B )
% 5.27/5.52 = A )
% 5.27/5.52 => ( C
% 5.27/5.52 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_implies_diff
% 5.27/5.52 thf(fact_4050_add__implies__diff,axiom,
% 5.27/5.52 ! [C: rat,B: rat,A: rat] :
% 5.27/5.52 ( ( ( plus_plus_rat @ C @ B )
% 5.27/5.52 = A )
% 5.27/5.52 => ( C
% 5.27/5.52 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_implies_diff
% 5.27/5.52 thf(fact_4051_add__implies__diff,axiom,
% 5.27/5.52 ! [C: nat,B: nat,A: nat] :
% 5.27/5.52 ( ( ( plus_plus_nat @ C @ B )
% 5.27/5.52 = A )
% 5.27/5.52 => ( C
% 5.27/5.52 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_implies_diff
% 5.27/5.52 thf(fact_4052_add__implies__diff,axiom,
% 5.27/5.52 ! [C: int,B: int,A: int] :
% 5.27/5.52 ( ( ( plus_plus_int @ C @ B )
% 5.27/5.52 = A )
% 5.27/5.52 => ( C
% 5.27/5.52 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_implies_diff
% 5.27/5.52 thf(fact_4053_diff__diff__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq
% 5.27/5.52 thf(fact_4054_diff__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq
% 5.27/5.52 thf(fact_4055_diff__diff__eq,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq
% 5.27/5.52 thf(fact_4056_diff__diff__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_diff_eq
% 5.27/5.52 thf(fact_4057_diff__divide__distrib,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_distrib
% 5.27/5.52 thf(fact_4058_diff__divide__distrib,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_distrib
% 5.27/5.52 thf(fact_4059_diff__divide__distrib,axiom,
% 5.27/5.52 ! [A: complex,B: complex,C: complex] :
% 5.27/5.52 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.27/5.52 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_distrib
% 5.27/5.52 thf(fact_4060_dvd__diff,axiom,
% 5.27/5.52 ! [X4: code_integer,Y: code_integer,Z: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ X4 @ Y )
% 5.27/5.52 => ( ( dvd_dvd_Code_integer @ X4 @ Z )
% 5.27/5.52 => ( dvd_dvd_Code_integer @ X4 @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff
% 5.27/5.52 thf(fact_4061_dvd__diff,axiom,
% 5.27/5.52 ! [X4: real,Y: real,Z: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ X4 @ Y )
% 5.27/5.52 => ( ( dvd_dvd_real @ X4 @ Z )
% 5.27/5.52 => ( dvd_dvd_real @ X4 @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff
% 5.27/5.52 thf(fact_4062_dvd__diff,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat,Z: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ X4 @ Y )
% 5.27/5.52 => ( ( dvd_dvd_rat @ X4 @ Z )
% 5.27/5.52 => ( dvd_dvd_rat @ X4 @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff
% 5.27/5.52 thf(fact_4063_dvd__diff,axiom,
% 5.27/5.52 ! [X4: int,Y: int,Z: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ X4 @ Y )
% 5.27/5.52 => ( ( dvd_dvd_int @ X4 @ Z )
% 5.27/5.52 => ( dvd_dvd_int @ X4 @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff
% 5.27/5.52 thf(fact_4064_dvd__diff__commute,axiom,
% 5.27/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff_commute
% 5.27/5.52 thf(fact_4065_dvd__diff__commute,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.27/5.52 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff_commute
% 5.27/5.52 thf(fact_4066_zero__induct__lemma,axiom,
% 5.27/5.52 ! [P: nat > $o,K: nat,I2: nat] :
% 5.27/5.52 ( ( P @ K )
% 5.27/5.52 => ( ! [N3: nat] :
% 5.27/5.52 ( ( P @ ( suc @ N3 ) )
% 5.27/5.52 => ( P @ N3 ) )
% 5.27/5.52 => ( P @ ( minus_minus_nat @ K @ I2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % zero_induct_lemma
% 5.27/5.52 thf(fact_4067_diffs0__imp__equal,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ( minus_minus_nat @ M @ N2 )
% 5.27/5.52 = zero_zero_nat )
% 5.27/5.52 => ( ( ( minus_minus_nat @ N2 @ M )
% 5.27/5.52 = zero_zero_nat )
% 5.27/5.52 => ( M = N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diffs0_imp_equal
% 5.27/5.52 thf(fact_4068_minus__nat_Odiff__0,axiom,
% 5.27/5.52 ! [M: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.27/5.52 = M ) ).
% 5.27/5.52
% 5.27/5.52 % minus_nat.diff_0
% 5.27/5.52 thf(fact_4069_mod__diff__right__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.27/5.52 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_right_eq
% 5.27/5.52 thf(fact_4070_mod__diff__right__eq,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.27/5.52 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_right_eq
% 5.27/5.52 thf(fact_4071_mod__diff__left__eq,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.27/5.52 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_left_eq
% 5.27/5.52 thf(fact_4072_mod__diff__left__eq,axiom,
% 5.27/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.27/5.52 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_left_eq
% 5.27/5.52 thf(fact_4073_mod__diff__cong,axiom,
% 5.27/5.52 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.27/5.52 ( ( ( modulo_modulo_int @ A @ C )
% 5.27/5.52 = ( modulo_modulo_int @ A4 @ C ) )
% 5.27/5.52 => ( ( ( modulo_modulo_int @ B @ C )
% 5.27/5.52 = ( modulo_modulo_int @ B4 @ C ) )
% 5.27/5.52 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.52 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_cong
% 5.27/5.52 thf(fact_4074_mod__diff__cong,axiom,
% 5.27/5.52 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.27/5.52 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.27/5.52 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.27/5.52 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_cong
% 5.27/5.52 thf(fact_4075_mod__diff__eq,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.27/5.52 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_eq
% 5.27/5.52 thf(fact_4076_mod__diff__eq,axiom,
% 5.27/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.27/5.52 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_diff_eq
% 5.27/5.52 thf(fact_4077_diff__less__mono2,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,L: nat] :
% 5.27/5.52 ( ( ord_less_nat @ M @ N2 )
% 5.27/5.52 => ( ( ord_less_nat @ M @ L )
% 5.27/5.52 => ( ord_less_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_mono2
% 5.27/5.52 thf(fact_4078_less__imp__diff__less,axiom,
% 5.27/5.52 ! [J: nat,K: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_nat @ J @ K )
% 5.27/5.52 => ( ord_less_nat @ ( minus_minus_nat @ J @ N2 ) @ K ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_imp_diff_less
% 5.27/5.52 thf(fact_4079_signed__take__bit__mult,axiom,
% 5.27/5.52 ! [N2: nat,K: int,L: int] :
% 5.27/5.52 ( ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.27/5.52 = ( bit_ri631733984087533419it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_mult
% 5.27/5.52 thf(fact_4080_eq__diff__iff,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.52 => ( ( ( minus_minus_nat @ M @ K )
% 5.27/5.52 = ( minus_minus_nat @ N2 @ K ) )
% 5.27/5.52 = ( M = N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_diff_iff
% 5.27/5.52 thf(fact_4081_le__diff__iff,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.27/5.52 = ( ord_less_eq_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_iff
% 5.27/5.52 thf(fact_4082_Nat_Odiff__diff__eq,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.52 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.27/5.52 = ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.diff_diff_eq
% 5.27/5.52 thf(fact_4083_diff__le__mono,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,L: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N2 @ L ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_mono
% 5.27/5.52 thf(fact_4084_diff__le__self,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_self
% 5.27/5.52 thf(fact_4085_le__diff__iff_H,axiom,
% 5.27/5.52 ! [A: nat,C: nat,B: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ C )
% 5.27/5.52 => ( ( ord_less_eq_nat @ B @ C )
% 5.27/5.52 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.27/5.52 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_iff'
% 5.27/5.52 thf(fact_4086_diff__le__mono2,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,L: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N2 ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_mono2
% 5.27/5.52 thf(fact_4087_signed__take__bit__add,axiom,
% 5.27/5.52 ! [N2: nat,K: int,L: int] :
% 5.27/5.52 ( ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( bit_ri631733984087533419it_int @ N2 @ L ) ) )
% 5.27/5.52 = ( bit_ri631733984087533419it_int @ N2 @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_add
% 5.27/5.52 thf(fact_4088_Nat_Odiff__cancel,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N2 ) )
% 5.27/5.52 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.diff_cancel
% 5.27/5.52 thf(fact_4089_diff__cancel2,axiom,
% 5.27/5.52 ! [M: nat,K: nat,N2: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.52 = ( minus_minus_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_cancel2
% 5.27/5.52 thf(fact_4090_diff__add__inverse,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ N2 @ M ) @ N2 )
% 5.27/5.52 = M ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_inverse
% 5.27/5.52 thf(fact_4091_diff__add__inverse2,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ N2 )
% 5.27/5.52 = M ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_inverse2
% 5.27/5.52 thf(fact_4092_diff__mult__distrib,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,K: nat] :
% 5.27/5.52 ( ( times_times_nat @ ( minus_minus_nat @ M @ N2 ) @ K )
% 5.27/5.52 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_mult_distrib
% 5.27/5.52 thf(fact_4093_diff__mult__distrib2,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_mult_distrib2
% 5.27/5.52 thf(fact_4094_dvd__diff__nat,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ K @ M )
% 5.27/5.52 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.27/5.52 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diff_nat
% 5.27/5.52 thf(fact_4095_concat__bit__assoc,axiom,
% 5.27/5.52 ! [N2: nat,K: int,M: nat,L: int,R3: int] :
% 5.27/5.52 ( ( bit_concat_bit @ N2 @ K @ ( bit_concat_bit @ M @ L @ R3 ) )
% 5.27/5.52 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N2 ) @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 ) ) ).
% 5.27/5.52
% 5.27/5.52 % concat_bit_assoc
% 5.27/5.52 thf(fact_4096_subset__decode__imp__le,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N2 ) )
% 5.27/5.52 => ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % subset_decode_imp_le
% 5.27/5.52 thf(fact_4097_le__iff__diff__le__0,axiom,
% 5.27/5.52 ( ord_less_eq_real
% 5.27/5.52 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_iff_diff_le_0
% 5.27/5.52 thf(fact_4098_le__iff__diff__le__0,axiom,
% 5.27/5.52 ( ord_less_eq_rat
% 5.27/5.52 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_iff_diff_le_0
% 5.27/5.52 thf(fact_4099_le__iff__diff__le__0,axiom,
% 5.27/5.52 ( ord_less_eq_int
% 5.27/5.52 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_iff_diff_le_0
% 5.27/5.52 thf(fact_4100_less__iff__diff__less__0,axiom,
% 5.27/5.52 ( ord_less_real
% 5.27/5.52 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_iff_diff_less_0
% 5.27/5.52 thf(fact_4101_less__iff__diff__less__0,axiom,
% 5.27/5.52 ( ord_less_rat
% 5.27/5.52 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_iff_diff_less_0
% 5.27/5.52 thf(fact_4102_less__iff__diff__less__0,axiom,
% 5.27/5.52 ( ord_less_int
% 5.27/5.52 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_iff_diff_less_0
% 5.27/5.52 thf(fact_4103_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( ( minus_minus_nat @ B @ A )
% 5.27/5.52 = C )
% 5.27/5.52 = ( B
% 5.27/5.52 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.27/5.52 thf(fact_4104_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.27/5.52 = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.27/5.52 thf(fact_4105_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.27/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.27/5.52 thf(fact_4106_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.27/5.52 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.27/5.52 thf(fact_4107_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.27/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.27/5.52 thf(fact_4108_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.27/5.52 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.27/5.52 thf(fact_4109_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.27/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.27/5.52 thf(fact_4110_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.27/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.27/5.52 thf(fact_4111_le__add__diff,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_add_diff
% 5.27/5.52 thf(fact_4112_add__le__add__imp__diff__le,axiom,
% 5.27/5.52 ! [I2: real,K: real,N2: real,J: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.27/5.52 => ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_real @ N2 @ ( plus_plus_real @ J @ K ) )
% 5.27/5.52 => ( ord_less_eq_real @ ( minus_minus_real @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_add_imp_diff_le
% 5.27/5.52 thf(fact_4113_add__le__add__imp__diff__le,axiom,
% 5.27/5.52 ! [I2: rat,K: rat,N2: rat,J: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.27/5.52 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_rat @ N2 @ ( plus_plus_rat @ J @ K ) )
% 5.27/5.52 => ( ord_less_eq_rat @ ( minus_minus_rat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_add_imp_diff_le
% 5.27/5.52 thf(fact_4114_add__le__add__imp__diff__le,axiom,
% 5.27/5.52 ! [I2: nat,K: nat,N2: nat,J: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.27/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ ( plus_plus_nat @ J @ K ) )
% 5.27/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_add_imp_diff_le
% 5.27/5.52 thf(fact_4115_add__le__add__imp__diff__le,axiom,
% 5.27/5.52 ! [I2: int,K: int,N2: int,J: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.27/5.52 => ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_int @ N2 @ ( plus_plus_int @ J @ K ) )
% 5.27/5.52 => ( ord_less_eq_int @ ( minus_minus_int @ N2 @ K ) @ J ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_add_imp_diff_le
% 5.27/5.52 thf(fact_4116_diff__add,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.27/5.52 = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add
% 5.27/5.52 thf(fact_4117_add__le__imp__le__diff,axiom,
% 5.27/5.52 ! [I2: real,K: real,N2: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( plus_plus_real @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ord_less_eq_real @ I2 @ ( minus_minus_real @ N2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_imp_le_diff
% 5.27/5.52 thf(fact_4118_add__le__imp__le__diff,axiom,
% 5.27/5.52 ! [I2: rat,K: rat,N2: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ord_less_eq_rat @ I2 @ ( minus_minus_rat @ N2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_imp_le_diff
% 5.27/5.52 thf(fact_4119_add__le__imp__le__diff,axiom,
% 5.27/5.52 ! [I2: nat,K: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ N2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_imp_le_diff
% 5.27/5.52 thf(fact_4120_add__le__imp__le__diff,axiom,
% 5.27/5.52 ! [I2: int,K: int,N2: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ K ) @ N2 )
% 5.27/5.52 => ( ord_less_eq_int @ I2 @ ( minus_minus_int @ N2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_le_imp_le_diff
% 5.27/5.52 thf(fact_4121_le__diff__eq,axiom,
% 5.27/5.52 ! [A: real,C: real,B: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.27/5.52 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_eq
% 5.27/5.52 thf(fact_4122_le__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,C: rat,B: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.27/5.52 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_eq
% 5.27/5.52 thf(fact_4123_le__diff__eq,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.27/5.52 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_eq
% 5.27/5.52 thf(fact_4124_diff__le__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_eq
% 5.27/5.52 thf(fact_4125_diff__le__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_eq
% 5.27/5.52 thf(fact_4126_diff__le__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_eq
% 5.27/5.52 thf(fact_4127_diff__less__eq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real] :
% 5.27/5.52 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_eq
% 5.27/5.52 thf(fact_4128_diff__less__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat] :
% 5.27/5.52 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_eq
% 5.27/5.52 thf(fact_4129_diff__less__eq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int] :
% 5.27/5.52 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.27/5.52 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_eq
% 5.27/5.52 thf(fact_4130_less__diff__eq,axiom,
% 5.27/5.52 ! [A: real,C: real,B: real] :
% 5.27/5.52 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.27/5.52 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_eq
% 5.27/5.52 thf(fact_4131_less__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,C: rat,B: rat] :
% 5.27/5.52 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.27/5.52 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_eq
% 5.27/5.52 thf(fact_4132_less__diff__eq,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.27/5.52 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_eq
% 5.27/5.52 thf(fact_4133_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ~ ( ord_less_real @ A @ B )
% 5.27/5.52 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.27/5.52 = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % linordered_semidom_class.add_diff_inverse
% 5.27/5.52 thf(fact_4134_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ~ ( ord_less_rat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.52 = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % linordered_semidom_class.add_diff_inverse
% 5.27/5.52 thf(fact_4135_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ~ ( ord_less_nat @ A @ B )
% 5.27/5.52 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.52 = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % linordered_semidom_class.add_diff_inverse
% 5.27/5.52 thf(fact_4136_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ~ ( ord_less_int @ A @ B )
% 5.27/5.52 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.27/5.52 = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % linordered_semidom_class.add_diff_inverse
% 5.27/5.52 thf(fact_4137_square__diff__square__factored,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ ( times_times_rat @ Y @ Y ) )
% 5.27/5.52 = ( times_times_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_rat @ X4 @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_square_factored
% 5.27/5.52 thf(fact_4138_square__diff__square__factored,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex] :
% 5.27/5.52 ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ ( times_times_complex @ Y @ Y ) )
% 5.27/5.52 = ( times_times_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_complex @ X4 @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_square_factored
% 5.27/5.52 thf(fact_4139_square__diff__square__factored,axiom,
% 5.27/5.52 ! [X4: real,Y: real] :
% 5.27/5.52 ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) )
% 5.27/5.52 = ( times_times_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ X4 @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_square_factored
% 5.27/5.52 thf(fact_4140_square__diff__square__factored,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ ( times_times_int @ Y @ Y ) )
% 5.27/5.52 = ( times_times_int @ ( plus_plus_int @ X4 @ Y ) @ ( minus_minus_int @ X4 @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_square_factored
% 5.27/5.52 thf(fact_4141_eq__add__iff2,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( C
% 5.27/5.52 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff2
% 5.27/5.52 thf(fact_4142_eq__add__iff2,axiom,
% 5.27/5.52 ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 5.27/5.52 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( C
% 5.27/5.52 = ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff2
% 5.27/5.52 thf(fact_4143_eq__add__iff2,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( C
% 5.27/5.52 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff2
% 5.27/5.52 thf(fact_4144_eq__add__iff2,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( C
% 5.27/5.52 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff2
% 5.27/5.52 thf(fact_4145_eq__add__iff1,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C )
% 5.27/5.52 = D ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff1
% 5.27/5.52 thf(fact_4146_eq__add__iff1,axiom,
% 5.27/5.52 ! [A: complex,E2: complex,C: complex,B: complex,D: complex] :
% 5.27/5.52 ( ( ( plus_plus_complex @ ( times_times_complex @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_complex @ ( times_times_complex @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ( plus_plus_complex @ ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ E2 ) @ C )
% 5.27/5.52 = D ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff1
% 5.27/5.52 thf(fact_4147_eq__add__iff1,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C )
% 5.27/5.52 = D ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff1
% 5.27/5.52 thf(fact_4148_eq__add__iff1,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C )
% 5.27/5.52 = ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C )
% 5.27/5.52 = D ) ) ).
% 5.27/5.52
% 5.27/5.52 % eq_add_iff1
% 5.27/5.52 thf(fact_4149_mult__diff__mult,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat,A: rat,B: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.27/5.52 = ( plus_plus_rat @ ( times_times_rat @ X4 @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X4 @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_diff_mult
% 5.27/5.52 thf(fact_4150_mult__diff__mult,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex,A: complex,B: complex] :
% 5.27/5.52 ( ( minus_minus_complex @ ( times_times_complex @ X4 @ Y ) @ ( times_times_complex @ A @ B ) )
% 5.27/5.52 = ( plus_plus_complex @ ( times_times_complex @ X4 @ ( minus_minus_complex @ Y @ B ) ) @ ( times_times_complex @ ( minus_minus_complex @ X4 @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_diff_mult
% 5.27/5.52 thf(fact_4151_mult__diff__mult,axiom,
% 5.27/5.52 ! [X4: real,Y: real,A: real,B: real] :
% 5.27/5.52 ( ( minus_minus_real @ ( times_times_real @ X4 @ Y ) @ ( times_times_real @ A @ B ) )
% 5.27/5.52 = ( plus_plus_real @ ( times_times_real @ X4 @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X4 @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_diff_mult
% 5.27/5.52 thf(fact_4152_mult__diff__mult,axiom,
% 5.27/5.52 ! [X4: int,Y: int,A: int,B: int] :
% 5.27/5.52 ( ( minus_minus_int @ ( times_times_int @ X4 @ Y ) @ ( times_times_int @ A @ B ) )
% 5.27/5.52 = ( plus_plus_int @ ( times_times_int @ X4 @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X4 @ A ) @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_diff_mult
% 5.27/5.52 thf(fact_4153_mod__eq__dvd__iff,axiom,
% 5.27/5.52 ! [A: int,C: int,B: int] :
% 5.27/5.52 ( ( ( modulo_modulo_int @ A @ C )
% 5.27/5.52 = ( modulo_modulo_int @ B @ C ) )
% 5.27/5.52 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_eq_dvd_iff
% 5.27/5.52 thf(fact_4154_mod__eq__dvd__iff,axiom,
% 5.27/5.52 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.27/5.52 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.27/5.52 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_eq_dvd_iff
% 5.27/5.52 thf(fact_4155_dvd__minus__mod,axiom,
% 5.27/5.52 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_mod
% 5.27/5.52 thf(fact_4156_dvd__minus__mod,axiom,
% 5.27/5.52 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_mod
% 5.27/5.52 thf(fact_4157_dvd__minus__mod,axiom,
% 5.27/5.52 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_mod
% 5.27/5.52 thf(fact_4158_diff__less__Suc,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ ( suc @ M ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_Suc
% 5.27/5.52 thf(fact_4159_Suc__diff__Suc,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ N2 @ M )
% 5.27/5.52 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.52 = ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Suc_diff_Suc
% 5.27/5.52 thf(fact_4160_diff__less,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.52 => ( ord_less_nat @ ( minus_minus_nat @ M @ N2 ) @ M ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less
% 5.27/5.52 thf(fact_4161_Suc__diff__le,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.27/5.52 = ( suc @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Suc_diff_le
% 5.27/5.52 thf(fact_4162_diff__less__mono,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat] :
% 5.27/5.52 ( ( ord_less_nat @ A @ B )
% 5.27/5.52 => ( ( ord_less_eq_nat @ C @ A )
% 5.27/5.52 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_less_mono
% 5.27/5.52 thf(fact_4163_less__diff__iff,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.52 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N2 @ K ) )
% 5.27/5.52 = ( ord_less_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_iff
% 5.27/5.52 thf(fact_4164_diff__add__0,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ N2 @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.52 = zero_zero_nat ) ).
% 5.27/5.52
% 5.27/5.52 % diff_add_0
% 5.27/5.52 thf(fact_4165_less__diff__conv,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.52 ( ( ord_less_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.27/5.52 = ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_conv
% 5.27/5.52 thf(fact_4166_add__diff__inverse__nat,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ~ ( ord_less_nat @ M @ N2 )
% 5.27/5.52 => ( ( plus_plus_nat @ N2 @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = M ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_diff_inverse_nat
% 5.27/5.52 thf(fact_4167_Nat_Ole__imp__diff__is__add,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.52 => ( ( ( minus_minus_nat @ J @ I2 )
% 5.27/5.52 = K )
% 5.27/5.52 = ( J
% 5.27/5.52 = ( plus_plus_nat @ K @ I2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.le_imp_diff_is_add
% 5.27/5.52 thf(fact_4168_Nat_Odiff__add__assoc2,axiom,
% 5.27/5.52 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I2 ) @ K )
% 5.27/5.52 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.diff_add_assoc2
% 5.27/5.52 thf(fact_4169_Nat_Odiff__add__assoc,axiom,
% 5.27/5.52 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ I2 @ J ) @ K )
% 5.27/5.52 = ( plus_plus_nat @ I2 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.diff_add_assoc
% 5.27/5.52 thf(fact_4170_Nat_Ole__diff__conv2,axiom,
% 5.27/5.52 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.52 => ( ( ord_less_eq_nat @ I2 @ ( minus_minus_nat @ J @ K ) )
% 5.27/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ K ) @ J ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Nat.le_diff_conv2
% 5.27/5.52 thf(fact_4171_le__diff__conv,axiom,
% 5.27/5.52 ! [J: nat,K: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.27/5.52 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_diff_conv
% 5.27/5.52 thf(fact_4172_diff__Suc__eq__diff__pred,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.27/5.52 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_Suc_eq_diff_pred
% 5.27/5.52 thf(fact_4173_int__le__induct,axiom,
% 5.27/5.52 ! [I2: int,K: int,P: int > $o] :
% 5.27/5.52 ( ( ord_less_eq_int @ I2 @ K )
% 5.27/5.52 => ( ( P @ K )
% 5.27/5.52 => ( ! [I4: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ I4 @ K )
% 5.27/5.52 => ( ( P @ I4 )
% 5.27/5.52 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.27/5.52 => ( P @ I2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % int_le_induct
% 5.27/5.52 thf(fact_4174_dvd__minus__self,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.52 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.52 | ( dvd_dvd_nat @ M @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_self
% 5.27/5.52 thf(fact_4175_int__less__induct,axiom,
% 5.27/5.52 ! [I2: int,K: int,P: int > $o] :
% 5.27/5.52 ( ( ord_less_int @ I2 @ K )
% 5.27/5.52 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.27/5.52 => ( ! [I4: int] :
% 5.27/5.52 ( ( ord_less_int @ I4 @ K )
% 5.27/5.52 => ( ( P @ I4 )
% 5.27/5.52 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.27/5.52 => ( P @ I2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % int_less_induct
% 5.27/5.52 thf(fact_4176_dvd__diffD,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 => ( ( dvd_dvd_nat @ K @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diffD
% 5.27/5.52 thf(fact_4177_dvd__diffD1,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 => ( ( dvd_dvd_nat @ K @ M )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( dvd_dvd_nat @ K @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_diffD1
% 5.27/5.52 thf(fact_4178_less__eq__dvd__minus,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ( dvd_dvd_nat @ M @ N2 )
% 5.27/5.52 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_eq_dvd_minus
% 5.27/5.52 thf(fact_4179_mod__geq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ~ ( ord_less_nat @ M @ N2 )
% 5.27/5.52 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.27/5.52 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_geq
% 5.27/5.52 thf(fact_4180_mod__if,axiom,
% 5.27/5.52 ( modulo_modulo_nat
% 5.27/5.52 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( ord_less_nat @ M6 @ N ) @ M6 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_if
% 5.27/5.52 thf(fact_4181_le__mod__geq,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.27/5.52 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_mod_geq
% 5.27/5.52 thf(fact_4182_signed__take__bit__int__less__eq,axiom,
% 5.27/5.52 ! [N2: nat,K: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.27/5.52 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_int_less_eq
% 5.27/5.52 thf(fact_4183_ordered__ring__class_Ole__add__iff2,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff2
% 5.27/5.52 thf(fact_4184_ordered__ring__class_Ole__add__iff2,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff2
% 5.27/5.52 thf(fact_4185_ordered__ring__class_Ole__add__iff2,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff2
% 5.27/5.52 thf(fact_4186_ordered__ring__class_Ole__add__iff1,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff1
% 5.27/5.52 thf(fact_4187_ordered__ring__class_Ole__add__iff1,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff1
% 5.27/5.52 thf(fact_4188_ordered__ring__class_Ole__add__iff1,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % ordered_ring_class.le_add_iff1
% 5.27/5.52 thf(fact_4189_less__add__iff1,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff1
% 5.27/5.52 thf(fact_4190_less__add__iff1,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff1
% 5.27/5.52 thf(fact_4191_less__add__iff1,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff1
% 5.27/5.52 thf(fact_4192_less__add__iff2,axiom,
% 5.27/5.52 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.52 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff2
% 5.27/5.52 thf(fact_4193_less__add__iff2,axiom,
% 5.27/5.52 ! [A: rat,E2: rat,C: rat,B: rat,D: rat] :
% 5.27/5.52 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E2 ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff2
% 5.27/5.52 thf(fact_4194_less__add__iff2,axiom,
% 5.27/5.52 ! [A: int,E2: int,C: int,B: int,D: int] :
% 5.27/5.52 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E2 ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E2 ) @ D ) )
% 5.27/5.52 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_add_iff2
% 5.27/5.52 thf(fact_4195_divide__diff__eq__iff,axiom,
% 5.27/5.52 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.52 ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Z ) @ Y )
% 5.27/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divide_diff_eq_iff
% 5.27/5.52 thf(fact_4196_divide__diff__eq__iff,axiom,
% 5.27/5.52 ! [Z: real,X4: real,Y: real] :
% 5.27/5.52 ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Z ) @ Y )
% 5.27/5.52 = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divide_diff_eq_iff
% 5.27/5.52 thf(fact_4197_divide__diff__eq__iff,axiom,
% 5.27/5.52 ! [Z: complex,X4: complex,Y: complex] :
% 5.27/5.52 ( ( Z != zero_zero_complex )
% 5.27/5.52 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Z ) @ Y )
% 5.27/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X4 @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divide_diff_eq_iff
% 5.27/5.52 thf(fact_4198_diff__divide__eq__iff,axiom,
% 5.27/5.52 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.52 ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( minus_minus_rat @ X4 @ ( divide_divide_rat @ Y @ Z ) )
% 5.27/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_eq_iff
% 5.27/5.52 thf(fact_4199_diff__divide__eq__iff,axiom,
% 5.27/5.52 ! [Z: real,X4: real,Y: real] :
% 5.27/5.52 ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( minus_minus_real @ X4 @ ( divide_divide_real @ Y @ Z ) )
% 5.27/5.52 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_eq_iff
% 5.27/5.52 thf(fact_4200_diff__divide__eq__iff,axiom,
% 5.27/5.52 ! [Z: complex,X4: complex,Y: complex] :
% 5.27/5.52 ( ( Z != zero_zero_complex )
% 5.27/5.52 => ( ( minus_minus_complex @ X4 @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.27/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ Y ) @ Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_divide_eq_iff
% 5.27/5.52 thf(fact_4201_diff__frac__eq,axiom,
% 5.27/5.52 ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 5.27/5.52 ( ( Y != zero_zero_rat )
% 5.27/5.52 => ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( minus_minus_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.27/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_frac_eq
% 5.27/5.52 thf(fact_4202_diff__frac__eq,axiom,
% 5.27/5.52 ! [Y: real,Z: real,X4: real,W: real] :
% 5.27/5.52 ( ( Y != zero_zero_real )
% 5.27/5.52 => ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( minus_minus_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.27/5.52 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_frac_eq
% 5.27/5.52 thf(fact_4203_diff__frac__eq,axiom,
% 5.27/5.52 ! [Y: complex,Z: complex,X4: complex,W: complex] :
% 5.27/5.52 ( ( Y != zero_zero_complex )
% 5.27/5.52 => ( ( Z != zero_zero_complex )
% 5.27/5.52 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X4 @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.27/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X4 @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_frac_eq
% 5.27/5.52 thf(fact_4204_add__divide__eq__if__simps_I4_J,axiom,
% 5.27/5.52 ! [Z: rat,A: rat,B: rat] :
% 5.27/5.52 ( ( ( Z = zero_zero_rat )
% 5.27/5.52 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.27/5.52 = A ) )
% 5.27/5.52 & ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.27/5.52 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_divide_eq_if_simps(4)
% 5.27/5.52 thf(fact_4205_add__divide__eq__if__simps_I4_J,axiom,
% 5.27/5.52 ! [Z: real,A: real,B: real] :
% 5.27/5.52 ( ( ( Z = zero_zero_real )
% 5.27/5.52 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.27/5.52 = A ) )
% 5.27/5.52 & ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.27/5.52 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_divide_eq_if_simps(4)
% 5.27/5.52 thf(fact_4206_add__divide__eq__if__simps_I4_J,axiom,
% 5.27/5.52 ! [Z: complex,A: complex,B: complex] :
% 5.27/5.52 ( ( ( Z = zero_zero_complex )
% 5.27/5.52 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.27/5.52 = A ) )
% 5.27/5.52 & ( ( Z != zero_zero_complex )
% 5.27/5.52 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.27/5.52 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_divide_eq_if_simps(4)
% 5.27/5.52 thf(fact_4207_square__diff__one__factored,axiom,
% 5.27/5.52 ! [X4: rat] :
% 5.27/5.52 ( ( minus_minus_rat @ ( times_times_rat @ X4 @ X4 ) @ one_one_rat )
% 5.27/5.52 = ( times_times_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_one_factored
% 5.27/5.52 thf(fact_4208_square__diff__one__factored,axiom,
% 5.27/5.52 ! [X4: complex] :
% 5.27/5.52 ( ( minus_minus_complex @ ( times_times_complex @ X4 @ X4 ) @ one_one_complex )
% 5.27/5.52 = ( times_times_complex @ ( plus_plus_complex @ X4 @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_one_factored
% 5.27/5.52 thf(fact_4209_square__diff__one__factored,axiom,
% 5.27/5.52 ! [X4: real] :
% 5.27/5.52 ( ( minus_minus_real @ ( times_times_real @ X4 @ X4 ) @ one_one_real )
% 5.27/5.52 = ( times_times_real @ ( plus_plus_real @ X4 @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_one_factored
% 5.27/5.52 thf(fact_4210_square__diff__one__factored,axiom,
% 5.27/5.52 ! [X4: int] :
% 5.27/5.52 ( ( minus_minus_int @ ( times_times_int @ X4 @ X4 ) @ one_one_int )
% 5.27/5.52 = ( times_times_int @ ( plus_plus_int @ X4 @ one_one_int ) @ ( minus_minus_int @ X4 @ one_one_int ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % square_diff_one_factored
% 5.27/5.52 thf(fact_4211_inf__period_I4_J,axiom,
% 5.27/5.52 ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.27/5.52 => ! [X2: code_integer,K4: code_integer] :
% 5.27/5.52 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) ) )
% 5.27/5.52 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(4)
% 5.27/5.52 thf(fact_4212_inf__period_I4_J,axiom,
% 5.27/5.52 ! [D: rat,D4: rat,T2: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ D @ D4 )
% 5.27/5.52 => ! [X2: rat,K4: rat] :
% 5.27/5.52 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) ) )
% 5.27/5.52 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(4)
% 5.27/5.52 thf(fact_4213_inf__period_I4_J,axiom,
% 5.27/5.52 ! [D: complex,D4: complex,T2: complex] :
% 5.27/5.52 ( ( dvd_dvd_complex @ D @ D4 )
% 5.27/5.52 => ! [X2: complex,K4: complex] :
% 5.27/5.52 ( ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) ) )
% 5.27/5.52 = ( ~ ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(4)
% 5.27/5.52 thf(fact_4214_inf__period_I4_J,axiom,
% 5.27/5.52 ! [D: real,D4: real,T2: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ D @ D4 )
% 5.27/5.52 => ! [X2: real,K4: real] :
% 5.27/5.52 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) ) )
% 5.27/5.52 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(4)
% 5.27/5.52 thf(fact_4215_inf__period_I4_J,axiom,
% 5.27/5.52 ! [D: int,D4: int,T2: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.27/5.52 => ! [X2: int,K4: int] :
% 5.27/5.52 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) ) )
% 5.27/5.52 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(4)
% 5.27/5.52 thf(fact_4216_inf__period_I3_J,axiom,
% 5.27/5.52 ! [D: code_integer,D4: code_integer,T2: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.27/5.52 => ! [X2: code_integer,K4: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X2 @ T2 ) )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X2 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(3)
% 5.27/5.52 thf(fact_4217_inf__period_I3_J,axiom,
% 5.27/5.52 ! [D: rat,D4: rat,T2: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ D @ D4 )
% 5.27/5.52 => ! [X2: rat,K4: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X2 @ T2 ) )
% 5.27/5.52 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X2 @ ( times_times_rat @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(3)
% 5.27/5.52 thf(fact_4218_inf__period_I3_J,axiom,
% 5.27/5.52 ! [D: complex,D4: complex,T2: complex] :
% 5.27/5.52 ( ( dvd_dvd_complex @ D @ D4 )
% 5.27/5.52 => ! [X2: complex,K4: complex] :
% 5.27/5.52 ( ( dvd_dvd_complex @ D @ ( plus_plus_complex @ X2 @ T2 ) )
% 5.27/5.52 = ( dvd_dvd_complex @ D @ ( plus_plus_complex @ ( minus_minus_complex @ X2 @ ( times_times_complex @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(3)
% 5.27/5.52 thf(fact_4219_inf__period_I3_J,axiom,
% 5.27/5.52 ! [D: real,D4: real,T2: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ D @ D4 )
% 5.27/5.52 => ! [X2: real,K4: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X2 @ T2 ) )
% 5.27/5.52 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X2 @ ( times_times_real @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(3)
% 5.27/5.52 thf(fact_4220_inf__period_I3_J,axiom,
% 5.27/5.52 ! [D: int,D4: int,T2: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ D @ D4 )
% 5.27/5.52 => ! [X2: int,K4: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X2 @ T2 ) )
% 5.27/5.52 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X2 @ ( times_times_int @ K4 @ D4 ) ) @ T2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % inf_period(3)
% 5.27/5.52 thf(fact_4221_minus__mult__div__eq__mod,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.27/5.52 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_div_eq_mod
% 5.27/5.52 thf(fact_4222_minus__mult__div__eq__mod,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.27/5.52 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_div_eq_mod
% 5.27/5.52 thf(fact_4223_minus__mult__div__eq__mod,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.27/5.52 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_div_eq_mod
% 5.27/5.52 thf(fact_4224_minus__mod__eq__mult__div,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.27/5.52 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_mult_div
% 5.27/5.52 thf(fact_4225_minus__mod__eq__mult__div,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.27/5.52 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_mult_div
% 5.27/5.52 thf(fact_4226_minus__mod__eq__mult__div,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.27/5.52 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_mult_div
% 5.27/5.52 thf(fact_4227_minus__mod__eq__div__mult,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.27/5.52 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_div_mult
% 5.27/5.52 thf(fact_4228_minus__mod__eq__div__mult,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.27/5.52 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_div_mult
% 5.27/5.52 thf(fact_4229_minus__mod__eq__div__mult,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.27/5.52 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mod_eq_div_mult
% 5.27/5.52 thf(fact_4230_minus__div__mult__eq__mod,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.27/5.52 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_div_mult_eq_mod
% 5.27/5.52 thf(fact_4231_minus__div__mult__eq__mod,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.27/5.52 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_div_mult_eq_mod
% 5.27/5.52 thf(fact_4232_minus__div__mult__eq__mod,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.27/5.52 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_div_mult_eq_mod
% 5.27/5.52 thf(fact_4233_diff__Suc__less,axiom,
% 5.27/5.52 ! [N2: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ord_less_nat @ ( minus_minus_nat @ N2 @ ( suc @ I2 ) ) @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_Suc_less
% 5.27/5.52 thf(fact_4234_nat__diff__split,axiom,
% 5.27/5.52 ! [P: nat > $o,A: nat,B: nat] :
% 5.27/5.52 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.52 = ( ( ( ord_less_nat @ A @ B )
% 5.27/5.52 => ( P @ zero_zero_nat ) )
% 5.27/5.52 & ! [D5: nat] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( plus_plus_nat @ B @ D5 ) )
% 5.27/5.52 => ( P @ D5 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_diff_split
% 5.27/5.52 thf(fact_4235_nat__diff__split__asm,axiom,
% 5.27/5.52 ! [P: nat > $o,A: nat,B: nat] :
% 5.27/5.52 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.52 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.27/5.52 & ~ ( P @ zero_zero_nat ) )
% 5.27/5.52 | ? [D5: nat] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( plus_plus_nat @ B @ D5 ) )
% 5.27/5.52 & ~ ( P @ D5 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_diff_split_asm
% 5.27/5.52 thf(fact_4236_less__diff__conv2,axiom,
% 5.27/5.52 ! [K: nat,J: nat,I2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ K @ J )
% 5.27/5.52 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I2 )
% 5.27/5.52 = ( ord_less_nat @ J @ ( plus_plus_nat @ I2 @ K ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % less_diff_conv2
% 5.27/5.52 thf(fact_4237_nat__diff__add__eq2,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_diff_add_eq2
% 5.27/5.52 thf(fact_4238_nat__diff__add__eq1,axiom,
% 5.27/5.52 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ J @ I2 )
% 5.27/5.52 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_diff_add_eq1
% 5.27/5.52 thf(fact_4239_nat__le__add__iff2,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_le_add_iff2
% 5.27/5.52 thf(fact_4240_nat__le__add__iff1,axiom,
% 5.27/5.52 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ J @ I2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_le_add_iff1
% 5.27/5.52 thf(fact_4241_nat__eq__add__iff2,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.27/5.52 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( M
% 5.27/5.52 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_eq_add_iff2
% 5.27/5.52 thf(fact_4242_nat__eq__add__iff1,axiom,
% 5.27/5.52 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ J @ I2 )
% 5.27/5.52 => ( ( ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M )
% 5.27/5.52 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M )
% 5.27/5.52 = N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_eq_add_iff1
% 5.27/5.52 thf(fact_4243_plusinfinity,axiom,
% 5.27/5.52 ! [D: int,P6: int > $o,P: int > $o] :
% 5.27/5.52 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.52 => ( ! [X5: int,K2: int] :
% 5.27/5.52 ( ( P6 @ X5 )
% 5.27/5.52 = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.27/5.52 => ( ? [Z3: int] :
% 5.27/5.52 ! [X5: int] :
% 5.27/5.52 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.52 => ( ( P @ X5 )
% 5.27/5.52 = ( P6 @ X5 ) ) )
% 5.27/5.52 => ( ? [X_1: int] : ( P6 @ X_1 )
% 5.27/5.52 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % plusinfinity
% 5.27/5.52 thf(fact_4244_minusinfinity,axiom,
% 5.27/5.52 ! [D: int,P1: int > $o,P: int > $o] :
% 5.27/5.52 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.52 => ( ! [X5: int,K2: int] :
% 5.27/5.52 ( ( P1 @ X5 )
% 5.27/5.52 = ( P1 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.27/5.52 => ( ? [Z3: int] :
% 5.27/5.52 ! [X5: int] :
% 5.27/5.52 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.52 => ( ( P @ X5 )
% 5.27/5.52 = ( P1 @ X5 ) ) )
% 5.27/5.52 => ( ? [X_1: int] : ( P1 @ X_1 )
% 5.27/5.52 => ? [X_12: int] : ( P @ X_12 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minusinfinity
% 5.27/5.52 thf(fact_4245_int__induct,axiom,
% 5.27/5.52 ! [P: int > $o,K: int,I2: int] :
% 5.27/5.52 ( ( P @ K )
% 5.27/5.52 => ( ! [I4: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ K @ I4 )
% 5.27/5.52 => ( ( P @ I4 )
% 5.27/5.52 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.27/5.52 => ( ! [I4: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ I4 @ K )
% 5.27/5.52 => ( ( P @ I4 )
% 5.27/5.52 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.27/5.52 => ( P @ I2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % int_induct
% 5.27/5.52 thf(fact_4246_mod__eq__dvd__iff__nat,axiom,
% 5.27/5.52 ! [N2: nat,M: nat,Q3: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( ( modulo_modulo_nat @ M @ Q3 )
% 5.27/5.52 = ( modulo_modulo_nat @ N2 @ Q3 ) )
% 5.27/5.52 = ( dvd_dvd_nat @ Q3 @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_eq_dvd_iff_nat
% 5.27/5.52 thf(fact_4247_modulo__nat__def,axiom,
% 5.27/5.52 ( modulo_modulo_nat
% 5.27/5.52 = ( ^ [M6: nat,N: nat] : ( minus_minus_nat @ M6 @ ( times_times_nat @ ( divide_divide_nat @ M6 @ N ) @ N ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % modulo_nat_def
% 5.27/5.52 thf(fact_4248_frac__le__eq,axiom,
% 5.27/5.52 ! [Y: real,Z: real,X4: real,W: real] :
% 5.27/5.52 ( ( Y != zero_zero_real )
% 5.27/5.52 => ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( ord_less_eq_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.27/5.52 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % frac_le_eq
% 5.27/5.52 thf(fact_4249_frac__le__eq,axiom,
% 5.27/5.52 ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 5.27/5.52 ( ( Y != zero_zero_rat )
% 5.27/5.52 => ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.27/5.52 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % frac_le_eq
% 5.27/5.52 thf(fact_4250_frac__less__eq,axiom,
% 5.27/5.52 ! [Y: rat,Z: rat,X4: rat,W: rat] :
% 5.27/5.52 ( ( Y != zero_zero_rat )
% 5.27/5.52 => ( ( Z != zero_zero_rat )
% 5.27/5.52 => ( ( ord_less_rat @ ( divide_divide_rat @ X4 @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.27/5.52 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X4 @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % frac_less_eq
% 5.27/5.52 thf(fact_4251_frac__less__eq,axiom,
% 5.27/5.52 ! [Y: real,Z: real,X4: real,W: real] :
% 5.27/5.52 ( ( Y != zero_zero_real )
% 5.27/5.52 => ( ( Z != zero_zero_real )
% 5.27/5.52 => ( ( ord_less_real @ ( divide_divide_real @ X4 @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.27/5.52 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X4 @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % frac_less_eq
% 5.27/5.52 thf(fact_4252_power2__commute,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex] :
% 5.27/5.52 ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( power_power_complex @ ( minus_minus_complex @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_commute
% 5.27/5.52 thf(fact_4253_power2__commute,axiom,
% 5.27/5.52 ! [X4: real,Y: real] :
% 5.27/5.52 ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( power_power_real @ ( minus_minus_real @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_commute
% 5.27/5.52 thf(fact_4254_power2__commute,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat] :
% 5.27/5.52 ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( power_power_rat @ ( minus_minus_rat @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_commute
% 5.27/5.52 thf(fact_4255_power2__commute,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( power_power_int @ ( minus_minus_int @ Y @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_commute
% 5.27/5.52 thf(fact_4256_power__diff,axiom,
% 5.27/5.52 ! [A: rat,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_rat )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4257_power__diff,axiom,
% 5.27/5.52 ! [A: nat,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_nat )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4258_power__diff,axiom,
% 5.27/5.52 ! [A: int,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_int )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4259_power__diff,axiom,
% 5.27/5.52 ! [A: real,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_real )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4260_power__diff,axiom,
% 5.27/5.52 ! [A: complex,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_complex )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4261_power__diff,axiom,
% 5.27/5.52 ! [A: code_integer,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.52 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff
% 5.27/5.52 thf(fact_4262_Suc__pred_H,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( N2
% 5.27/5.52 = ( suc @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Suc_pred'
% 5.27/5.52 thf(fact_4263_Suc__diff__eq__diff__pred,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( minus_minus_nat @ ( suc @ M ) @ N2 )
% 5.27/5.52 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Suc_diff_eq_diff_pred
% 5.27/5.52 thf(fact_4264_div__geq,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ~ ( ord_less_nat @ M @ N2 )
% 5.27/5.52 => ( ( divide_divide_nat @ M @ N2 )
% 5.27/5.52 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % div_geq
% 5.27/5.52 thf(fact_4265_div__if,axiom,
% 5.27/5.52 ( divide_divide_nat
% 5.27/5.52 = ( ^ [M6: nat,N: nat] :
% 5.27/5.52 ( if_nat
% 5.27/5.52 @ ( ( ord_less_nat @ M6 @ N )
% 5.27/5.52 | ( N = zero_zero_nat ) )
% 5.27/5.52 @ zero_zero_nat
% 5.27/5.52 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % div_if
% 5.27/5.52 thf(fact_4266_add__eq__if,axiom,
% 5.27/5.52 ( plus_plus_nat
% 5.27/5.52 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_eq_if
% 5.27/5.52 thf(fact_4267_nat__less__add__iff1,axiom,
% 5.27/5.52 ! [J: nat,I2: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ J @ I2 )
% 5.27/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I2 @ J ) @ U ) @ M ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_less_add_iff1
% 5.27/5.52 thf(fact_4268_nat__less__add__iff2,axiom,
% 5.27/5.52 ! [I2: nat,J: nat,U: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.52 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I2 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N2 ) )
% 5.27/5.52 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I2 ) @ U ) @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % nat_less_add_iff2
% 5.27/5.52 thf(fact_4269_mult__eq__if,axiom,
% 5.27/5.52 ( times_times_nat
% 5.27/5.52 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M6 @ one_one_nat ) @ N ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_eq_if
% 5.27/5.52 thf(fact_4270_decr__mult__lemma,axiom,
% 5.27/5.52 ! [D: int,P: int > $o,K: int] :
% 5.27/5.52 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.52 => ( ! [X5: int] :
% 5.27/5.52 ( ( P @ X5 )
% 5.27/5.52 => ( P @ ( minus_minus_int @ X5 @ D ) ) )
% 5.27/5.52 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.52 => ! [X2: int] :
% 5.27/5.52 ( ( P @ X2 )
% 5.27/5.52 => ( P @ ( minus_minus_int @ X2 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % decr_mult_lemma
% 5.27/5.52 thf(fact_4271_dvd__minus__add,axiom,
% 5.27/5.52 ! [Q3: nat,N2: nat,R3: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ Q3 @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ Q3 @ ( times_times_nat @ R3 @ M ) )
% 5.27/5.52 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N2 @ Q3 ) )
% 5.27/5.52 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N2 @ ( minus_minus_nat @ ( times_times_nat @ R3 @ M ) @ Q3 ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_add
% 5.27/5.52 thf(fact_4272_mod__nat__eqI,axiom,
% 5.27/5.52 ! [R3: nat,N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ R3 @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ R3 @ M )
% 5.27/5.52 => ( ( dvd_dvd_nat @ N2 @ ( minus_minus_nat @ M @ R3 ) )
% 5.27/5.52 => ( ( modulo_modulo_nat @ M @ N2 )
% 5.27/5.52 = R3 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_nat_eqI
% 5.27/5.52 thf(fact_4273_mod__pos__geq,axiom,
% 5.27/5.52 ! [L: int,K: int] :
% 5.27/5.52 ( ( ord_less_int @ zero_zero_int @ L )
% 5.27/5.52 => ( ( ord_less_eq_int @ L @ K )
% 5.27/5.52 => ( ( modulo_modulo_int @ K @ L )
% 5.27/5.52 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L ) @ L ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_pos_geq
% 5.27/5.52 thf(fact_4274_scaling__mono,axiom,
% 5.27/5.52 ! [U: real,V: real,R3: real,S: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ U @ V )
% 5.27/5.52 => ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 5.27/5.52 => ( ( ord_less_eq_real @ R3 @ S )
% 5.27/5.52 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R3 @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % scaling_mono
% 5.27/5.52 thf(fact_4275_scaling__mono,axiom,
% 5.27/5.52 ! [U: rat,V: rat,R3: rat,S: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ U @ V )
% 5.27/5.52 => ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 5.27/5.52 => ( ( ord_less_eq_rat @ R3 @ S )
% 5.27/5.52 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R3 @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % scaling_mono
% 5.27/5.52 thf(fact_4276_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 != zero_zero_nat )
% 5.27/5.52 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.52 != zero_zero_nat ) ) ).
% 5.27/5.52
% 5.27/5.52 % exp_not_zero_imp_exp_diff_not_zero
% 5.27/5.52 thf(fact_4277_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 != zero_zero_int )
% 5.27/5.52 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.52 != zero_zero_int ) ) ).
% 5.27/5.52
% 5.27/5.52 % exp_not_zero_imp_exp_diff_not_zero
% 5.27/5.52 thf(fact_4278_power__diff__power__eq,axiom,
% 5.27/5.52 ! [A: nat,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_nat )
% 5.27/5.52 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.27/5.52 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.27/5.52 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N2 ) )
% 5.27/5.52 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff_power_eq
% 5.27/5.52 thf(fact_4279_power__diff__power__eq,axiom,
% 5.27/5.52 ! [A: int,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_zero_int )
% 5.27/5.52 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.27/5.52 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.27/5.52 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N2 ) )
% 5.27/5.52 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff_power_eq
% 5.27/5.52 thf(fact_4280_power__diff__power__eq,axiom,
% 5.27/5.52 ! [A: code_integer,N2: nat,M: nat] :
% 5.27/5.52 ( ( A != zero_z3403309356797280102nteger )
% 5.27/5.52 => ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.27/5.52 = ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ M @ N2 ) ) ) )
% 5.27/5.52 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.27/5.52 = ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ A @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_diff_power_eq
% 5.27/5.52 thf(fact_4281_signed__take__bit__int__less__exp,axiom,
% 5.27/5.52 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_int_less_exp
% 5.27/5.52 thf(fact_4282_power__eq__if,axiom,
% 5.27/5.52 ( power_power_rat
% 5.27/5.52 = ( ^ [P5: rat,M6: nat] : ( if_rat @ ( M6 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P5 @ ( power_power_rat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_eq_if
% 5.27/5.52 thf(fact_4283_power__eq__if,axiom,
% 5.27/5.52 ( power_power_complex
% 5.27/5.52 = ( ^ [P5: complex,M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P5 @ ( power_power_complex @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_eq_if
% 5.27/5.52 thf(fact_4284_power__eq__if,axiom,
% 5.27/5.52 ( power_power_real
% 5.27/5.52 = ( ^ [P5: real,M6: nat] : ( if_real @ ( M6 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P5 @ ( power_power_real @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_eq_if
% 5.27/5.52 thf(fact_4285_power__eq__if,axiom,
% 5.27/5.52 ( power_power_nat
% 5.27/5.52 = ( ^ [P5: nat,M6: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P5 @ ( power_power_nat @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_eq_if
% 5.27/5.52 thf(fact_4286_power__eq__if,axiom,
% 5.27/5.52 ( power_power_int
% 5.27/5.52 = ( ^ [P5: int,M6: nat] : ( if_int @ ( M6 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P5 @ ( power_power_int @ P5 @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_eq_if
% 5.27/5.52 thf(fact_4287_power__minus__mult,axiom,
% 5.27/5.52 ! [N2: nat,A: complex] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.27/5.52 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_minus_mult
% 5.27/5.52 thf(fact_4288_power__minus__mult,axiom,
% 5.27/5.52 ! [N2: nat,A: real] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.27/5.52 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_minus_mult
% 5.27/5.52 thf(fact_4289_power__minus__mult,axiom,
% 5.27/5.52 ! [N2: nat,A: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.27/5.52 = ( power_power_nat @ A @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_minus_mult
% 5.27/5.52 thf(fact_4290_power__minus__mult,axiom,
% 5.27/5.52 ! [N2: nat,A: int] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ A )
% 5.27/5.52 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power_minus_mult
% 5.27/5.52 thf(fact_4291_diff__le__diff__pow,axiom,
% 5.27/5.52 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.27/5.52 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N2 ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % diff_le_diff_pow
% 5.27/5.52 thf(fact_4292_le__div__geq,axiom,
% 5.27/5.52 ! [N2: nat,M: nat] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.52 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.52 => ( ( divide_divide_nat @ M @ N2 )
% 5.27/5.52 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % le_div_geq
% 5.27/5.52 thf(fact_4293_even__diff__iff,axiom,
% 5.27/5.52 ! [K: int,L: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L ) )
% 5.27/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_diff_iff
% 5.27/5.52 thf(fact_4294_even__signed__take__bit__iff,axiom,
% 5.27/5.52 ! [M: nat,A: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_signed_take_bit_iff
% 5.27/5.52 thf(fact_4295_even__signed__take__bit__iff,axiom,
% 5.27/5.52 ! [M: nat,A: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.27/5.52 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_signed_take_bit_iff
% 5.27/5.52 thf(fact_4296_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.27/5.52 ! [K: int,N2: nat] :
% 5.27/5.52 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.27/5.52 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_int_greater_eq_self_iff
% 5.27/5.52 thf(fact_4297_signed__take__bit__int__less__self__iff,axiom,
% 5.27/5.52 ! [N2: nat,K: int] :
% 5.27/5.52 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.27/5.52 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_int_less_self_iff
% 5.27/5.52 thf(fact_4298_div__pos__geq,axiom,
% 5.27/5.52 ! [L: int,K: int] :
% 5.27/5.52 ( ( ord_less_int @ zero_zero_int @ L )
% 5.27/5.52 => ( ( ord_less_eq_int @ L @ K )
% 5.27/5.52 => ( ( divide_divide_int @ K @ L )
% 5.27/5.52 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L ) @ L ) @ one_one_int ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % div_pos_geq
% 5.27/5.52 thf(fact_4299_add__0__iff,axiom,
% 5.27/5.52 ! [B: complex,A: complex] :
% 5.27/5.52 ( ( B
% 5.27/5.52 = ( plus_plus_complex @ B @ A ) )
% 5.27/5.52 = ( A = zero_zero_complex ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_0_iff
% 5.27/5.52 thf(fact_4300_add__0__iff,axiom,
% 5.27/5.52 ! [B: real,A: real] :
% 5.27/5.52 ( ( B
% 5.27/5.52 = ( plus_plus_real @ B @ A ) )
% 5.27/5.52 = ( A = zero_zero_real ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_0_iff
% 5.27/5.52 thf(fact_4301_add__0__iff,axiom,
% 5.27/5.52 ! [B: rat,A: rat] :
% 5.27/5.52 ( ( B
% 5.27/5.52 = ( plus_plus_rat @ B @ A ) )
% 5.27/5.52 = ( A = zero_zero_rat ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_0_iff
% 5.27/5.52 thf(fact_4302_add__0__iff,axiom,
% 5.27/5.52 ! [B: nat,A: nat] :
% 5.27/5.52 ( ( B
% 5.27/5.52 = ( plus_plus_nat @ B @ A ) )
% 5.27/5.52 = ( A = zero_zero_nat ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_0_iff
% 5.27/5.52 thf(fact_4303_add__0__iff,axiom,
% 5.27/5.52 ! [B: int,A: int] :
% 5.27/5.52 ( ( B
% 5.27/5.52 = ( plus_plus_int @ B @ A ) )
% 5.27/5.52 = ( A = zero_zero_int ) ) ).
% 5.27/5.52
% 5.27/5.52 % add_0_iff
% 5.27/5.52 thf(fact_4304_crossproduct__eq,axiom,
% 5.27/5.52 ! [W: rat,Y: rat,X4: rat,Z: rat] :
% 5.27/5.52 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X4 @ Z ) )
% 5.27/5.52 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X4 @ Y ) ) )
% 5.27/5.52 = ( ( W = X4 )
% 5.27/5.52 | ( Y = Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_eq
% 5.27/5.52 thf(fact_4305_crossproduct__eq,axiom,
% 5.27/5.52 ! [W: complex,Y: complex,X4: complex,Z: complex] :
% 5.27/5.52 ( ( ( plus_plus_complex @ ( times_times_complex @ W @ Y ) @ ( times_times_complex @ X4 @ Z ) )
% 5.27/5.52 = ( plus_plus_complex @ ( times_times_complex @ W @ Z ) @ ( times_times_complex @ X4 @ Y ) ) )
% 5.27/5.52 = ( ( W = X4 )
% 5.27/5.52 | ( Y = Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_eq
% 5.27/5.52 thf(fact_4306_crossproduct__eq,axiom,
% 5.27/5.52 ! [W: real,Y: real,X4: real,Z: real] :
% 5.27/5.52 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X4 @ Z ) )
% 5.27/5.52 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X4 @ Y ) ) )
% 5.27/5.52 = ( ( W = X4 )
% 5.27/5.52 | ( Y = Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_eq
% 5.27/5.52 thf(fact_4307_crossproduct__eq,axiom,
% 5.27/5.52 ! [W: nat,Y: nat,X4: nat,Z: nat] :
% 5.27/5.52 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X4 @ Z ) )
% 5.27/5.52 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X4 @ Y ) ) )
% 5.27/5.52 = ( ( W = X4 )
% 5.27/5.52 | ( Y = Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_eq
% 5.27/5.52 thf(fact_4308_crossproduct__eq,axiom,
% 5.27/5.52 ! [W: int,Y: int,X4: int,Z: int] :
% 5.27/5.52 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X4 @ Z ) )
% 5.27/5.52 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X4 @ Y ) ) )
% 5.27/5.52 = ( ( W = X4 )
% 5.27/5.52 | ( Y = Z ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_eq
% 5.27/5.52 thf(fact_4309_crossproduct__noteq,axiom,
% 5.27/5.52 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.52 ( ( ( A != B )
% 5.27/5.52 & ( C != D ) )
% 5.27/5.52 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.27/5.52 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_noteq
% 5.27/5.52 thf(fact_4310_crossproduct__noteq,axiom,
% 5.27/5.52 ! [A: complex,B: complex,C: complex,D: complex] :
% 5.27/5.52 ( ( ( A != B )
% 5.27/5.52 & ( C != D ) )
% 5.27/5.52 = ( ( plus_plus_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ D ) )
% 5.27/5.52 != ( plus_plus_complex @ ( times_times_complex @ A @ D ) @ ( times_times_complex @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_noteq
% 5.27/5.52 thf(fact_4311_crossproduct__noteq,axiom,
% 5.27/5.52 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.52 ( ( ( A != B )
% 5.27/5.52 & ( C != D ) )
% 5.27/5.52 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.27/5.52 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_noteq
% 5.27/5.52 thf(fact_4312_crossproduct__noteq,axiom,
% 5.27/5.52 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.27/5.52 ( ( ( A != B )
% 5.27/5.52 & ( C != D ) )
% 5.27/5.52 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.27/5.52 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_noteq
% 5.27/5.52 thf(fact_4313_crossproduct__noteq,axiom,
% 5.27/5.52 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.52 ( ( ( A != B )
% 5.27/5.52 & ( C != D ) )
% 5.27/5.52 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.27/5.52 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % crossproduct_noteq
% 5.27/5.52 thf(fact_4314_power2__diff,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat] :
% 5.27/5.52 ( ( power_power_rat @ ( minus_minus_rat @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_diff
% 5.27/5.52 thf(fact_4315_power2__diff,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex] :
% 5.27/5.52 ( ( power_power_complex @ ( minus_minus_complex @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_diff
% 5.27/5.52 thf(fact_4316_power2__diff,axiom,
% 5.27/5.52 ! [X4: real,Y: real] :
% 5.27/5.52 ( ( power_power_real @ ( minus_minus_real @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_diff
% 5.27/5.52 thf(fact_4317_power2__diff,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( power_power_int @ ( minus_minus_int @ X4 @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.52 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X4 @ ( 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 ) ) @ X4 ) @ Y ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % power2_diff
% 5.27/5.52 thf(fact_4318_mult__exp__mod__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,A: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_exp_mod_exp_eq
% 5.27/5.52 thf(fact_4319_mult__exp__mod__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,A: int] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_exp_mod_exp_eq
% 5.27/5.52 thf(fact_4320_mult__exp__mod__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat,A: code_integer] :
% 5.27/5.52 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.52 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_exp_mod_exp_eq
% 5.27/5.52 thf(fact_4321_int__power__div__base,axiom,
% 5.27/5.52 ! [M: nat,K: int] :
% 5.27/5.52 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.52 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.27/5.52 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.27/5.52 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % int_power_div_base
% 5.27/5.52 thf(fact_4322_divmod__digit__1_I2_J,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.52 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.27/5.52 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.52 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.52 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_digit_1(2)
% 5.27/5.52 thf(fact_4323_divmod__digit__1_I2_J,axiom,
% 5.27/5.52 ! [A: nat,B: nat] :
% 5.27/5.52 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.27/5.52 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.27/5.52 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.52 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.52 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_digit_1(2)
% 5.27/5.52 thf(fact_4324_divmod__digit__1_I2_J,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.27/5.52 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.52 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.27/5.52 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.27/5.52 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_digit_1(2)
% 5.27/5.52 thf(fact_4325_even__mask__div__iff_H,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff'
% 5.27/5.52 thf(fact_4326_even__mask__div__iff_H,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff'
% 5.27/5.52 thf(fact_4327_even__mask__div__iff_H,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff'
% 5.27/5.52 thf(fact_4328_even__mod__4__div__2,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.52 = ( suc @ zero_zero_nat ) )
% 5.27/5.52 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mod_4_div_2
% 5.27/5.52 thf(fact_4329_even__mask__div__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 = zero_zero_nat )
% 5.27/5.52 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff
% 5.27/5.52 thf(fact_4330_even__mask__div__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 = zero_zero_int )
% 5.27/5.52 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff
% 5.27/5.52 thf(fact_4331_even__mask__div__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 = zero_z3403309356797280102nteger )
% 5.27/5.52 | ( ord_less_eq_nat @ M @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % even_mask_div_iff
% 5.27/5.52 thf(fact_4332_exp__div__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_times_nat
% 5.27/5.52 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.52 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.27/5.52 != zero_zero_nat )
% 5.27/5.52 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.27/5.52 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % exp_div_exp_eq
% 5.27/5.52 thf(fact_4333_exp__div__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_times_int
% 5.27/5.52 @ ( zero_n2684676970156552555ol_int
% 5.27/5.52 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.27/5.52 != zero_zero_int )
% 5.27/5.52 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.27/5.52 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % exp_div_exp_eq
% 5.27/5.52 thf(fact_4334_exp__div__exp__eq,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.52 = ( times_3573771949741848930nteger
% 5.27/5.52 @ ( zero_n356916108424825756nteger
% 5.27/5.52 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.27/5.52 != zero_z3403309356797280102nteger )
% 5.27/5.52 & ( ord_less_eq_nat @ N2 @ M ) ) )
% 5.27/5.52 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % exp_div_exp_eq
% 5.27/5.52 thf(fact_4335_neg__zmod__mult__2,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.27/5.52 => ( ( 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 ) )
% 5.27/5.52 = ( 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 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_zmod_mult_2
% 5.27/5.52 thf(fact_4336_divmod__step__eq,axiom,
% 5.27/5.52 ! [L: num,R3: nat,Q3: nat] :
% 5.27/5.52 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.27/5.52 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 5.27/5.52 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ one_one_nat ) @ ( minus_minus_nat @ R3 @ ( numeral_numeral_nat @ L ) ) ) ) )
% 5.27/5.52 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R3 )
% 5.27/5.52 => ( ( unique5026877609467782581ep_nat @ L @ ( product_Pair_nat_nat @ Q3 @ R3 ) )
% 5.27/5.52 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_step_eq
% 5.27/5.52 thf(fact_4337_divmod__step__eq,axiom,
% 5.27/5.52 ! [L: num,R3: int,Q3: int] :
% 5.27/5.52 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.27/5.52 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.52 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ one_one_int ) @ ( minus_minus_int @ R3 @ ( numeral_numeral_int @ L ) ) ) ) )
% 5.27/5.52 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R3 )
% 5.27/5.52 => ( ( unique5024387138958732305ep_int @ L @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.52 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_step_eq
% 5.27/5.52 thf(fact_4338_divmod__step__eq,axiom,
% 5.27/5.52 ! [L: num,R3: code_integer,Q3: code_integer] :
% 5.27/5.52 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.27/5.52 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 5.27/5.52 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R3 @ ( numera6620942414471956472nteger @ L ) ) ) ) )
% 5.27/5.52 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R3 )
% 5.27/5.52 => ( ( unique4921790084139445826nteger @ L @ ( produc1086072967326762835nteger @ Q3 @ R3 ) )
% 5.27/5.52 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q3 ) @ R3 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % divmod_step_eq
% 5.27/5.52 thf(fact_4339_signed__take__bit__rec,axiom,
% 5.27/5.52 ( bit_ri6519982836138164636nteger
% 5.27/5.52 = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = 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 @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_rec
% 5.27/5.52 thf(fact_4340_signed__take__bit__rec,axiom,
% 5.27/5.52 ( bit_ri631733984087533419it_int
% 5.27/5.52 = ( ^ [N: nat,A3: int] : ( if_int @ ( N = 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 @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % signed_take_bit_rec
% 5.27/5.52 thf(fact_4341_take__bit__rec,axiom,
% 5.27/5.52 ( bit_se1745604003318907178nteger
% 5.27/5.52 = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( N = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_rec
% 5.27/5.52 thf(fact_4342_take__bit__rec,axiom,
% 5.27/5.52 ( bit_se2923211474154528505it_int
% 5.27/5.52 = ( ^ [N: nat,A3: int] : ( if_int @ ( N = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_rec
% 5.27/5.52 thf(fact_4343_take__bit__rec,axiom,
% 5.27/5.52 ( bit_se2925701944663578781it_nat
% 5.27/5.52 = ( ^ [N: nat,A3: nat] : ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_rec
% 5.27/5.52 thf(fact_4344_odd__mod__4__div__2,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.52 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.27/5.52 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % odd_mod_4_div_2
% 5.27/5.52 thf(fact_4345_Bernoulli__inequality__even,axiom,
% 5.27/5.52 ! [N2: nat,X4: real] :
% 5.27/5.52 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.52 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Bernoulli_inequality_even
% 5.27/5.52 thf(fact_4346_Suc__0__xor__eq,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.52 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.52 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.52 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Suc_0_xor_eq
% 5.27/5.52 thf(fact_4347_add_Oinverse__inverse,axiom,
% 5.27/5.52 ! [A: real] :
% 5.27/5.52 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_inverse
% 5.27/5.52 thf(fact_4348_add_Oinverse__inverse,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_inverse
% 5.27/5.52 thf(fact_4349_add_Oinverse__inverse,axiom,
% 5.27/5.52 ! [A: complex] :
% 5.27/5.52 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_inverse
% 5.27/5.52 thf(fact_4350_add_Oinverse__inverse,axiom,
% 5.27/5.52 ! [A: code_integer] :
% 5.27/5.52 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_inverse
% 5.27/5.52 thf(fact_4351_add_Oinverse__inverse,axiom,
% 5.27/5.52 ! [A: rat] :
% 5.27/5.52 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_inverse
% 5.27/5.52 thf(fact_4352_neg__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( ( uminus_uminus_real @ A )
% 5.27/5.52 = ( uminus_uminus_real @ B ) )
% 5.27/5.52 = ( A = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_iff_equal
% 5.27/5.52 thf(fact_4353_neg__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( ( uminus_uminus_int @ A )
% 5.27/5.52 = ( uminus_uminus_int @ B ) )
% 5.27/5.52 = ( A = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_iff_equal
% 5.27/5.52 thf(fact_4354_neg__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.52 = ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.52 = ( A = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_iff_equal
% 5.27/5.52 thf(fact_4355_neg__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.52 = ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.52 = ( A = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_iff_equal
% 5.27/5.52 thf(fact_4356_neg__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( ( uminus_uminus_rat @ A )
% 5.27/5.52 = ( uminus_uminus_rat @ B ) )
% 5.27/5.52 = ( A = B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_iff_equal
% 5.27/5.52 thf(fact_4357_Compl__anti__mono,axiom,
% 5.27/5.52 ! [A2: set_int,B3: set_int] :
% 5.27/5.52 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.27/5.52 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % Compl_anti_mono
% 5.27/5.52 thf(fact_4358_Compl__subset__Compl__iff,axiom,
% 5.27/5.52 ! [A2: set_int,B3: set_int] :
% 5.27/5.52 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 5.27/5.52 = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % Compl_subset_Compl_iff
% 5.27/5.52 thf(fact_4359_of__nat__eq__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ( semiri5074537144036343181t_real @ M )
% 5.27/5.52 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % of_nat_eq_iff
% 5.27/5.52 thf(fact_4360_of__nat__eq__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ( semiri1314217659103216013at_int @ M )
% 5.27/5.52 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % of_nat_eq_iff
% 5.27/5.52 thf(fact_4361_of__nat__eq__iff,axiom,
% 5.27/5.52 ! [M: nat,N2: nat] :
% 5.27/5.52 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.27/5.52 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % of_nat_eq_iff
% 5.27/5.52 thf(fact_4362_semiring__norm_I90_J,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( bit1 @ M )
% 5.27/5.52 = ( bit1 @ N2 ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % semiring_norm(90)
% 5.27/5.52 thf(fact_4363_bit_Oxor__left__self,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_se6526347334894502574or_int @ X4 @ Y ) )
% 5.27/5.52 = Y ) ).
% 5.27/5.52
% 5.27/5.52 % bit.xor_left_self
% 5.27/5.52 thf(fact_4364_idiff__0,axiom,
% 5.27/5.52 ! [N2: extended_enat] :
% 5.27/5.52 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N2 )
% 5.27/5.52 = zero_z5237406670263579293d_enat ) ).
% 5.27/5.52
% 5.27/5.52 % idiff_0
% 5.27/5.52 thf(fact_4365_idiff__0__right,axiom,
% 5.27/5.52 ! [N2: extended_enat] :
% 5.27/5.52 ( ( minus_3235023915231533773d_enat @ N2 @ zero_z5237406670263579293d_enat )
% 5.27/5.52 = N2 ) ).
% 5.27/5.52
% 5.27/5.52 % idiff_0_right
% 5.27/5.52 thf(fact_4366_neg__le__iff__le,axiom,
% 5.27/5.52 ! [B: real,A: real] :
% 5.27/5.52 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.27/5.52 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_le_iff_le
% 5.27/5.52 thf(fact_4367_neg__le__iff__le,axiom,
% 5.27/5.52 ! [B: code_integer,A: code_integer] :
% 5.27/5.52 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.52 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_le_iff_le
% 5.27/5.52 thf(fact_4368_neg__le__iff__le,axiom,
% 5.27/5.52 ! [B: rat,A: rat] :
% 5.27/5.52 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.27/5.52 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_le_iff_le
% 5.27/5.52 thf(fact_4369_neg__le__iff__le,axiom,
% 5.27/5.52 ! [B: int,A: int] :
% 5.27/5.52 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.27/5.52 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_le_iff_le
% 5.27/5.52 thf(fact_4370_add_Oinverse__neutral,axiom,
% 5.27/5.52 ( ( uminus_uminus_real @ zero_zero_real )
% 5.27/5.52 = zero_zero_real ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_neutral
% 5.27/5.52 thf(fact_4371_add_Oinverse__neutral,axiom,
% 5.27/5.52 ( ( uminus_uminus_int @ zero_zero_int )
% 5.27/5.52 = zero_zero_int ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_neutral
% 5.27/5.52 thf(fact_4372_add_Oinverse__neutral,axiom,
% 5.27/5.52 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.27/5.52 = zero_zero_complex ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_neutral
% 5.27/5.52 thf(fact_4373_add_Oinverse__neutral,axiom,
% 5.27/5.52 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.27/5.52 = zero_z3403309356797280102nteger ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_neutral
% 5.27/5.52 thf(fact_4374_add_Oinverse__neutral,axiom,
% 5.27/5.52 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.27/5.52 = zero_zero_rat ) ).
% 5.27/5.52
% 5.27/5.52 % add.inverse_neutral
% 5.27/5.52 thf(fact_4375_neg__0__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: real] :
% 5.27/5.52 ( ( zero_zero_real
% 5.27/5.52 = ( uminus_uminus_real @ A ) )
% 5.27/5.52 = ( zero_zero_real = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_0_equal_iff_equal
% 5.27/5.52 thf(fact_4376_neg__0__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( zero_zero_int
% 5.27/5.52 = ( uminus_uminus_int @ A ) )
% 5.27/5.52 = ( zero_zero_int = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_0_equal_iff_equal
% 5.27/5.52 thf(fact_4377_neg__0__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: complex] :
% 5.27/5.52 ( ( zero_zero_complex
% 5.27/5.52 = ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.52 = ( zero_zero_complex = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_0_equal_iff_equal
% 5.27/5.52 thf(fact_4378_neg__0__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: code_integer] :
% 5.27/5.52 ( ( zero_z3403309356797280102nteger
% 5.27/5.52 = ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.52 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_0_equal_iff_equal
% 5.27/5.52 thf(fact_4379_neg__0__equal__iff__equal,axiom,
% 5.27/5.52 ! [A: rat] :
% 5.27/5.52 ( ( zero_zero_rat
% 5.27/5.52 = ( uminus_uminus_rat @ A ) )
% 5.27/5.52 = ( zero_zero_rat = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_0_equal_iff_equal
% 5.27/5.52 thf(fact_4380_neg__equal__0__iff__equal,axiom,
% 5.27/5.52 ! [A: real] :
% 5.27/5.52 ( ( ( uminus_uminus_real @ A )
% 5.27/5.52 = zero_zero_real )
% 5.27/5.52 = ( A = zero_zero_real ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_0_iff_equal
% 5.27/5.52 thf(fact_4381_neg__equal__0__iff__equal,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( ( uminus_uminus_int @ A )
% 5.27/5.52 = zero_zero_int )
% 5.27/5.52 = ( A = zero_zero_int ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_0_iff_equal
% 5.27/5.52 thf(fact_4382_neg__equal__0__iff__equal,axiom,
% 5.27/5.52 ! [A: complex] :
% 5.27/5.52 ( ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.52 = zero_zero_complex )
% 5.27/5.52 = ( A = zero_zero_complex ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_0_iff_equal
% 5.27/5.52 thf(fact_4383_neg__equal__0__iff__equal,axiom,
% 5.27/5.52 ! [A: code_integer] :
% 5.27/5.52 ( ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.52 = zero_z3403309356797280102nteger )
% 5.27/5.52 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_0_iff_equal
% 5.27/5.52 thf(fact_4384_neg__equal__0__iff__equal,axiom,
% 5.27/5.52 ! [A: rat] :
% 5.27/5.52 ( ( ( uminus_uminus_rat @ A )
% 5.27/5.52 = zero_zero_rat )
% 5.27/5.52 = ( A = zero_zero_rat ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_0_iff_equal
% 5.27/5.52 thf(fact_4385_equal__neg__zero,axiom,
% 5.27/5.52 ! [A: real] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( uminus_uminus_real @ A ) )
% 5.27/5.52 = ( A = zero_zero_real ) ) ).
% 5.27/5.52
% 5.27/5.52 % equal_neg_zero
% 5.27/5.52 thf(fact_4386_equal__neg__zero,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( uminus_uminus_int @ A ) )
% 5.27/5.52 = ( A = zero_zero_int ) ) ).
% 5.27/5.52
% 5.27/5.52 % equal_neg_zero
% 5.27/5.52 thf(fact_4387_equal__neg__zero,axiom,
% 5.27/5.52 ! [A: code_integer] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.52 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.52
% 5.27/5.52 % equal_neg_zero
% 5.27/5.52 thf(fact_4388_equal__neg__zero,axiom,
% 5.27/5.52 ! [A: rat] :
% 5.27/5.52 ( ( A
% 5.27/5.52 = ( uminus_uminus_rat @ A ) )
% 5.27/5.52 = ( A = zero_zero_rat ) ) ).
% 5.27/5.52
% 5.27/5.52 % equal_neg_zero
% 5.27/5.52 thf(fact_4389_neg__equal__zero,axiom,
% 5.27/5.52 ! [A: real] :
% 5.27/5.52 ( ( ( uminus_uminus_real @ A )
% 5.27/5.52 = A )
% 5.27/5.52 = ( A = zero_zero_real ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_zero
% 5.27/5.52 thf(fact_4390_neg__equal__zero,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( ( uminus_uminus_int @ A )
% 5.27/5.52 = A )
% 5.27/5.52 = ( A = zero_zero_int ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_zero
% 5.27/5.52 thf(fact_4391_neg__equal__zero,axiom,
% 5.27/5.52 ! [A: code_integer] :
% 5.27/5.52 ( ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.52 = A )
% 5.27/5.52 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_zero
% 5.27/5.52 thf(fact_4392_neg__equal__zero,axiom,
% 5.27/5.52 ! [A: rat] :
% 5.27/5.52 ( ( ( uminus_uminus_rat @ A )
% 5.27/5.52 = A )
% 5.27/5.52 = ( A = zero_zero_rat ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_equal_zero
% 5.27/5.52 thf(fact_4393_neg__less__iff__less,axiom,
% 5.27/5.52 ! [B: real,A: real] :
% 5.27/5.52 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.27/5.52 = ( ord_less_real @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_less_iff_less
% 5.27/5.52 thf(fact_4394_neg__less__iff__less,axiom,
% 5.27/5.52 ! [B: int,A: int] :
% 5.27/5.52 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.27/5.52 = ( ord_less_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_less_iff_less
% 5.27/5.52 thf(fact_4395_neg__less__iff__less,axiom,
% 5.27/5.52 ! [B: code_integer,A: code_integer] :
% 5.27/5.52 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.52 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_less_iff_less
% 5.27/5.52 thf(fact_4396_neg__less__iff__less,axiom,
% 5.27/5.52 ! [B: rat,A: rat] :
% 5.27/5.52 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.27/5.52 = ( ord_less_rat @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_less_iff_less
% 5.27/5.52 thf(fact_4397_neg__numeral__eq__iff,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.27/5.52 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_numeral_eq_iff
% 5.27/5.52 thf(fact_4398_neg__numeral__eq__iff,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.27/5.52 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_numeral_eq_iff
% 5.27/5.52 thf(fact_4399_neg__numeral__eq__iff,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.27/5.52 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_numeral_eq_iff
% 5.27/5.52 thf(fact_4400_neg__numeral__eq__iff,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.27/5.52 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_numeral_eq_iff
% 5.27/5.52 thf(fact_4401_neg__numeral__eq__iff,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.27/5.52 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.52 = ( M = N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % neg_numeral_eq_iff
% 5.27/5.52 thf(fact_4402_mult__minus__left,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.52 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_left
% 5.27/5.52 thf(fact_4403_mult__minus__left,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.52 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_left
% 5.27/5.52 thf(fact_4404_mult__minus__left,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.27/5.52 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_left
% 5.27/5.52 thf(fact_4405_mult__minus__left,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.52 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_left
% 5.27/5.52 thf(fact_4406_mult__minus__left,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.52 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_left
% 5.27/5.52 thf(fact_4407_minus__mult__minus,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.27/5.52 = ( times_times_real @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_minus
% 5.27/5.52 thf(fact_4408_minus__mult__minus,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.27/5.52 = ( times_times_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_minus
% 5.27/5.52 thf(fact_4409_minus__mult__minus,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.52 = ( times_times_complex @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_minus
% 5.27/5.52 thf(fact_4410_minus__mult__minus,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.52 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_minus
% 5.27/5.52 thf(fact_4411_minus__mult__minus,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.27/5.52 = ( times_times_rat @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_mult_minus
% 5.27/5.52 thf(fact_4412_mult__minus__right,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.27/5.52 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_right
% 5.27/5.52 thf(fact_4413_mult__minus__right,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.52 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_right
% 5.27/5.52 thf(fact_4414_mult__minus__right,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.52 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_right
% 5.27/5.52 thf(fact_4415_mult__minus__right,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.52 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_right
% 5.27/5.52 thf(fact_4416_mult__minus__right,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.27/5.52 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mult_minus_right
% 5.27/5.52 thf(fact_4417_minus__add__distrib,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.27/5.52 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_distrib
% 5.27/5.52 thf(fact_4418_minus__add__distrib,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.52 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_distrib
% 5.27/5.52 thf(fact_4419_minus__add__distrib,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.27/5.52 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_distrib
% 5.27/5.52 thf(fact_4420_minus__add__distrib,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.52 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_distrib
% 5.27/5.52 thf(fact_4421_minus__add__distrib,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.52 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_distrib
% 5.27/5.52 thf(fact_4422_minus__add__cancel,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_cancel
% 5.27/5.52 thf(fact_4423_minus__add__cancel,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_cancel
% 5.27/5.52 thf(fact_4424_minus__add__cancel,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_cancel
% 5.27/5.52 thf(fact_4425_minus__add__cancel,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_cancel
% 5.27/5.52 thf(fact_4426_minus__add__cancel,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % minus_add_cancel
% 5.27/5.52 thf(fact_4427_add__minus__cancel,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % add_minus_cancel
% 5.27/5.52 thf(fact_4428_add__minus__cancel,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % add_minus_cancel
% 5.27/5.52 thf(fact_4429_add__minus__cancel,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % add_minus_cancel
% 5.27/5.52 thf(fact_4430_add__minus__cancel,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % add_minus_cancel
% 5.27/5.52 thf(fact_4431_add__minus__cancel,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.27/5.52 = B ) ).
% 5.27/5.52
% 5.27/5.52 % add_minus_cancel
% 5.27/5.52 thf(fact_4432_minus__diff__eq,axiom,
% 5.27/5.52 ! [A: real,B: real] :
% 5.27/5.52 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.27/5.52 = ( minus_minus_real @ B @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_diff_eq
% 5.27/5.52 thf(fact_4433_minus__diff__eq,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.27/5.52 = ( minus_minus_int @ B @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_diff_eq
% 5.27/5.52 thf(fact_4434_minus__diff__eq,axiom,
% 5.27/5.52 ! [A: complex,B: complex] :
% 5.27/5.52 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.27/5.52 = ( minus_minus_complex @ B @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_diff_eq
% 5.27/5.52 thf(fact_4435_minus__diff__eq,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.27/5.52 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_diff_eq
% 5.27/5.52 thf(fact_4436_minus__diff__eq,axiom,
% 5.27/5.52 ! [A: rat,B: rat] :
% 5.27/5.52 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.52 = ( minus_minus_rat @ B @ A ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_diff_eq
% 5.27/5.52 thf(fact_4437_div__minus__minus,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.27/5.52 = ( divide_divide_int @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % div_minus_minus
% 5.27/5.52 thf(fact_4438_div__minus__minus,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.52 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.27/5.52
% 5.27/5.52 % div_minus_minus
% 5.27/5.52 thf(fact_4439_dvd__minus__iff,axiom,
% 5.27/5.52 ! [X4: real,Y: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ X4 @ ( uminus_uminus_real @ Y ) )
% 5.27/5.52 = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_iff
% 5.27/5.52 thf(fact_4440_dvd__minus__iff,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ X4 @ ( uminus_uminus_int @ Y ) )
% 5.27/5.52 = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_iff
% 5.27/5.52 thf(fact_4441_dvd__minus__iff,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex] :
% 5.27/5.52 ( ( dvd_dvd_complex @ X4 @ ( uminus1482373934393186551omplex @ Y ) )
% 5.27/5.52 = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_iff
% 5.27/5.52 thf(fact_4442_dvd__minus__iff,axiom,
% 5.27/5.52 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ X4 @ ( uminus1351360451143612070nteger @ Y ) )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_iff
% 5.27/5.52 thf(fact_4443_dvd__minus__iff,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ X4 @ ( uminus_uminus_rat @ Y ) )
% 5.27/5.52 = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % dvd_minus_iff
% 5.27/5.52 thf(fact_4444_minus__dvd__iff,axiom,
% 5.27/5.52 ! [X4: real,Y: real] :
% 5.27/5.52 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X4 ) @ Y )
% 5.27/5.52 = ( dvd_dvd_real @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_dvd_iff
% 5.27/5.52 thf(fact_4445_minus__dvd__iff,axiom,
% 5.27/5.52 ! [X4: int,Y: int] :
% 5.27/5.52 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X4 ) @ Y )
% 5.27/5.52 = ( dvd_dvd_int @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_dvd_iff
% 5.27/5.52 thf(fact_4446_minus__dvd__iff,axiom,
% 5.27/5.52 ! [X4: complex,Y: complex] :
% 5.27/5.52 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y )
% 5.27/5.52 = ( dvd_dvd_complex @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_dvd_iff
% 5.27/5.52 thf(fact_4447_minus__dvd__iff,axiom,
% 5.27/5.52 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.52 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X4 ) @ Y )
% 5.27/5.52 = ( dvd_dvd_Code_integer @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_dvd_iff
% 5.27/5.52 thf(fact_4448_minus__dvd__iff,axiom,
% 5.27/5.52 ! [X4: rat,Y: rat] :
% 5.27/5.52 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X4 ) @ Y )
% 5.27/5.52 = ( dvd_dvd_rat @ X4 @ Y ) ) ).
% 5.27/5.52
% 5.27/5.52 % minus_dvd_iff
% 5.27/5.52 thf(fact_4449_semiring__norm_I88_J,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( bit0 @ M )
% 5.27/5.52 != ( bit1 @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % semiring_norm(88)
% 5.27/5.52 thf(fact_4450_semiring__norm_I89_J,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( bit1 @ M )
% 5.27/5.52 != ( bit0 @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % semiring_norm(89)
% 5.27/5.52 thf(fact_4451_semiring__norm_I84_J,axiom,
% 5.27/5.52 ! [N2: num] :
% 5.27/5.52 ( one
% 5.27/5.52 != ( bit1 @ N2 ) ) ).
% 5.27/5.52
% 5.27/5.52 % semiring_norm(84)
% 5.27/5.52 thf(fact_4452_semiring__norm_I86_J,axiom,
% 5.27/5.52 ! [M: num] :
% 5.27/5.52 ( ( bit1 @ M )
% 5.27/5.52 != one ) ).
% 5.27/5.52
% 5.27/5.52 % semiring_norm(86)
% 5.27/5.52 thf(fact_4453_mod__minus__minus,axiom,
% 5.27/5.52 ! [A: int,B: int] :
% 5.27/5.52 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.27/5.52 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_minus_minus
% 5.27/5.52 thf(fact_4454_mod__minus__minus,axiom,
% 5.27/5.52 ! [A: code_integer,B: code_integer] :
% 5.27/5.52 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.52 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % mod_minus_minus
% 5.27/5.52 thf(fact_4455_take__bit__of__0,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( bit_se2923211474154528505it_int @ N2 @ zero_zero_int )
% 5.27/5.52 = zero_zero_int ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_of_0
% 5.27/5.52 thf(fact_4456_take__bit__of__0,axiom,
% 5.27/5.52 ! [N2: nat] :
% 5.27/5.52 ( ( bit_se2925701944663578781it_nat @ N2 @ zero_zero_nat )
% 5.27/5.52 = zero_zero_nat ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_of_0
% 5.27/5.52 thf(fact_4457_real__add__minus__iff,axiom,
% 5.27/5.52 ! [X4: real,A: real] :
% 5.27/5.52 ( ( ( plus_plus_real @ X4 @ ( uminus_uminus_real @ A ) )
% 5.27/5.52 = zero_zero_real )
% 5.27/5.52 = ( X4 = A ) ) ).
% 5.27/5.52
% 5.27/5.52 % real_add_minus_iff
% 5.27/5.52 thf(fact_4458_bit_Oxor__self,axiom,
% 5.27/5.52 ! [X4: int] :
% 5.27/5.52 ( ( bit_se6526347334894502574or_int @ X4 @ X4 )
% 5.27/5.52 = zero_zero_int ) ).
% 5.27/5.52
% 5.27/5.52 % bit.xor_self
% 5.27/5.52 thf(fact_4459_xor__self__eq,axiom,
% 5.27/5.52 ! [A: nat] :
% 5.27/5.52 ( ( bit_se6528837805403552850or_nat @ A @ A )
% 5.27/5.52 = zero_zero_nat ) ).
% 5.27/5.52
% 5.27/5.52 % xor_self_eq
% 5.27/5.52 thf(fact_4460_xor__self__eq,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( bit_se6526347334894502574or_int @ A @ A )
% 5.27/5.52 = zero_zero_int ) ).
% 5.27/5.52
% 5.27/5.52 % xor_self_eq
% 5.27/5.52 thf(fact_4461_xor_Oleft__neutral,axiom,
% 5.27/5.52 ! [A: nat] :
% 5.27/5.52 ( ( bit_se6528837805403552850or_nat @ zero_zero_nat @ A )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % xor.left_neutral
% 5.27/5.52 thf(fact_4462_xor_Oleft__neutral,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( bit_se6526347334894502574or_int @ zero_zero_int @ A )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % xor.left_neutral
% 5.27/5.52 thf(fact_4463_xor_Oright__neutral,axiom,
% 5.27/5.52 ! [A: nat] :
% 5.27/5.52 ( ( bit_se6528837805403552850or_nat @ A @ zero_zero_nat )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % xor.right_neutral
% 5.27/5.52 thf(fact_4464_xor_Oright__neutral,axiom,
% 5.27/5.52 ! [A: int] :
% 5.27/5.52 ( ( bit_se6526347334894502574or_int @ A @ zero_zero_int )
% 5.27/5.52 = A ) ).
% 5.27/5.52
% 5.27/5.52 % xor.right_neutral
% 5.27/5.52 thf(fact_4465_take__bit__xor,axiom,
% 5.27/5.52 ! [N2: nat,A: int,B: int] :
% 5.27/5.52 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.27/5.52 = ( bit_se6526347334894502574or_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_xor
% 5.27/5.52 thf(fact_4466_take__bit__xor,axiom,
% 5.27/5.52 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.52 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.27/5.52 = ( bit_se6528837805403552850or_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.27/5.52
% 5.27/5.52 % take_bit_xor
% 5.27/5.52 thf(fact_4467_concat__bit__of__zero__2,axiom,
% 5.27/5.52 ! [N2: nat,K: int] :
% 5.27/5.52 ( ( bit_concat_bit @ N2 @ K @ zero_zero_int )
% 5.27/5.52 = ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.27/5.52
% 5.27/5.52 % concat_bit_of_zero_2
% 5.27/5.52 thf(fact_4468_semiring__norm_I80_J,axiom,
% 5.27/5.52 ! [M: num,N2: num] :
% 5.27/5.52 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( ord_less_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(80)
% 5.27/5.53 thf(fact_4469_semiring__norm_I73_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(73)
% 5.27/5.53 thf(fact_4470_neg__less__eq__nonneg,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.27/5.53 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_eq_nonneg
% 5.27/5.53 thf(fact_4471_neg__less__eq__nonneg,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.27/5.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_eq_nonneg
% 5.27/5.53 thf(fact_4472_neg__less__eq__nonneg,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.27/5.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_eq_nonneg
% 5.27/5.53 thf(fact_4473_neg__less__eq__nonneg,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.27/5.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_eq_nonneg
% 5.27/5.53 thf(fact_4474_less__eq__neg__nonpos,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.27/5.53 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_eq_neg_nonpos
% 5.27/5.53 thf(fact_4475_less__eq__neg__nonpos,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_eq_neg_nonpos
% 5.27/5.53 thf(fact_4476_less__eq__neg__nonpos,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.27/5.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_eq_neg_nonpos
% 5.27/5.53 thf(fact_4477_less__eq__neg__nonpos,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.27/5.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_eq_neg_nonpos
% 5.27/5.53 thf(fact_4478_neg__le__0__iff__le,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.27/5.53 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_le_0_iff_le
% 5.27/5.53 thf(fact_4479_neg__le__0__iff__le,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.27/5.53 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_le_0_iff_le
% 5.27/5.53 thf(fact_4480_neg__le__0__iff__le,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.27/5.53 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_le_0_iff_le
% 5.27/5.53 thf(fact_4481_neg__le__0__iff__le,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.27/5.53 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_le_0_iff_le
% 5.27/5.53 thf(fact_4482_neg__0__le__iff__le,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.53 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_le_iff_le
% 5.27/5.53 thf(fact_4483_neg__0__le__iff__le,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.53 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_le_iff_le
% 5.27/5.53 thf(fact_4484_neg__0__le__iff__le,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.53 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_le_iff_le
% 5.27/5.53 thf(fact_4485_neg__0__le__iff__le,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.53 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_le_iff_le
% 5.27/5.53 thf(fact_4486_less__neg__neg,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.27/5.53 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_neg_neg
% 5.27/5.53 thf(fact_4487_less__neg__neg,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.27/5.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_neg_neg
% 5.27/5.53 thf(fact_4488_less__neg__neg,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_neg_neg
% 5.27/5.53 thf(fact_4489_less__neg__neg,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.27/5.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_neg_neg
% 5.27/5.53 thf(fact_4490_neg__less__pos,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.27/5.53 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_pos
% 5.27/5.53 thf(fact_4491_neg__less__pos,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.27/5.53 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_pos
% 5.27/5.53 thf(fact_4492_neg__less__pos,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.27/5.53 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_pos
% 5.27/5.53 thf(fact_4493_neg__less__pos,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.27/5.53 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_pos
% 5.27/5.53 thf(fact_4494_neg__0__less__iff__less,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.53 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_less_iff_less
% 5.27/5.53 thf(fact_4495_neg__0__less__iff__less,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.53 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_less_iff_less
% 5.27/5.53 thf(fact_4496_neg__0__less__iff__less,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.53 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_less_iff_less
% 5.27/5.53 thf(fact_4497_neg__0__less__iff__less,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.53 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_0_less_iff_less
% 5.27/5.53 thf(fact_4498_neg__less__0__iff__less,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.27/5.53 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_0_iff_less
% 5.27/5.53 thf(fact_4499_neg__less__0__iff__less,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.27/5.53 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_0_iff_less
% 5.27/5.53 thf(fact_4500_neg__less__0__iff__less,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.27/5.53 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_0_iff_less
% 5.27/5.53 thf(fact_4501_neg__less__0__iff__less,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.27/5.53 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_less_0_iff_less
% 5.27/5.53 thf(fact_4502_ab__left__minus,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % ab_left_minus
% 5.27/5.53 thf(fact_4503_ab__left__minus,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % ab_left_minus
% 5.27/5.53 thf(fact_4504_ab__left__minus,axiom,
% 5.27/5.53 ! [A: complex] :
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % ab_left_minus
% 5.27/5.53 thf(fact_4505_ab__left__minus,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % ab_left_minus
% 5.27/5.53 thf(fact_4506_ab__left__minus,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % ab_left_minus
% 5.27/5.53 thf(fact_4507_add_Oright__inverse,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % add.right_inverse
% 5.27/5.53 thf(fact_4508_add_Oright__inverse,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % add.right_inverse
% 5.27/5.53 thf(fact_4509_add_Oright__inverse,axiom,
% 5.27/5.53 ! [A: complex] :
% 5.27/5.53 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % add.right_inverse
% 5.27/5.53 thf(fact_4510_add_Oright__inverse,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % add.right_inverse
% 5.27/5.53 thf(fact_4511_add_Oright__inverse,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % add.right_inverse
% 5.27/5.53 thf(fact_4512_diff__0,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.27/5.53 = ( uminus_uminus_real @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_0
% 5.27/5.53 thf(fact_4513_diff__0,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.27/5.53 = ( uminus_uminus_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_0
% 5.27/5.53 thf(fact_4514_diff__0,axiom,
% 5.27/5.53 ! [A: complex] :
% 5.27/5.53 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_0
% 5.27/5.53 thf(fact_4515_diff__0,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_0
% 5.27/5.53 thf(fact_4516_diff__0,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.27/5.53 = ( uminus_uminus_rat @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_0
% 5.27/5.53 thf(fact_4517_add__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4518_add__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4519_add__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4520_add__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4521_add__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4522_mult__minus1,axiom,
% 5.27/5.53 ! [Z: real] :
% 5.27/5.53 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.27/5.53 = ( uminus_uminus_real @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1
% 5.27/5.53 thf(fact_4523_mult__minus1,axiom,
% 5.27/5.53 ! [Z: int] :
% 5.27/5.53 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.27/5.53 = ( uminus_uminus_int @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1
% 5.27/5.53 thf(fact_4524_mult__minus1,axiom,
% 5.27/5.53 ! [Z: complex] :
% 5.27/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1
% 5.27/5.53 thf(fact_4525_mult__minus1,axiom,
% 5.27/5.53 ! [Z: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1
% 5.27/5.53 thf(fact_4526_mult__minus1,axiom,
% 5.27/5.53 ! [Z: rat] :
% 5.27/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.27/5.53 = ( uminus_uminus_rat @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1
% 5.27/5.53 thf(fact_4527_mult__minus1__right,axiom,
% 5.27/5.53 ! [Z: real] :
% 5.27/5.53 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( uminus_uminus_real @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1_right
% 5.27/5.53 thf(fact_4528_mult__minus1__right,axiom,
% 5.27/5.53 ! [Z: int] :
% 5.27/5.53 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( uminus_uminus_int @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1_right
% 5.27/5.53 thf(fact_4529_mult__minus1__right,axiom,
% 5.27/5.53 ! [Z: complex] :
% 5.27/5.53 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1_right
% 5.27/5.53 thf(fact_4530_mult__minus1__right,axiom,
% 5.27/5.53 ! [Z: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1_right
% 5.27/5.53 thf(fact_4531_mult__minus1__right,axiom,
% 5.27/5.53 ! [Z: rat] :
% 5.27/5.53 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( uminus_uminus_rat @ Z ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_minus1_right
% 5.27/5.53 thf(fact_4532_uminus__add__conv__diff,axiom,
% 5.27/5.53 ! [A: real,B: real] :
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.53 = ( minus_minus_real @ B @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % uminus_add_conv_diff
% 5.27/5.53 thf(fact_4533_uminus__add__conv__diff,axiom,
% 5.27/5.53 ! [A: int,B: int] :
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.53 = ( minus_minus_int @ B @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % uminus_add_conv_diff
% 5.27/5.53 thf(fact_4534_uminus__add__conv__diff,axiom,
% 5.27/5.53 ! [A: complex,B: complex] :
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.27/5.53 = ( minus_minus_complex @ B @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % uminus_add_conv_diff
% 5.27/5.53 thf(fact_4535_uminus__add__conv__diff,axiom,
% 5.27/5.53 ! [A: code_integer,B: code_integer] :
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.53 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % uminus_add_conv_diff
% 5.27/5.53 thf(fact_4536_uminus__add__conv__diff,axiom,
% 5.27/5.53 ! [A: rat,B: rat] :
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.53 = ( minus_minus_rat @ B @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % uminus_add_conv_diff
% 5.27/5.53 thf(fact_4537_diff__minus__eq__add,axiom,
% 5.27/5.53 ! [A: real,B: real] :
% 5.27/5.53 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.27/5.53 = ( plus_plus_real @ A @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_minus_eq_add
% 5.27/5.53 thf(fact_4538_diff__minus__eq__add,axiom,
% 5.27/5.53 ! [A: int,B: int] :
% 5.27/5.53 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.53 = ( plus_plus_int @ A @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_minus_eq_add
% 5.27/5.53 thf(fact_4539_diff__minus__eq__add,axiom,
% 5.27/5.53 ! [A: complex,B: complex] :
% 5.27/5.53 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.53 = ( plus_plus_complex @ A @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_minus_eq_add
% 5.27/5.53 thf(fact_4540_diff__minus__eq__add,axiom,
% 5.27/5.53 ! [A: code_integer,B: code_integer] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.53 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_minus_eq_add
% 5.27/5.53 thf(fact_4541_diff__minus__eq__add,axiom,
% 5.27/5.53 ! [A: rat,B: rat] :
% 5.27/5.53 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.27/5.53 = ( plus_plus_rat @ A @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_minus_eq_add
% 5.27/5.53 thf(fact_4542_divide__minus1,axiom,
% 5.27/5.53 ! [X4: real] :
% 5.27/5.53 ( ( divide_divide_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( uminus_uminus_real @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_minus1
% 5.27/5.53 thf(fact_4543_divide__minus1,axiom,
% 5.27/5.53 ! [X4: complex] :
% 5.27/5.53 ( ( divide1717551699836669952omplex @ X4 @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_minus1
% 5.27/5.53 thf(fact_4544_divide__minus1,axiom,
% 5.27/5.53 ! [X4: rat] :
% 5.27/5.53 ( ( divide_divide_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( uminus_uminus_rat @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_minus1
% 5.27/5.53 thf(fact_4545_div__minus1__right,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( uminus_uminus_int @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % div_minus1_right
% 5.27/5.53 thf(fact_4546_div__minus1__right,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.27/5.53
% 5.27/5.53 % div_minus1_right
% 5.27/5.53 thf(fact_4547_of__nat__0,axiom,
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0
% 5.27/5.53 thf(fact_4548_of__nat__0,axiom,
% 5.27/5.53 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0
% 5.27/5.53 thf(fact_4549_of__nat__0,axiom,
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0
% 5.27/5.53 thf(fact_4550_of__nat__0,axiom,
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0
% 5.27/5.53 thf(fact_4551_of__nat__0,axiom,
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.27/5.53 = zero_zero_nat ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0
% 5.27/5.53 thf(fact_4552_of__nat__0__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( zero_zero_complex
% 5.27/5.53 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.27/5.53 = ( zero_zero_nat = N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_eq_iff
% 5.27/5.53 thf(fact_4553_of__nat__0__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( zero_zero_rat
% 5.27/5.53 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.53 = ( zero_zero_nat = N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_eq_iff
% 5.27/5.53 thf(fact_4554_of__nat__0__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( zero_zero_real
% 5.27/5.53 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( zero_zero_nat = N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_eq_iff
% 5.27/5.53 thf(fact_4555_of__nat__0__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( zero_zero_int
% 5.27/5.53 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( zero_zero_nat = N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_eq_iff
% 5.27/5.53 thf(fact_4556_of__nat__0__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( zero_zero_nat
% 5.27/5.53 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( zero_zero_nat = N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_eq_iff
% 5.27/5.53 thf(fact_4557_of__nat__eq__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ( semiri8010041392384452111omplex @ M )
% 5.27/5.53 = zero_zero_complex )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_0_iff
% 5.27/5.53 thf(fact_4558_of__nat__eq__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ( semiri681578069525770553at_rat @ M )
% 5.27/5.53 = zero_zero_rat )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_0_iff
% 5.27/5.53 thf(fact_4559_of__nat__eq__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ( semiri5074537144036343181t_real @ M )
% 5.27/5.53 = zero_zero_real )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_0_iff
% 5.27/5.53 thf(fact_4560_of__nat__eq__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ( semiri1314217659103216013at_int @ M )
% 5.27/5.53 = zero_zero_int )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_0_iff
% 5.27/5.53 thf(fact_4561_of__nat__eq__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.27/5.53 = zero_zero_nat )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_0_iff
% 5.27/5.53 thf(fact_4562_of__nat__less__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_iff
% 5.27/5.53 thf(fact_4563_of__nat__less__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_iff
% 5.27/5.53 thf(fact_4564_of__nat__less__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_iff
% 5.27/5.53 thf(fact_4565_of__nat__less__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_iff
% 5.27/5.53 thf(fact_4566_of__nat__le__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_iff
% 5.27/5.53 thf(fact_4567_of__nat__le__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_iff
% 5.27/5.53 thf(fact_4568_of__nat__le__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_iff
% 5.27/5.53 thf(fact_4569_of__nat__le__iff,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_iff
% 5.27/5.53 thf(fact_4570_of__nat__numeral,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( semiri4216267220026989637d_enat @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.53 = ( numera1916890842035813515d_enat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_numeral
% 5.27/5.53 thf(fact_4571_of__nat__numeral,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.53 = ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_numeral
% 5.27/5.53 thf(fact_4572_of__nat__numeral,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.53 = ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_numeral
% 5.27/5.53 thf(fact_4573_of__nat__numeral,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.53 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_numeral
% 5.27/5.53 thf(fact_4574_of__nat__numeral,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.53 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_numeral
% 5.27/5.53 thf(fact_4575_minus__mod__self1,axiom,
% 5.27/5.53 ! [B: int,A: int] :
% 5.27/5.53 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.27/5.53 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % minus_mod_self1
% 5.27/5.53 thf(fact_4576_minus__mod__self1,axiom,
% 5.27/5.53 ! [B: code_integer,A: code_integer] :
% 5.27/5.53 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.27/5.53 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % minus_mod_self1
% 5.27/5.53 thf(fact_4577_of__nat__add,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N2 ) )
% 5.27/5.53 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_add
% 5.27/5.53 thf(fact_4578_of__nat__add,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N2 ) )
% 5.27/5.53 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_add
% 5.27/5.53 thf(fact_4579_of__nat__add,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) )
% 5.27/5.53 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_add
% 5.27/5.53 thf(fact_4580_of__nat__add,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.27/5.53 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_add
% 5.27/5.53 thf(fact_4581_of__nat__mult,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N2 ) )
% 5.27/5.53 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_mult
% 5.27/5.53 thf(fact_4582_of__nat__mult,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N2 ) )
% 5.27/5.53 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_mult
% 5.27/5.53 thf(fact_4583_of__nat__mult,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N2 ) )
% 5.27/5.53 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_mult
% 5.27/5.53 thf(fact_4584_of__nat__mult,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N2 ) )
% 5.27/5.53 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_mult
% 5.27/5.53 thf(fact_4585_take__bit__0,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_0
% 5.27/5.53 thf(fact_4586_take__bit__0,axiom,
% 5.27/5.53 ! [A: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.27/5.53 = zero_zero_nat ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_0
% 5.27/5.53 thf(fact_4587_of__nat__eq__1__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( semiri8010041392384452111omplex @ N2 )
% 5.27/5.53 = one_one_complex )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_1_iff
% 5.27/5.53 thf(fact_4588_of__nat__eq__1__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( semiri681578069525770553at_rat @ N2 )
% 5.27/5.53 = one_one_rat )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_1_iff
% 5.27/5.53 thf(fact_4589_of__nat__eq__1__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( semiri5074537144036343181t_real @ N2 )
% 5.27/5.53 = one_one_real )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_1_iff
% 5.27/5.53 thf(fact_4590_of__nat__eq__1__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( semiri1314217659103216013at_int @ N2 )
% 5.27/5.53 = one_one_int )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_1_iff
% 5.27/5.53 thf(fact_4591_of__nat__eq__1__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( semiri1316708129612266289at_nat @ N2 )
% 5.27/5.53 = one_one_nat )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_1_iff
% 5.27/5.53 thf(fact_4592_of__nat__1__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( one_one_complex
% 5.27/5.53 = ( semiri8010041392384452111omplex @ N2 ) )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1_eq_iff
% 5.27/5.53 thf(fact_4593_of__nat__1__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( one_one_rat
% 5.27/5.53 = ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1_eq_iff
% 5.27/5.53 thf(fact_4594_of__nat__1__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( one_one_real
% 5.27/5.53 = ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1_eq_iff
% 5.27/5.53 thf(fact_4595_of__nat__1__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( one_one_int
% 5.27/5.53 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1_eq_iff
% 5.27/5.53 thf(fact_4596_of__nat__1__eq__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( one_one_nat
% 5.27/5.53 = ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( N2 = one_one_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1_eq_iff
% 5.27/5.53 thf(fact_4597_of__nat__1,axiom,
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.27/5.53 = one_one_complex ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1
% 5.27/5.53 thf(fact_4598_of__nat__1,axiom,
% 5.27/5.53 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.27/5.53 = one_one_rat ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1
% 5.27/5.53 thf(fact_4599_of__nat__1,axiom,
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.27/5.53 = one_one_real ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1
% 5.27/5.53 thf(fact_4600_of__nat__1,axiom,
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1
% 5.27/5.53 thf(fact_4601_of__nat__1,axiom,
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.27/5.53 = one_one_nat ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_1
% 5.27/5.53 thf(fact_4602_take__bit__Suc__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ one_one_int )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_Suc_1
% 5.27/5.53 thf(fact_4603_take__bit__Suc__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ one_one_nat )
% 5.27/5.53 = one_one_nat ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_Suc_1
% 5.27/5.53 thf(fact_4604_take__bit__numeral__1,axiom,
% 5.27/5.53 ! [L: num] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ one_one_int )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_numeral_1
% 5.27/5.53 thf(fact_4605_take__bit__numeral__1,axiom,
% 5.27/5.53 ! [L: num] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ one_one_nat )
% 5.27/5.53 = one_one_nat ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_numeral_1
% 5.27/5.53 thf(fact_4606_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ( semiri8010041392384452111omplex @ X4 )
% 5.27/5.53 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.27/5.53 = ( X4
% 5.27/5.53 = ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4607_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ( semiri5074537144036343181t_real @ X4 )
% 5.27/5.53 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.27/5.53 = ( X4
% 5.27/5.53 = ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4608_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ( semiri1314217659103216013at_int @ X4 )
% 5.27/5.53 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.27/5.53 = ( X4
% 5.27/5.53 = ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4609_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ( semiri1316708129612266289at_nat @ X4 )
% 5.27/5.53 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.27/5.53 = ( X4
% 5.27/5.53 = ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4610_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.27/5.53 = ( semiri8010041392384452111omplex @ X4 ) )
% 5.27/5.53 = ( ( power_power_nat @ B @ W )
% 5.27/5.53 = X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4611_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.27/5.53 = ( semiri5074537144036343181t_real @ X4 ) )
% 5.27/5.53 = ( ( power_power_nat @ B @ W )
% 5.27/5.53 = X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4612_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.27/5.53 = ( semiri1314217659103216013at_int @ X4 ) )
% 5.27/5.53 = ( ( power_power_nat @ B @ W )
% 5.27/5.53 = X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4613_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.27/5.53 = ( semiri1316708129612266289at_nat @ X4 ) )
% 5.27/5.53 = ( ( power_power_nat @ B @ W )
% 5.27/5.53 = X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_eq_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4614_of__nat__power,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N2 ) )
% 5.27/5.53 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power
% 5.27/5.53 thf(fact_4615_of__nat__power,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N2 ) )
% 5.27/5.53 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power
% 5.27/5.53 thf(fact_4616_of__nat__power,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N2 ) )
% 5.27/5.53 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power
% 5.27/5.53 thf(fact_4617_of__nat__power,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N2 ) )
% 5.27/5.53 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power
% 5.27/5.53 thf(fact_4618_signed__take__bit__of__minus__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_ri6519982836138164636nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_of_minus_1
% 5.27/5.53 thf(fact_4619_signed__take__bit__of__minus__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_of_minus_1
% 5.27/5.53 thf(fact_4620_semiring__norm_I9_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.53 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(9)
% 5.27/5.53 thf(fact_4621_semiring__norm_I7_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( bit1 @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(7)
% 5.27/5.53 thf(fact_4622_semiring__norm_I15_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.53 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(15)
% 5.27/5.53 thf(fact_4623_semiring__norm_I14_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(14)
% 5.27/5.53 thf(fact_4624_semiring__norm_I81_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.53 = ( ord_less_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(81)
% 5.27/5.53 thf(fact_4625_semiring__norm_I72_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(72)
% 5.27/5.53 thf(fact_4626_semiring__norm_I77_J,axiom,
% 5.27/5.53 ! [N2: num] : ( ord_less_num @ one @ ( bit1 @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(77)
% 5.27/5.53 thf(fact_4627_semiring__norm_I70_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(70)
% 5.27/5.53 thf(fact_4628_dbl__simps_I1_J,axiom,
% 5.27/5.53 ! [K: num] :
% 5.27/5.53 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(1)
% 5.27/5.53 thf(fact_4629_dbl__simps_I1_J,axiom,
% 5.27/5.53 ! [K: num] :
% 5.27/5.53 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(1)
% 5.27/5.53 thf(fact_4630_dbl__simps_I1_J,axiom,
% 5.27/5.53 ! [K: num] :
% 5.27/5.53 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(1)
% 5.27/5.53 thf(fact_4631_dbl__simps_I1_J,axiom,
% 5.27/5.53 ! [K: num] :
% 5.27/5.53 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(1)
% 5.27/5.53 thf(fact_4632_dbl__simps_I1_J,axiom,
% 5.27/5.53 ! [K: num] :
% 5.27/5.53 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(1)
% 5.27/5.53 thf(fact_4633_of__nat__of__bool,axiom,
% 5.27/5.53 ! [P: $o] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.27/5.53 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_of_bool
% 5.27/5.53 thf(fact_4634_of__nat__of__bool,axiom,
% 5.27/5.53 ! [P: $o] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.27/5.53 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_of_bool
% 5.27/5.53 thf(fact_4635_of__nat__of__bool,axiom,
% 5.27/5.53 ! [P: $o] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.27/5.53 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_of_bool
% 5.27/5.53 thf(fact_4636_of__nat__of__bool,axiom,
% 5.27/5.53 ! [P: $o] :
% 5.27/5.53 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.27/5.53 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_of_bool
% 5.27/5.53 thf(fact_4637_add__neg__numeral__special_I7_J,axiom,
% 5.27/5.53 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(7)
% 5.27/5.53 thf(fact_4638_add__neg__numeral__special_I7_J,axiom,
% 5.27/5.53 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(7)
% 5.27/5.53 thf(fact_4639_add__neg__numeral__special_I7_J,axiom,
% 5.27/5.53 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(7)
% 5.27/5.53 thf(fact_4640_add__neg__numeral__special_I7_J,axiom,
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(7)
% 5.27/5.53 thf(fact_4641_add__neg__numeral__special_I7_J,axiom,
% 5.27/5.53 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(7)
% 5.27/5.53 thf(fact_4642_add__neg__numeral__special_I8_J,axiom,
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(8)
% 5.27/5.53 thf(fact_4643_add__neg__numeral__special_I8_J,axiom,
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(8)
% 5.27/5.53 thf(fact_4644_add__neg__numeral__special_I8_J,axiom,
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(8)
% 5.27/5.53 thf(fact_4645_add__neg__numeral__special_I8_J,axiom,
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(8)
% 5.27/5.53 thf(fact_4646_add__neg__numeral__special_I8_J,axiom,
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(8)
% 5.27/5.53 thf(fact_4647_diff__numeral__special_I12_J,axiom,
% 5.27/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = zero_zero_real ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(12)
% 5.27/5.53 thf(fact_4648_diff__numeral__special_I12_J,axiom,
% 5.27/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(12)
% 5.27/5.53 thf(fact_4649_diff__numeral__special_I12_J,axiom,
% 5.27/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = zero_zero_complex ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(12)
% 5.27/5.53 thf(fact_4650_diff__numeral__special_I12_J,axiom,
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(12)
% 5.27/5.53 thf(fact_4651_diff__numeral__special_I12_J,axiom,
% 5.27/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = zero_zero_rat ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(12)
% 5.27/5.53 thf(fact_4652_numeral__eq__neg__one__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_eq_neg_one_iff
% 5.27/5.53 thf(fact_4653_numeral__eq__neg__one__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_eq_neg_one_iff
% 5.27/5.53 thf(fact_4654_numeral__eq__neg__one__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_eq_neg_one_iff
% 5.27/5.53 thf(fact_4655_numeral__eq__neg__one__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_eq_neg_one_iff
% 5.27/5.53 thf(fact_4656_numeral__eq__neg__one__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_eq_neg_one_iff
% 5.27/5.53 thf(fact_4657_neg__one__eq__numeral__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_real @ one_one_real )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_eq_numeral_iff
% 5.27/5.53 thf(fact_4658_neg__one__eq__numeral__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_int @ one_one_int )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_eq_numeral_iff
% 5.27/5.53 thf(fact_4659_neg__one__eq__numeral__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_eq_numeral_iff
% 5.27/5.53 thf(fact_4660_neg__one__eq__numeral__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_eq_numeral_iff
% 5.27/5.53 thf(fact_4661_neg__one__eq__numeral__iff,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( N2 = one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_eq_numeral_iff
% 5.27/5.53 thf(fact_4662_of__nat__le__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_0_iff
% 5.27/5.53 thf(fact_4663_of__nat__le__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_0_iff
% 5.27/5.53 thf(fact_4664_of__nat__le__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_0_iff
% 5.27/5.53 thf(fact_4665_of__nat__le__0__iff,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.27/5.53 = ( M = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_0_iff
% 5.27/5.53 thf(fact_4666_left__minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat,A: real] :
% 5.27/5.53 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ A ) )
% 5.27/5.53 = A ) ).
% 5.27/5.53
% 5.27/5.53 % left_minus_one_mult_self
% 5.27/5.53 thf(fact_4667_left__minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat,A: int] :
% 5.27/5.53 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ A ) )
% 5.27/5.53 = A ) ).
% 5.27/5.53
% 5.27/5.53 % left_minus_one_mult_self
% 5.27/5.53 thf(fact_4668_left__minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat,A: complex] :
% 5.27/5.53 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ A ) )
% 5.27/5.53 = A ) ).
% 5.27/5.53
% 5.27/5.53 % left_minus_one_mult_self
% 5.27/5.53 thf(fact_4669_left__minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat,A: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ A ) )
% 5.27/5.53 = A ) ).
% 5.27/5.53
% 5.27/5.53 % left_minus_one_mult_self
% 5.27/5.53 thf(fact_4670_left__minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat,A: rat] :
% 5.27/5.53 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ A ) )
% 5.27/5.53 = A ) ).
% 5.27/5.53
% 5.27/5.53 % left_minus_one_mult_self
% 5.27/5.53 thf(fact_4671_minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) )
% 5.27/5.53 = one_one_real ) ).
% 5.27/5.53
% 5.27/5.53 % minus_one_mult_self
% 5.27/5.53 thf(fact_4672_minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % minus_one_mult_self
% 5.27/5.53 thf(fact_4673_minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) )
% 5.27/5.53 = one_one_complex ) ).
% 5.27/5.53
% 5.27/5.53 % minus_one_mult_self
% 5.27/5.53 thf(fact_4674_minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) )
% 5.27/5.53 = one_one_Code_integer ) ).
% 5.27/5.53
% 5.27/5.53 % minus_one_mult_self
% 5.27/5.53 thf(fact_4675_minus__one__mult__self,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) )
% 5.27/5.53 = one_one_rat ) ).
% 5.27/5.53
% 5.27/5.53 % minus_one_mult_self
% 5.27/5.53 thf(fact_4676_mod__minus1__right,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = zero_zero_int ) ).
% 5.27/5.53
% 5.27/5.53 % mod_minus1_right
% 5.27/5.53 thf(fact_4677_mod__minus1__right,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = zero_z3403309356797280102nteger ) ).
% 5.27/5.53
% 5.27/5.53 % mod_minus1_right
% 5.27/5.53 thf(fact_4678_of__nat__Suc,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.27/5.53 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_Suc
% 5.27/5.53 thf(fact_4679_of__nat__Suc,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.27/5.53 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_Suc
% 5.27/5.53 thf(fact_4680_of__nat__Suc,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.27/5.53 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_Suc
% 5.27/5.53 thf(fact_4681_of__nat__Suc,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.27/5.53 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_Suc
% 5.27/5.53 thf(fact_4682_of__nat__Suc,axiom,
% 5.27/5.53 ! [M: nat] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.27/5.53 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_Suc
% 5.27/5.53 thf(fact_4683_take__bit__of__1__eq__0__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.27/5.53 = zero_zero_int )
% 5.27/5.53 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_1_eq_0_iff
% 5.27/5.53 thf(fact_4684_take__bit__of__1__eq__0__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.27/5.53 = zero_zero_nat )
% 5.27/5.53 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_1_eq_0_iff
% 5.27/5.53 thf(fact_4685_semiring__norm_I168_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: real] :
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.27/5.53 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(168)
% 5.27/5.53 thf(fact_4686_semiring__norm_I168_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: int] :
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.27/5.53 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(168)
% 5.27/5.53 thf(fact_4687_semiring__norm_I168_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: complex] :
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.27/5.53 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(168)
% 5.27/5.53 thf(fact_4688_semiring__norm_I168_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: code_integer] :
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.27/5.53 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(168)
% 5.27/5.53 thf(fact_4689_semiring__norm_I168_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: rat] :
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.27/5.53 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(168)
% 5.27/5.53 thf(fact_4690_diff__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(3)
% 5.27/5.53 thf(fact_4691_diff__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(3)
% 5.27/5.53 thf(fact_4692_diff__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(3)
% 5.27/5.53 thf(fact_4693_diff__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(3)
% 5.27/5.53 thf(fact_4694_diff__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(3)
% 5.27/5.53 thf(fact_4695_diff__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(2)
% 5.27/5.53 thf(fact_4696_diff__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(2)
% 5.27/5.53 thf(fact_4697_diff__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(2)
% 5.27/5.53 thf(fact_4698_diff__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(2)
% 5.27/5.53 thf(fact_4699_diff__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_simps(2)
% 5.27/5.53 thf(fact_4700_zdiv__numeral__Bit1,axiom,
% 5.27/5.53 ! [V: num,W: num] :
% 5.27/5.53 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.27/5.53 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % zdiv_numeral_Bit1
% 5.27/5.53 thf(fact_4701_semiring__norm_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( plus_plus_num @ one @ ( bit0 @ N2 ) )
% 5.27/5.53 = ( bit1 @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(3)
% 5.27/5.53 thf(fact_4702_semiring__norm_I4_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( plus_plus_num @ one @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( bit0 @ ( plus_plus_num @ N2 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(4)
% 5.27/5.53 thf(fact_4703_semiring__norm_I5_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.27/5.53 = ( bit1 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(5)
% 5.27/5.53 thf(fact_4704_semiring__norm_I8_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.27/5.53 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(8)
% 5.27/5.53 thf(fact_4705_semiring__norm_I10_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(10)
% 5.27/5.53 thf(fact_4706_semiring__norm_I172_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: real] :
% 5.27/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(172)
% 5.27/5.53 thf(fact_4707_semiring__norm_I172_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: int] :
% 5.27/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(172)
% 5.27/5.53 thf(fact_4708_semiring__norm_I172_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: complex] :
% 5.27/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(172)
% 5.27/5.53 thf(fact_4709_semiring__norm_I172_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(172)
% 5.27/5.53 thf(fact_4710_semiring__norm_I172_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: rat] :
% 5.27/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(172)
% 5.27/5.53 thf(fact_4711_semiring__norm_I171_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: real] :
% 5.27/5.53 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(171)
% 5.27/5.53 thf(fact_4712_semiring__norm_I171_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: int] :
% 5.27/5.53 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(171)
% 5.27/5.53 thf(fact_4713_semiring__norm_I171_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: complex] :
% 5.27/5.53 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(171)
% 5.27/5.53 thf(fact_4714_semiring__norm_I171_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(171)
% 5.27/5.53 thf(fact_4715_semiring__norm_I171_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: rat] :
% 5.27/5.53 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.27/5.53 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(171)
% 5.27/5.53 thf(fact_4716_semiring__norm_I170_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: real] :
% 5.27/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.27/5.53 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(170)
% 5.27/5.53 thf(fact_4717_semiring__norm_I170_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: int] :
% 5.27/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.27/5.53 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(170)
% 5.27/5.53 thf(fact_4718_semiring__norm_I170_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: complex] :
% 5.27/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.27/5.53 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(170)
% 5.27/5.53 thf(fact_4719_semiring__norm_I170_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: code_integer] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.27/5.53 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(170)
% 5.27/5.53 thf(fact_4720_semiring__norm_I170_J,axiom,
% 5.27/5.53 ! [V: num,W: num,Y: rat] :
% 5.27/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.27/5.53 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(170)
% 5.27/5.53 thf(fact_4721_mult__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4722_mult__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4723_mult__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4724_mult__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4725_mult__neg__numeral__simps_I3_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(3)
% 5.27/5.53 thf(fact_4726_mult__neg__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(2)
% 5.27/5.53 thf(fact_4727_mult__neg__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(2)
% 5.27/5.53 thf(fact_4728_mult__neg__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(2)
% 5.27/5.53 thf(fact_4729_mult__neg__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(2)
% 5.27/5.53 thf(fact_4730_mult__neg__numeral__simps_I2_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(2)
% 5.27/5.53 thf(fact_4731_mult__neg__numeral__simps_I1_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_real @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(1)
% 5.27/5.53 thf(fact_4732_mult__neg__numeral__simps_I1_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(1)
% 5.27/5.53 thf(fact_4733_mult__neg__numeral__simps_I1_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(1)
% 5.27/5.53 thf(fact_4734_mult__neg__numeral__simps_I1_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(1)
% 5.27/5.53 thf(fact_4735_mult__neg__numeral__simps_I1_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_rat @ ( times_times_num @ M @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mult_neg_numeral_simps(1)
% 5.27/5.53 thf(fact_4736_neg__numeral__le__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_le_iff
% 5.27/5.53 thf(fact_4737_neg__numeral__le__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_le_iff
% 5.27/5.53 thf(fact_4738_neg__numeral__le__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_le_iff
% 5.27/5.53 thf(fact_4739_neg__numeral__le__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( ord_less_eq_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_le_iff
% 5.27/5.53 thf(fact_4740_neg__numeral__less__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( ord_less_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_iff
% 5.27/5.53 thf(fact_4741_neg__numeral__less__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( ord_less_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_iff
% 5.27/5.53 thf(fact_4742_neg__numeral__less__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( ord_less_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_iff
% 5.27/5.53 thf(fact_4743_neg__numeral__less__iff,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( ord_less_num @ N2 @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_iff
% 5.27/5.53 thf(fact_4744_take__bit__of__Suc__0,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.53 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_Suc_0
% 5.27/5.53 thf(fact_4745_semiring__norm_I16_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N2 ) @ ( bit0 @ ( times_times_num @ M @ N2 ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(16)
% 5.27/5.53 thf(fact_4746_semiring__norm_I79_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(79)
% 5.27/5.53 thf(fact_4747_semiring__norm_I74_J,axiom,
% 5.27/5.53 ! [M: num,N2: num] :
% 5.27/5.53 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.53 = ( ord_less_num @ M @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % semiring_norm(74)
% 5.27/5.53 thf(fact_4748_not__neg__one__le__neg__numeral__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % not_neg_one_le_neg_numeral_iff
% 5.27/5.53 thf(fact_4749_not__neg__one__le__neg__numeral__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % not_neg_one_le_neg_numeral_iff
% 5.27/5.53 thf(fact_4750_not__neg__one__le__neg__numeral__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % not_neg_one_le_neg_numeral_iff
% 5.27/5.53 thf(fact_4751_not__neg__one__le__neg__numeral__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % not_neg_one_le_neg_numeral_iff
% 5.27/5.53 thf(fact_4752_le__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: real,B: real,W: num] :
% 5.27/5.53 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.27/5.53 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % le_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4753_le__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: rat,B: rat,W: num] :
% 5.27/5.53 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.27/5.53 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % le_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4754_divide__le__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: real,W: num,A: real] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.27/5.53 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_le_eq_numeral1(2)
% 5.27/5.53 thf(fact_4755_divide__le__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: rat,W: num,A: rat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.27/5.53 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_le_eq_numeral1(2)
% 5.27/5.53 thf(fact_4756_eq__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: real,B: real,W: num] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.27/5.53 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.53 != zero_zero_real )
% 5.27/5.53 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.53 = B ) )
% 5.27/5.53 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.53 = zero_zero_real )
% 5.27/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % eq_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4757_eq__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: complex,B: complex,W: num] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.27/5.53 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.53 != zero_zero_complex )
% 5.27/5.53 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.53 = B ) )
% 5.27/5.53 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.53 = zero_zero_complex )
% 5.27/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % eq_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4758_eq__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: rat,B: rat,W: num] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.27/5.53 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.53 != zero_zero_rat )
% 5.27/5.53 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.53 = B ) )
% 5.27/5.53 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.53 = zero_zero_rat )
% 5.27/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % eq_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4759_divide__eq__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: real,W: num,A: real] :
% 5.27/5.53 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.53 = A )
% 5.27/5.53 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.53 != zero_zero_real )
% 5.27/5.53 => ( B
% 5.27/5.53 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.27/5.53 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.53 = zero_zero_real )
% 5.27/5.53 => ( A = zero_zero_real ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_eq_eq_numeral1(2)
% 5.27/5.53 thf(fact_4760_divide__eq__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: complex,W: num,A: complex] :
% 5.27/5.53 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.53 = A )
% 5.27/5.53 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.53 != zero_zero_complex )
% 5.27/5.53 => ( B
% 5.27/5.53 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.27/5.53 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.53 = zero_zero_complex )
% 5.27/5.53 => ( A = zero_zero_complex ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_eq_eq_numeral1(2)
% 5.27/5.53 thf(fact_4761_divide__eq__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: rat,W: num,A: rat] :
% 5.27/5.53 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.53 = A )
% 5.27/5.53 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.53 != zero_zero_rat )
% 5.27/5.53 => ( B
% 5.27/5.53 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.27/5.53 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.53 = zero_zero_rat )
% 5.27/5.53 => ( A = zero_zero_rat ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_eq_eq_numeral1(2)
% 5.27/5.53 thf(fact_4762_neg__numeral__less__neg__one__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_neg_one_iff
% 5.27/5.53 thf(fact_4763_neg__numeral__less__neg__one__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_neg_one_iff
% 5.27/5.53 thf(fact_4764_neg__numeral__less__neg__one__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_neg_one_iff
% 5.27/5.53 thf(fact_4765_neg__numeral__less__neg__one__iff,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( M != one ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_numeral_less_neg_one_iff
% 5.27/5.53 thf(fact_4766_less__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: real,B: real,W: num] :
% 5.27/5.53 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.27/5.53 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4767_less__divide__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [A: rat,B: rat,W: num] :
% 5.27/5.53 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.27/5.53 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % less_divide_eq_numeral1(2)
% 5.27/5.53 thf(fact_4768_divide__less__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: real,W: num,A: real] :
% 5.27/5.53 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.27/5.53 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_less_eq_numeral1(2)
% 5.27/5.53 thf(fact_4769_divide__less__eq__numeral1_I2_J,axiom,
% 5.27/5.53 ! [B: rat,W: num,A: rat] :
% 5.27/5.53 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.27/5.53 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.27/5.53
% 5.27/5.53 % divide_less_eq_numeral1(2)
% 5.27/5.53 thf(fact_4770_of__nat__0__less__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_less_iff
% 5.27/5.53 thf(fact_4771_of__nat__0__less__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_less_iff
% 5.27/5.53 thf(fact_4772_of__nat__0__less__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_less_iff
% 5.27/5.53 thf(fact_4773_of__nat__0__less__iff,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_0_less_iff
% 5.27/5.53 thf(fact_4774_power2__minus,axiom,
% 5.27/5.53 ! [A: real] :
% 5.27/5.53 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power2_minus
% 5.27/5.53 thf(fact_4775_power2__minus,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power2_minus
% 5.27/5.53 thf(fact_4776_power2__minus,axiom,
% 5.27/5.53 ! [A: complex] :
% 5.27/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power2_minus
% 5.27/5.53 thf(fact_4777_power2__minus,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power2_minus
% 5.27/5.53 thf(fact_4778_power2__minus,axiom,
% 5.27/5.53 ! [A: rat] :
% 5.27/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power2_minus
% 5.27/5.53 thf(fact_4779_xor__numerals_I3_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(3)
% 5.27/5.53 thf(fact_4780_xor__numerals_I3_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(3)
% 5.27/5.53 thf(fact_4781_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4782_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4783_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4784_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4785_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4786_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4787_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4788_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4789_xor__numerals_I1_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(1)
% 5.27/5.53 thf(fact_4790_xor__numerals_I1_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( bit1 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(1)
% 5.27/5.53 thf(fact_4791_xor__numerals_I2_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(2)
% 5.27/5.53 thf(fact_4792_xor__numerals_I2_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( bit0 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(2)
% 5.27/5.53 thf(fact_4793_xor__numerals_I5_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(5)
% 5.27/5.53 thf(fact_4794_xor__numerals_I5_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 5.27/5.53 = ( numeral_numeral_int @ ( bit1 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(5)
% 5.27/5.53 thf(fact_4795_xor__numerals_I8_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(8)
% 5.27/5.53 thf(fact_4796_xor__numerals_I8_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 5.27/5.53 = ( numeral_numeral_int @ ( bit0 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(8)
% 5.27/5.53 thf(fact_4797_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4798_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4799_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4800_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,B: nat,W: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ B @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4801_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4802_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4803_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4804_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.27/5.53 ! [B: nat,W: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_of_nat_power_cancel_iff
% 5.27/5.53 thf(fact_4805_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [Y: nat,X4: num,N2: nat] :
% 5.27/5.53 ( ( ( semiri4216267220026989637d_enat @ Y )
% 5.27/5.53 = ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 ) )
% 5.27/5.53 = ( Y
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_eq_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4806_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [Y: nat,X4: num,N2: nat] :
% 5.27/5.53 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.27/5.53 = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 5.27/5.53 = ( Y
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_eq_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4807_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [Y: nat,X4: num,N2: nat] :
% 5.27/5.53 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.27/5.53 = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.53 = ( Y
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_eq_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4808_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [Y: nat,X4: num,N2: nat] :
% 5.27/5.53 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.27/5.53 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 5.27/5.53 = ( Y
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_eq_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4809_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [Y: nat,X4: num,N2: nat] :
% 5.27/5.53 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 5.27/5.53 = ( Y
% 5.27/5.53 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_eq_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4810_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: num,N2: nat,Y: nat] :
% 5.27/5.53 ( ( ( power_8040749407984259932d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ N2 )
% 5.27/5.53 = ( semiri4216267220026989637d_enat @ Y ) )
% 5.27/5.53 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4811_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: num,N2: nat,Y: nat] :
% 5.27/5.53 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 5.27/5.53 = ( semiri8010041392384452111omplex @ Y ) )
% 5.27/5.53 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4812_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: num,N2: nat,Y: nat] :
% 5.27/5.53 ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 5.27/5.53 = ( semiri5074537144036343181t_real @ Y ) )
% 5.27/5.53 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4813_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: num,N2: nat,Y: nat] :
% 5.27/5.53 ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.53 = ( semiri1314217659103216013at_int @ Y ) )
% 5.27/5.53 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4814_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [X4: num,N2: nat,Y: nat] :
% 5.27/5.53 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.27/5.53 = ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.53 = Y ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_eq_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4815_real__of__nat__less__numeral__iff,axiom,
% 5.27/5.53 ! [N2: nat,W: num] :
% 5.27/5.53 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( numeral_numeral_real @ W ) )
% 5.27/5.53 = ( ord_less_nat @ N2 @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % real_of_nat_less_numeral_iff
% 5.27/5.53 thf(fact_4816_numeral__less__real__of__nat__iff,axiom,
% 5.27/5.53 ! [W: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_less_real_of_nat_iff
% 5.27/5.53 thf(fact_4817_numeral__le__real__of__nat__iff,axiom,
% 5.27/5.53 ! [N2: num,M: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N2 ) @ M ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_le_real_of_nat_iff
% 5.27/5.53 thf(fact_4818_take__bit__of__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se1745604003318907178nteger @ N2 @ one_one_Code_integer )
% 5.27/5.53 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_1
% 5.27/5.53 thf(fact_4819_take__bit__of__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ N2 @ one_one_int )
% 5.27/5.53 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_1
% 5.27/5.53 thf(fact_4820_take__bit__of__1,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ N2 @ one_one_nat )
% 5.27/5.53 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_1
% 5.27/5.53 thf(fact_4821_add__neg__numeral__special_I9_J,axiom,
% 5.27/5.53 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(9)
% 5.27/5.53 thf(fact_4822_add__neg__numeral__special_I9_J,axiom,
% 5.27/5.53 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(9)
% 5.27/5.53 thf(fact_4823_add__neg__numeral__special_I9_J,axiom,
% 5.27/5.53 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(9)
% 5.27/5.53 thf(fact_4824_add__neg__numeral__special_I9_J,axiom,
% 5.27/5.53 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(9)
% 5.27/5.53 thf(fact_4825_add__neg__numeral__special_I9_J,axiom,
% 5.27/5.53 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % add_neg_numeral_special(9)
% 5.27/5.53 thf(fact_4826_diff__numeral__special_I10_J,axiom,
% 5.27/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(10)
% 5.27/5.53 thf(fact_4827_diff__numeral__special_I10_J,axiom,
% 5.27/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(10)
% 5.27/5.53 thf(fact_4828_diff__numeral__special_I10_J,axiom,
% 5.27/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(10)
% 5.27/5.53 thf(fact_4829_diff__numeral__special_I10_J,axiom,
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(10)
% 5.27/5.53 thf(fact_4830_diff__numeral__special_I10_J,axiom,
% 5.27/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(10)
% 5.27/5.53 thf(fact_4831_diff__numeral__special_I11_J,axiom,
% 5.27/5.53 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(11)
% 5.27/5.53 thf(fact_4832_diff__numeral__special_I11_J,axiom,
% 5.27/5.53 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(11)
% 5.27/5.53 thf(fact_4833_diff__numeral__special_I11_J,axiom,
% 5.27/5.53 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(11)
% 5.27/5.53 thf(fact_4834_diff__numeral__special_I11_J,axiom,
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(11)
% 5.27/5.53 thf(fact_4835_diff__numeral__special_I11_J,axiom,
% 5.27/5.53 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(11)
% 5.27/5.53 thf(fact_4836_minus__1__div__2__eq,axiom,
% 5.27/5.53 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % minus_1_div_2_eq
% 5.27/5.53 thf(fact_4837_minus__1__div__2__eq,axiom,
% 5.27/5.53 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.53
% 5.27/5.53 % minus_1_div_2_eq
% 5.27/5.53 thf(fact_4838_bits__minus__1__mod__2__eq,axiom,
% 5.27/5.53 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % bits_minus_1_mod_2_eq
% 5.27/5.53 thf(fact_4839_bits__minus__1__mod__2__eq,axiom,
% 5.27/5.53 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.53 = one_one_Code_integer ) ).
% 5.27/5.53
% 5.27/5.53 % bits_minus_1_mod_2_eq
% 5.27/5.53 thf(fact_4840_minus__1__mod__2__eq,axiom,
% 5.27/5.53 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % minus_1_mod_2_eq
% 5.27/5.53 thf(fact_4841_minus__1__mod__2__eq,axiom,
% 5.27/5.53 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.53 = one_one_Code_integer ) ).
% 5.27/5.53
% 5.27/5.53 % minus_1_mod_2_eq
% 5.27/5.53 thf(fact_4842_of__nat__zero__less__power__iff,axiom,
% 5.27/5.53 ! [X4: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X4 ) @ N2 ) )
% 5.27/5.53 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.53 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_zero_less_power_iff
% 5.27/5.53 thf(fact_4843_of__nat__zero__less__power__iff,axiom,
% 5.27/5.53 ! [X4: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X4 ) @ N2 ) )
% 5.27/5.53 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.53 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_zero_less_power_iff
% 5.27/5.53 thf(fact_4844_of__nat__zero__less__power__iff,axiom,
% 5.27/5.53 ! [X4: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X4 ) @ N2 ) )
% 5.27/5.53 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.53 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_zero_less_power_iff
% 5.27/5.53 thf(fact_4845_of__nat__zero__less__power__iff,axiom,
% 5.27/5.53 ! [X4: nat,N2: nat] :
% 5.27/5.53 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ N2 ) )
% 5.27/5.53 = ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.53 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_zero_less_power_iff
% 5.27/5.53 thf(fact_4846_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [A: real,N2: nat] :
% 5.27/5.53 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Power.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4847_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [A: int,N2: nat] :
% 5.27/5.53 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Power.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4848_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [A: complex,N2: nat] :
% 5.27/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Power.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4849_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [A: code_integer,N2: nat] :
% 5.27/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Power.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4850_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [A: rat,N2: nat] :
% 5.27/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Power.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4851_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [N2: nat,A: real] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.27/5.53 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Parity.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4852_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [N2: nat,A: int] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.27/5.53 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Parity.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4853_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [N2: nat,A: complex] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.27/5.53 = ( power_power_complex @ A @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Parity.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4854_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [N2: nat,A: code_integer] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.27/5.53 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Parity.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4855_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.27/5.53 ! [N2: nat,A: rat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.27/5.53 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Parity.ring_1_class.power_minus_even
% 5.27/5.53 thf(fact_4856_power__minus__odd,axiom,
% 5.27/5.53 ! [N2: nat,A: real] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus_odd
% 5.27/5.53 thf(fact_4857_power__minus__odd,axiom,
% 5.27/5.53 ! [N2: nat,A: int] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus_odd
% 5.27/5.53 thf(fact_4858_power__minus__odd,axiom,
% 5.27/5.53 ! [N2: nat,A: complex] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus_odd
% 5.27/5.53 thf(fact_4859_power__minus__odd,axiom,
% 5.27/5.53 ! [N2: nat,A: code_integer] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus_odd
% 5.27/5.53 thf(fact_4860_power__minus__odd,axiom,
% 5.27/5.53 ! [N2: nat,A: rat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus_odd
% 5.27/5.53 thf(fact_4861_even__take__bit__eq,axiom,
% 5.27/5.53 ! [N2: nat,A: code_integer] :
% 5.27/5.53 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N2 @ A ) )
% 5.27/5.53 = ( ( N2 = zero_zero_nat )
% 5.27/5.53 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_take_bit_eq
% 5.27/5.53 thf(fact_4862_even__take__bit__eq,axiom,
% 5.27/5.53 ! [N2: nat,A: int] :
% 5.27/5.53 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.27/5.53 = ( ( N2 = zero_zero_nat )
% 5.27/5.53 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_take_bit_eq
% 5.27/5.53 thf(fact_4863_even__take__bit__eq,axiom,
% 5.27/5.53 ! [N2: nat,A: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 5.27/5.53 = ( ( N2 = zero_zero_nat )
% 5.27/5.53 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_take_bit_eq
% 5.27/5.53 thf(fact_4864_xor__numerals_I7_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(7)
% 5.27/5.53 thf(fact_4865_xor__numerals_I7_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(7)
% 5.27/5.53 thf(fact_4866_diff__numeral__special_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(3)
% 5.27/5.53 thf(fact_4867_diff__numeral__special_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(3)
% 5.27/5.53 thf(fact_4868_diff__numeral__special_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.53 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(3)
% 5.27/5.53 thf(fact_4869_diff__numeral__special_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.53 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(3)
% 5.27/5.53 thf(fact_4870_diff__numeral__special_I3_J,axiom,
% 5.27/5.53 ! [N2: num] :
% 5.27/5.53 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.53 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(3)
% 5.27/5.53 thf(fact_4871_diff__numeral__special_I4_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(4)
% 5.27/5.53 thf(fact_4872_diff__numeral__special_I4_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(4)
% 5.27/5.53 thf(fact_4873_diff__numeral__special_I4_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(4)
% 5.27/5.53 thf(fact_4874_diff__numeral__special_I4_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(4)
% 5.27/5.53 thf(fact_4875_diff__numeral__special_I4_J,axiom,
% 5.27/5.53 ! [M: num] :
% 5.27/5.53 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % diff_numeral_special(4)
% 5.27/5.53 thf(fact_4876_Suc__div__eq__add3__div__numeral,axiom,
% 5.27/5.53 ! [M: nat,V: num] :
% 5.27/5.53 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.27/5.53 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Suc_div_eq_add3_div_numeral
% 5.27/5.53 thf(fact_4877_div__Suc__eq__div__add3,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.27/5.53 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % div_Suc_eq_div_add3
% 5.27/5.53 thf(fact_4878_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.27/5.53 ! [M: nat,V: num] :
% 5.27/5.53 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.27/5.53 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % Suc_mod_eq_add3_mod_numeral
% 5.27/5.53 thf(fact_4879_mod__Suc__eq__mod__add3,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N2 ) ) ) )
% 5.27/5.53 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % mod_Suc_eq_mod_add3
% 5.27/5.53 thf(fact_4880_signed__take__bit__Suc__minus__bit0,axiom,
% 5.27/5.53 ! [N2: nat,K: num] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.53 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_Suc_minus_bit0
% 5.27/5.53 thf(fact_4881_xor__nat__numerals_I4_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit0 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_nat_numerals(4)
% 5.27/5.53 thf(fact_4882_xor__nat__numerals_I3_J,axiom,
% 5.27/5.53 ! [X4: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_nat_numerals(3)
% 5.27/5.53 thf(fact_4883_xor__nat__numerals_I2_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_nat_numerals(2)
% 5.27/5.53 thf(fact_4884_xor__nat__numerals_I1_J,axiom,
% 5.27/5.53 ! [Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_nat_numerals(1)
% 5.27/5.53 thf(fact_4885_dbl__simps_I4_J,axiom,
% 5.27/5.53 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.53 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(4)
% 5.27/5.53 thf(fact_4886_dbl__simps_I4_J,axiom,
% 5.27/5.53 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.53 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(4)
% 5.27/5.53 thf(fact_4887_dbl__simps_I4_J,axiom,
% 5.27/5.53 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(4)
% 5.27/5.53 thf(fact_4888_dbl__simps_I4_J,axiom,
% 5.27/5.53 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(4)
% 5.27/5.53 thf(fact_4889_dbl__simps_I4_J,axiom,
% 5.27/5.53 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.53 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % dbl_simps(4)
% 5.27/5.53 thf(fact_4890_power__minus1__even,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = one_one_real ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus1_even
% 5.27/5.53 thf(fact_4891_power__minus1__even,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = one_one_int ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus1_even
% 5.27/5.53 thf(fact_4892_power__minus1__even,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = one_one_complex ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus1_even
% 5.27/5.53 thf(fact_4893_power__minus1__even,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = one_one_Code_integer ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus1_even
% 5.27/5.53 thf(fact_4894_power__minus1__even,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = one_one_rat ) ).
% 5.27/5.53
% 5.27/5.53 % power_minus1_even
% 5.27/5.53 thf(fact_4895_neg__one__even__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.27/5.53 = one_one_real ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_even_power
% 5.27/5.53 thf(fact_4896_neg__one__even__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.27/5.53 = one_one_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_even_power
% 5.27/5.53 thf(fact_4897_neg__one__even__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.27/5.53 = one_one_complex ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_even_power
% 5.27/5.53 thf(fact_4898_neg__one__even__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.27/5.53 = one_one_Code_integer ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_even_power
% 5.27/5.53 thf(fact_4899_neg__one__even__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.27/5.53 = one_one_rat ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_even_power
% 5.27/5.53 thf(fact_4900_neg__one__odd__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_odd_power
% 5.27/5.53 thf(fact_4901_neg__one__odd__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_odd_power
% 5.27/5.53 thf(fact_4902_neg__one__odd__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.27/5.53 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_odd_power
% 5.27/5.53 thf(fact_4903_neg__one__odd__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_odd_power
% 5.27/5.53 thf(fact_4904_neg__one__odd__power,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.53 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.27/5.53 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % neg_one_odd_power
% 5.27/5.53 thf(fact_4905_even__of__nat,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.27/5.53 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_of_nat
% 5.27/5.53 thf(fact_4906_even__of__nat,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.53 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_of_nat
% 5.27/5.53 thf(fact_4907_even__of__nat,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.53 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.53
% 5.27/5.53 % even_of_nat
% 5.27/5.53 thf(fact_4908_take__bit__Suc__0,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.27/5.53 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_Suc_0
% 5.27/5.53 thf(fact_4909_take__bit__Suc__0,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.27/5.53 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_Suc_0
% 5.27/5.53 thf(fact_4910_take__bit__Suc__0,axiom,
% 5.27/5.53 ! [A: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.27/5.53 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_Suc_0
% 5.27/5.53 thf(fact_4911_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4912_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4913_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4914_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_less_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4915_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4916_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4917_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4918_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.27/5.53 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_less_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4919_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4920_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X4 ) @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4921_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4922_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.27/5.53 ! [X4: nat,I2: num,N2: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ X4 @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_le_numeral_power_cancel_iff
% 5.27/5.53 thf(fact_4923_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I2 ) @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4924_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I2 ) @ N2 ) @ ( semiri681578069525770553at_rat @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4925_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ ( semiri1316708129612266289at_nat @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4926_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.27/5.53 ! [I2: num,N2: nat,X4: nat] :
% 5.27/5.53 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I2 ) @ N2 ) @ ( semiri1314217659103216013at_int @ X4 ) )
% 5.27/5.53 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I2 ) @ N2 ) @ X4 ) ) ).
% 5.27/5.53
% 5.27/5.53 % numeral_power_le_of_nat_cancel_iff
% 5.27/5.53 thf(fact_4927_signed__take__bit__0,axiom,
% 5.27/5.53 ! [A: code_integer] :
% 5.27/5.53 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.27/5.53 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_0
% 5.27/5.53 thf(fact_4928_signed__take__bit__0,axiom,
% 5.27/5.53 ! [A: int] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.27/5.53 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_0
% 5.27/5.53 thf(fact_4929_xor__numerals_I4_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(4)
% 5.27/5.53 thf(fact_4930_xor__numerals_I4_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.53 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(4)
% 5.27/5.53 thf(fact_4931_xor__numerals_I6_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(6)
% 5.27/5.53 thf(fact_4932_xor__numerals_I6_J,axiom,
% 5.27/5.53 ! [X4: num,Y: num] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.53 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor_numerals(6)
% 5.27/5.53 thf(fact_4933_take__bit__of__exp,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N2 @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_exp
% 5.27/5.53 thf(fact_4934_take__bit__of__exp,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_exp
% 5.27/5.53 thf(fact_4935_take__bit__of__exp,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.53 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N2 @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_exp
% 5.27/5.53 thf(fact_4936_take__bit__of__2,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se1745604003318907178nteger @ N2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_2
% 5.27/5.53 thf(fact_4937_take__bit__of__2,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_2
% 5.27/5.53 thf(fact_4938_take__bit__of__2,axiom,
% 5.27/5.53 ! [N2: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.53 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_2
% 5.27/5.53 thf(fact_4939_zmod__numeral__Bit1,axiom,
% 5.27/5.53 ! [V: num,W: num] :
% 5.27/5.53 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.27/5.53 = ( 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 ) ) ).
% 5.27/5.53
% 5.27/5.53 % zmod_numeral_Bit1
% 5.27/5.53 thf(fact_4940_signed__take__bit__Suc__bit1,axiom,
% 5.27/5.53 ! [N2: nat,K: num] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.27/5.53 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_Suc_bit1
% 5.27/5.53 thf(fact_4941_signed__take__bit__Suc__minus__bit1,axiom,
% 5.27/5.53 ! [N2: nat,K: num] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.53 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N2 @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_Suc_minus_bit1
% 5.27/5.53 thf(fact_4942_signed__take__bit__minus,axiom,
% 5.27/5.53 ! [N2: nat,K: int] :
% 5.27/5.53 ( ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) )
% 5.27/5.53 = ( bit_ri631733984087533419it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % signed_take_bit_minus
% 5.27/5.53 thf(fact_4943_minus__real__def,axiom,
% 5.27/5.53 ( minus_minus_real
% 5.27/5.53 = ( ^ [X: real,Y5: real] : ( plus_plus_real @ X @ ( uminus_uminus_real @ Y5 ) ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % minus_real_def
% 5.27/5.53 thf(fact_4944_xor_Oassoc,axiom,
% 5.27/5.53 ! [A: nat,B: nat,C: nat] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ C )
% 5.27/5.53 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.assoc
% 5.27/5.53 thf(fact_4945_xor_Oassoc,axiom,
% 5.27/5.53 ! [A: int,B: int,C: int] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ C )
% 5.27/5.53 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.assoc
% 5.27/5.53 thf(fact_4946_xor_Ocommute,axiom,
% 5.27/5.53 ( bit_se6528837805403552850or_nat
% 5.27/5.53 = ( ^ [A3: nat,B2: nat] : ( bit_se6528837805403552850or_nat @ B2 @ A3 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.commute
% 5.27/5.53 thf(fact_4947_xor_Ocommute,axiom,
% 5.27/5.53 ( bit_se6526347334894502574or_int
% 5.27/5.53 = ( ^ [A3: int,B2: int] : ( bit_se6526347334894502574or_int @ B2 @ A3 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.commute
% 5.27/5.53 thf(fact_4948_of__nat__xor__eq,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1316708129612266289at_nat @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 5.27/5.53 = ( bit_se6528837805403552850or_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_xor_eq
% 5.27/5.53 thf(fact_4949_of__nat__xor__eq,axiom,
% 5.27/5.53 ! [M: nat,N2: nat] :
% 5.27/5.53 ( ( semiri1314217659103216013at_int @ ( bit_se6528837805403552850or_nat @ M @ N2 ) )
% 5.27/5.53 = ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % of_nat_xor_eq
% 5.27/5.53 thf(fact_4950_take__bit__of__nat,axiom,
% 5.27/5.53 ! [N2: nat,M: nat] :
% 5.27/5.53 ( ( bit_se2923211474154528505it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 5.27/5.53 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_nat
% 5.27/5.53 thf(fact_4951_take__bit__of__nat,axiom,
% 5.27/5.53 ! [N2: nat,M: nat] :
% 5.27/5.53 ( ( bit_se2925701944663578781it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 5.27/5.53 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % take_bit_of_nat
% 5.27/5.53 thf(fact_4952_xor_Oleft__commute,axiom,
% 5.27/5.53 ! [B: nat,A: nat,C: nat] :
% 5.27/5.53 ( ( bit_se6528837805403552850or_nat @ B @ ( bit_se6528837805403552850or_nat @ A @ C ) )
% 5.27/5.53 = ( bit_se6528837805403552850or_nat @ A @ ( bit_se6528837805403552850or_nat @ B @ C ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.left_commute
% 5.27/5.53 thf(fact_4953_xor_Oleft__commute,axiom,
% 5.27/5.53 ! [B: int,A: int,C: int] :
% 5.27/5.53 ( ( bit_se6526347334894502574or_int @ B @ ( bit_se6526347334894502574or_int @ A @ C ) )
% 5.27/5.53 = ( bit_se6526347334894502574or_int @ A @ ( bit_se6526347334894502574or_int @ B @ C ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % xor.left_commute
% 5.27/5.53 thf(fact_4954_equation__minus__iff,axiom,
% 5.27/5.53 ! [A: real,B: real] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( uminus_uminus_real @ B ) )
% 5.27/5.53 = ( B
% 5.27/5.53 = ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % equation_minus_iff
% 5.27/5.53 thf(fact_4955_equation__minus__iff,axiom,
% 5.27/5.53 ! [A: int,B: int] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( uminus_uminus_int @ B ) )
% 5.27/5.53 = ( B
% 5.27/5.53 = ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % equation_minus_iff
% 5.27/5.53 thf(fact_4956_equation__minus__iff,axiom,
% 5.27/5.53 ! [A: complex,B: complex] :
% 5.27/5.53 ( ( A
% 5.27/5.53 = ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.53 = ( B
% 5.27/5.53 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.27/5.53
% 5.27/5.53 % equation_minus_iff
% 5.27/5.54 thf(fact_4957_equation__minus__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % equation_minus_iff
% 5.27/5.54 thf(fact_4958_equation__minus__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % equation_minus_iff
% 5.27/5.54 thf(fact_4959_minus__equation__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( uminus_uminus_real @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( uminus_uminus_real @ B )
% 5.27/5.54 = A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_equation_iff
% 5.27/5.54 thf(fact_4960_minus__equation__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( uminus_uminus_int @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( uminus_uminus_int @ B )
% 5.27/5.54 = A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_equation_iff
% 5.27/5.54 thf(fact_4961_minus__equation__iff,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( uminus1482373934393186551omplex @ B )
% 5.27/5.54 = A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_equation_iff
% 5.27/5.54 thf(fact_4962_minus__equation__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( uminus1351360451143612070nteger @ B )
% 5.27/5.54 = A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_equation_iff
% 5.27/5.54 thf(fact_4963_minus__equation__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( uminus_uminus_rat @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( uminus_uminus_rat @ B )
% 5.27/5.54 = A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_equation_iff
% 5.27/5.54 thf(fact_4964_power__minus__Bit1,axiom,
% 5.27/5.54 ! [X4: real,K: num] :
% 5.27/5.54 ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( uminus_uminus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit1
% 5.27/5.54 thf(fact_4965_power__minus__Bit1,axiom,
% 5.27/5.54 ! [X4: int,K: num] :
% 5.27/5.54 ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( uminus_uminus_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit1
% 5.27/5.54 thf(fact_4966_power__minus__Bit1,axiom,
% 5.27/5.54 ! [X4: complex,K: num] :
% 5.27/5.54 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit1
% 5.27/5.54 thf(fact_4967_power__minus__Bit1,axiom,
% 5.27/5.54 ! [X4: code_integer,K: num] :
% 5.27/5.54 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit1
% 5.27/5.54 thf(fact_4968_power__minus__Bit1,axiom,
% 5.27/5.54 ! [X4: rat,K: num] :
% 5.27/5.54 ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( uminus_uminus_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit1
% 5.27/5.54 thf(fact_4969_take__bit__add,axiom,
% 5.27/5.54 ! [N2: nat,A: int,B: int] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_add
% 5.27/5.54 thf(fact_4970_take__bit__add,axiom,
% 5.27/5.54 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.54 ( ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ N2 @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_add
% 5.27/5.54 thf(fact_4971_take__bit__tightened,axiom,
% 5.27/5.54 ! [N2: nat,A: int,B: int,M: nat] :
% 5.27/5.54 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.27/5.54 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_tightened
% 5.27/5.54 thf(fact_4972_take__bit__tightened,axiom,
% 5.27/5.54 ! [N2: nat,A: nat,B: nat,M: nat] :
% 5.27/5.54 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ N2 @ B ) )
% 5.27/5.54 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_tightened
% 5.27/5.54 thf(fact_4973_take__bit__tightened__less__eq__nat,axiom,
% 5.27/5.54 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q3 ) @ ( bit_se2925701944663578781it_nat @ N2 @ Q3 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_tightened_less_eq_nat
% 5.27/5.54 thf(fact_4974_take__bit__nat__less__eq__self,axiom,
% 5.27/5.54 ! [N2: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_nat_less_eq_self
% 5.27/5.54 thf(fact_4975_mult__of__nat__commute,axiom,
% 5.27/5.54 ! [X4: nat,Y: complex] :
% 5.27/5.54 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X4 ) @ Y )
% 5.27/5.54 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_of_nat_commute
% 5.27/5.54 thf(fact_4976_mult__of__nat__commute,axiom,
% 5.27/5.54 ! [X4: nat,Y: real] :
% 5.27/5.54 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X4 ) @ Y )
% 5.27/5.54 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_of_nat_commute
% 5.27/5.54 thf(fact_4977_mult__of__nat__commute,axiom,
% 5.27/5.54 ! [X4: nat,Y: int] :
% 5.27/5.54 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X4 ) @ Y )
% 5.27/5.54 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_of_nat_commute
% 5.27/5.54 thf(fact_4978_mult__of__nat__commute,axiom,
% 5.27/5.54 ! [X4: nat,Y: nat] :
% 5.27/5.54 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X4 ) @ Y )
% 5.27/5.54 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_of_nat_commute
% 5.27/5.54 thf(fact_4979_take__bit__mult,axiom,
% 5.27/5.54 ! [N2: nat,K: int,L: int] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ ( times_times_int @ K @ L ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_mult
% 5.27/5.54 thf(fact_4980_le__imp__neg__le,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.54 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_imp_neg_le
% 5.27/5.54 thf(fact_4981_le__imp__neg__le,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.27/5.54 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_imp_neg_le
% 5.27/5.54 thf(fact_4982_le__imp__neg__le,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.54 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_imp_neg_le
% 5.27/5.54 thf(fact_4983_le__imp__neg__le,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_eq_int @ A @ B )
% 5.27/5.54 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_imp_neg_le
% 5.27/5.54 thf(fact_4984_minus__le__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.54 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_le_iff
% 5.27/5.54 thf(fact_4985_minus__le__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.54 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_le_iff
% 5.27/5.54 thf(fact_4986_minus__le__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.54 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_le_iff
% 5.27/5.54 thf(fact_4987_minus__le__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_le_iff
% 5.27/5.54 thf(fact_4988_le__minus__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_iff
% 5.27/5.54 thf(fact_4989_le__minus__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_iff
% 5.27/5.54 thf(fact_4990_le__minus__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_iff
% 5.27/5.54 thf(fact_4991_le__minus__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_iff
% 5.27/5.54 thf(fact_4992_verit__negate__coefficient_I2_J,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_real @ A @ B )
% 5.27/5.54 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_negate_coefficient(2)
% 5.27/5.54 thf(fact_4993_verit__negate__coefficient_I2_J,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_int @ A @ B )
% 5.27/5.54 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_negate_coefficient(2)
% 5.27/5.54 thf(fact_4994_verit__negate__coefficient_I2_J,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.27/5.54 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_negate_coefficient(2)
% 5.27/5.54 thf(fact_4995_verit__negate__coefficient_I2_J,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_rat @ A @ B )
% 5.27/5.54 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_negate_coefficient(2)
% 5.27/5.54 thf(fact_4996_minus__less__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.54 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_less_iff
% 5.27/5.54 thf(fact_4997_minus__less__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_less_iff
% 5.27/5.54 thf(fact_4998_minus__less__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.54 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_less_iff
% 5.27/5.54 thf(fact_4999_minus__less__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.54 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_less_iff
% 5.27/5.54 thf(fact_5000_less__minus__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_iff
% 5.27/5.54 thf(fact_5001_less__minus__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_iff
% 5.27/5.54 thf(fact_5002_less__minus__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_iff
% 5.27/5.54 thf(fact_5003_less__minus__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_iff
% 5.27/5.54 thf(fact_5004_verit__eq__simplify_I14_J,axiom,
% 5.27/5.54 ! [X22: num,X32: num] :
% 5.27/5.54 ( ( bit0 @ X22 )
% 5.27/5.54 != ( bit1 @ X32 ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_eq_simplify(14)
% 5.27/5.54 thf(fact_5005_verit__eq__simplify_I12_J,axiom,
% 5.27/5.54 ! [X32: num] :
% 5.27/5.54 ( one
% 5.27/5.54 != ( bit1 @ X32 ) ) ).
% 5.27/5.54
% 5.27/5.54 % verit_eq_simplify(12)
% 5.27/5.54 thf(fact_5006_numeral__neq__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( numeral_numeral_real @ M )
% 5.27/5.54 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_numeral
% 5.27/5.54 thf(fact_5007_numeral__neq__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( numeral_numeral_int @ M )
% 5.27/5.54 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_numeral
% 5.27/5.54 thf(fact_5008_numeral__neq__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( numera6690914467698888265omplex @ M )
% 5.27/5.54 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_numeral
% 5.27/5.54 thf(fact_5009_numeral__neq__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( numera6620942414471956472nteger @ M )
% 5.27/5.54 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_numeral
% 5.27/5.54 thf(fact_5010_numeral__neq__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( numeral_numeral_rat @ M )
% 5.27/5.54 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_numeral
% 5.27/5.54 thf(fact_5011_neg__numeral__neq__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.27/5.54 != ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_neq_numeral
% 5.27/5.54 thf(fact_5012_neg__numeral__neq__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.27/5.54 != ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_neq_numeral
% 5.27/5.54 thf(fact_5013_neg__numeral__neq__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.27/5.54 != ( numera6690914467698888265omplex @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_neq_numeral
% 5.27/5.54 thf(fact_5014_neg__numeral__neq__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.27/5.54 != ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_neq_numeral
% 5.27/5.54 thf(fact_5015_neg__numeral__neq__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.27/5.54 != ( numeral_numeral_rat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_neq_numeral
% 5.27/5.54 thf(fact_5016_square__eq__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( times_times_real @ A @ A )
% 5.27/5.54 = ( times_times_real @ B @ B ) )
% 5.27/5.54 = ( ( A = B )
% 5.27/5.54 | ( A
% 5.27/5.54 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_iff
% 5.27/5.54 thf(fact_5017_square__eq__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( times_times_int @ A @ A )
% 5.27/5.54 = ( times_times_int @ B @ B ) )
% 5.27/5.54 = ( ( A = B )
% 5.27/5.54 | ( A
% 5.27/5.54 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_iff
% 5.27/5.54 thf(fact_5018_square__eq__iff,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( times_times_complex @ A @ A )
% 5.27/5.54 = ( times_times_complex @ B @ B ) )
% 5.27/5.54 = ( ( A = B )
% 5.27/5.54 | ( A
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_iff
% 5.27/5.54 thf(fact_5019_square__eq__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.27/5.54 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.27/5.54 = ( ( A = B )
% 5.27/5.54 | ( A
% 5.27/5.54 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_iff
% 5.27/5.54 thf(fact_5020_square__eq__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( times_times_rat @ A @ A )
% 5.27/5.54 = ( times_times_rat @ B @ B ) )
% 5.27/5.54 = ( ( A = B )
% 5.27/5.54 | ( A
% 5.27/5.54 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_iff
% 5.27/5.54 thf(fact_5021_minus__mult__commute,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.54 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_mult_commute
% 5.27/5.54 thf(fact_5022_minus__mult__commute,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_mult_commute
% 5.27/5.54 thf(fact_5023_minus__mult__commute,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.27/5.54 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_mult_commute
% 5.27/5.54 thf(fact_5024_minus__mult__commute,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.54 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_mult_commute
% 5.27/5.54 thf(fact_5025_minus__mult__commute,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.54 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_mult_commute
% 5.27/5.54 thf(fact_5026_one__neq__neg__one,axiom,
% 5.27/5.54 ( one_one_real
% 5.27/5.54 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_one
% 5.27/5.54 thf(fact_5027_one__neq__neg__one,axiom,
% 5.27/5.54 ( one_one_int
% 5.27/5.54 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_one
% 5.27/5.54 thf(fact_5028_one__neq__neg__one,axiom,
% 5.27/5.54 ( one_one_complex
% 5.27/5.54 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_one
% 5.27/5.54 thf(fact_5029_one__neq__neg__one,axiom,
% 5.27/5.54 ( one_one_Code_integer
% 5.27/5.54 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_one
% 5.27/5.54 thf(fact_5030_one__neq__neg__one,axiom,
% 5.27/5.54 ( one_one_rat
% 5.27/5.54 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_one
% 5.27/5.54 thf(fact_5031_add_Oinverse__distrib__swap,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.27/5.54 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_distrib_swap
% 5.27/5.54 thf(fact_5032_add_Oinverse__distrib__swap,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.54 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_distrib_swap
% 5.27/5.54 thf(fact_5033_add_Oinverse__distrib__swap,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.27/5.54 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_distrib_swap
% 5.27/5.54 thf(fact_5034_add_Oinverse__distrib__swap,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_distrib_swap
% 5.27/5.54 thf(fact_5035_add_Oinverse__distrib__swap,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.54 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_distrib_swap
% 5.27/5.54 thf(fact_5036_group__cancel_Oneg1,axiom,
% 5.27/5.54 ! [A2: real,K: real,A: real] :
% 5.27/5.54 ( ( A2
% 5.27/5.54 = ( plus_plus_real @ K @ A ) )
% 5.27/5.54 => ( ( uminus_uminus_real @ A2 )
% 5.27/5.54 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.neg1
% 5.27/5.54 thf(fact_5037_group__cancel_Oneg1,axiom,
% 5.27/5.54 ! [A2: int,K: int,A: int] :
% 5.27/5.54 ( ( A2
% 5.27/5.54 = ( plus_plus_int @ K @ A ) )
% 5.27/5.54 => ( ( uminus_uminus_int @ A2 )
% 5.27/5.54 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.neg1
% 5.27/5.54 thf(fact_5038_group__cancel_Oneg1,axiom,
% 5.27/5.54 ! [A2: complex,K: complex,A: complex] :
% 5.27/5.54 ( ( A2
% 5.27/5.54 = ( plus_plus_complex @ K @ A ) )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.27/5.54 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.neg1
% 5.27/5.54 thf(fact_5039_group__cancel_Oneg1,axiom,
% 5.27/5.54 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.27/5.54 ( ( A2
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.27/5.54 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.neg1
% 5.27/5.54 thf(fact_5040_group__cancel_Oneg1,axiom,
% 5.27/5.54 ! [A2: rat,K: rat,A: rat] :
% 5.27/5.54 ( ( A2
% 5.27/5.54 = ( plus_plus_rat @ K @ A ) )
% 5.27/5.54 => ( ( uminus_uminus_rat @ A2 )
% 5.27/5.54 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.neg1
% 5.27/5.54 thf(fact_5041_is__num__normalize_I8_J,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.27/5.54 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % is_num_normalize(8)
% 5.27/5.54 thf(fact_5042_is__num__normalize_I8_J,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.54 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % is_num_normalize(8)
% 5.27/5.54 thf(fact_5043_is__num__normalize_I8_J,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.27/5.54 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % is_num_normalize(8)
% 5.27/5.54 thf(fact_5044_is__num__normalize_I8_J,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % is_num_normalize(8)
% 5.27/5.54 thf(fact_5045_is__num__normalize_I8_J,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.54 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % is_num_normalize(8)
% 5.27/5.54 thf(fact_5046_take__bit__diff,axiom,
% 5.27/5.54 ! [N2: nat,K: int,L: int] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ L ) ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ L ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_diff
% 5.27/5.54 thf(fact_5047_minus__diff__minus,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_minus
% 5.27/5.54 thf(fact_5048_minus__diff__minus,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_minus
% 5.27/5.54 thf(fact_5049_minus__diff__minus,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_minus
% 5.27/5.54 thf(fact_5050_minus__diff__minus,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_minus
% 5.27/5.54 thf(fact_5051_minus__diff__minus,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_minus
% 5.27/5.54 thf(fact_5052_minus__diff__commute,axiom,
% 5.27/5.54 ! [B: real,A: real] :
% 5.27/5.54 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.27/5.54 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_commute
% 5.27/5.54 thf(fact_5053_minus__diff__commute,axiom,
% 5.27/5.54 ! [B: int,A: int] :
% 5.27/5.54 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.27/5.54 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_commute
% 5.27/5.54 thf(fact_5054_minus__diff__commute,axiom,
% 5.27/5.54 ! [B: complex,A: complex] :
% 5.27/5.54 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.27/5.54 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_commute
% 5.27/5.54 thf(fact_5055_minus__diff__commute,axiom,
% 5.27/5.54 ! [B: code_integer,A: code_integer] :
% 5.27/5.54 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.27/5.54 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_commute
% 5.27/5.54 thf(fact_5056_minus__diff__commute,axiom,
% 5.27/5.54 ! [B: rat,A: rat] :
% 5.27/5.54 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.27/5.54 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_diff_commute
% 5.27/5.54 thf(fact_5057_minus__divide__left,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.54 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_left
% 5.27/5.54 thf(fact_5058_minus__divide__left,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_left
% 5.27/5.54 thf(fact_5059_minus__divide__left,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.54 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_left
% 5.27/5.54 thf(fact_5060_minus__divide__divide,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( divide_divide_real @ A @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_divide
% 5.27/5.54 thf(fact_5061_minus__divide__divide,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_divide
% 5.27/5.54 thf(fact_5062_minus__divide__divide,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( divide_divide_rat @ A @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_divide
% 5.27/5.54 thf(fact_5063_minus__divide__right,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.54 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_right
% 5.27/5.54 thf(fact_5064_minus__divide__right,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_right
% 5.27/5.54 thf(fact_5065_minus__divide__right,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.54 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_right
% 5.27/5.54 thf(fact_5066_div__minus__right,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % div_minus_right
% 5.27/5.54 thf(fact_5067_div__minus__right,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % div_minus_right
% 5.27/5.54 thf(fact_5068_Diff__mono,axiom,
% 5.27/5.54 ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 5.27/5.54 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.27/5.54 => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 5.27/5.54 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % Diff_mono
% 5.27/5.54 thf(fact_5069_Diff__mono,axiom,
% 5.27/5.54 ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 5.27/5.54 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.27/5.54 => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 5.27/5.54 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % Diff_mono
% 5.27/5.54 thf(fact_5070_Diff__subset,axiom,
% 5.27/5.54 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.27/5.54
% 5.27/5.54 % Diff_subset
% 5.27/5.54 thf(fact_5071_Diff__subset,axiom,
% 5.27/5.54 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 5.27/5.54
% 5.27/5.54 % Diff_subset
% 5.27/5.54 thf(fact_5072_double__diff,axiom,
% 5.27/5.54 ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 5.27/5.54 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.27/5.54 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.27/5.54 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.27/5.54 = A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % double_diff
% 5.27/5.54 thf(fact_5073_double__diff,axiom,
% 5.27/5.54 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.27/5.54 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.27/5.54 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.27/5.54 => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.27/5.54 = A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % double_diff
% 5.27/5.54 thf(fact_5074_mod__minus__eq,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.27/5.54 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_eq
% 5.27/5.54 thf(fact_5075_mod__minus__eq,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.27/5.54 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_eq
% 5.27/5.54 thf(fact_5076_mod__minus__cong,axiom,
% 5.27/5.54 ! [A: int,B: int,A4: int] :
% 5.27/5.54 ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.54 = ( modulo_modulo_int @ A4 @ B ) )
% 5.27/5.54 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_cong
% 5.27/5.54 thf(fact_5077_mod__minus__cong,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 5.27/5.54 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.27/5.54 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 5.27/5.54 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.54 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_cong
% 5.27/5.54 thf(fact_5078_mod__minus__right,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_right
% 5.27/5.54 thf(fact_5079_mod__minus__right,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_minus_right
% 5.27/5.54 thf(fact_5080_psubset__imp__ex__mem,axiom,
% 5.27/5.54 ! [A2: set_real,B3: set_real] :
% 5.27/5.54 ( ( ord_less_set_real @ A2 @ B3 )
% 5.27/5.54 => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % psubset_imp_ex_mem
% 5.27/5.54 thf(fact_5081_psubset__imp__ex__mem,axiom,
% 5.27/5.54 ! [A2: set_complex,B3: set_complex] :
% 5.27/5.54 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.27/5.54 => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % psubset_imp_ex_mem
% 5.27/5.54 thf(fact_5082_psubset__imp__ex__mem,axiom,
% 5.27/5.54 ! [A2: set_int,B3: set_int] :
% 5.27/5.54 ( ( ord_less_set_int @ A2 @ B3 )
% 5.27/5.54 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % psubset_imp_ex_mem
% 5.27/5.54 thf(fact_5083_psubset__imp__ex__mem,axiom,
% 5.27/5.54 ! [A2: set_Pr1261947904930325089at_nat,B3: set_Pr1261947904930325089at_nat] :
% 5.27/5.54 ( ( ord_le7866589430770878221at_nat @ A2 @ B3 )
% 5.27/5.54 => ? [B5: product_prod_nat_nat] : ( member8440522571783428010at_nat @ B5 @ ( minus_1356011639430497352at_nat @ B3 @ A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % psubset_imp_ex_mem
% 5.27/5.54 thf(fact_5084_psubset__imp__ex__mem,axiom,
% 5.27/5.54 ! [A2: set_nat,B3: set_nat] :
% 5.27/5.54 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.27/5.54 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % psubset_imp_ex_mem
% 5.27/5.54 thf(fact_5085_concat__bit__eq__iff,axiom,
% 5.27/5.54 ! [N2: nat,K: int,L: int,R3: int,S: int] :
% 5.27/5.54 ( ( ( bit_concat_bit @ N2 @ K @ L )
% 5.27/5.54 = ( bit_concat_bit @ N2 @ R3 @ S ) )
% 5.27/5.54 = ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ R3 ) )
% 5.27/5.54 & ( L = S ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % concat_bit_eq_iff
% 5.27/5.54 thf(fact_5086_concat__bit__take__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,B: int] :
% 5.27/5.54 ( ( bit_concat_bit @ N2 @ ( bit_se2923211474154528505it_int @ N2 @ B ) )
% 5.27/5.54 = ( bit_concat_bit @ N2 @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % concat_bit_take_bit_eq
% 5.27/5.54 thf(fact_5087_real__of__nat__div2,axiom,
% 5.27/5.54 ! [N2: nat,X4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_of_nat_div2
% 5.27/5.54 thf(fact_5088_real__of__nat__div3,axiom,
% 5.27/5.54 ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 5.27/5.54
% 5.27/5.54 % real_of_nat_div3
% 5.27/5.54 thf(fact_5089_of__nat__0__le__iff,axiom,
% 5.27/5.54 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_0_le_iff
% 5.27/5.54 thf(fact_5090_of__nat__0__le__iff,axiom,
% 5.27/5.54 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_0_le_iff
% 5.27/5.54 thf(fact_5091_of__nat__0__le__iff,axiom,
% 5.27/5.54 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_0_le_iff
% 5.27/5.54 thf(fact_5092_of__nat__0__le__iff,axiom,
% 5.27/5.54 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_0_le_iff
% 5.27/5.54 thf(fact_5093_of__nat__less__0__iff,axiom,
% 5.27/5.54 ! [M: nat] :
% 5.27/5.54 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_0_iff
% 5.27/5.54 thf(fact_5094_of__nat__less__0__iff,axiom,
% 5.27/5.54 ! [M: nat] :
% 5.27/5.54 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_0_iff
% 5.27/5.54 thf(fact_5095_of__nat__less__0__iff,axiom,
% 5.27/5.54 ! [M: nat] :
% 5.27/5.54 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_0_iff
% 5.27/5.54 thf(fact_5096_of__nat__less__0__iff,axiom,
% 5.27/5.54 ! [M: nat] :
% 5.27/5.54 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_0_iff
% 5.27/5.54 thf(fact_5097_of__nat__neq__0,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( semiri8010041392384452111omplex @ ( suc @ N2 ) )
% 5.27/5.54 != zero_zero_complex ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_neq_0
% 5.27/5.54 thf(fact_5098_of__nat__neq__0,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( semiri681578069525770553at_rat @ ( suc @ N2 ) )
% 5.27/5.54 != zero_zero_rat ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_neq_0
% 5.27/5.54 thf(fact_5099_of__nat__neq__0,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( semiri5074537144036343181t_real @ ( suc @ N2 ) )
% 5.27/5.54 != zero_zero_real ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_neq_0
% 5.27/5.54 thf(fact_5100_of__nat__neq__0,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.27/5.54 != zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_neq_0
% 5.27/5.54 thf(fact_5101_of__nat__neq__0,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( semiri1316708129612266289at_nat @ ( suc @ N2 ) )
% 5.27/5.54 != zero_zero_nat ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_neq_0
% 5.27/5.54 thf(fact_5102_div__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: code_integer,M: nat,N2: nat] :
% 5.27/5.54 ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.27/5.54 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % div_mult2_eq'
% 5.27/5.54 thf(fact_5103_div__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: int,M: nat,N2: nat] :
% 5.27/5.54 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.54 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % div_mult2_eq'
% 5.27/5.54 thf(fact_5104_div__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: nat,M: nat,N2: nat] :
% 5.27/5.54 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.27/5.54 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % div_mult2_eq'
% 5.27/5.54 thf(fact_5105_of__nat__less__imp__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.54 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_imp_less
% 5.27/5.54 thf(fact_5106_of__nat__less__imp__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.54 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_imp_less
% 5.27/5.54 thf(fact_5107_of__nat__less__imp__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.54 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_imp_less
% 5.27/5.54 thf(fact_5108_of__nat__less__imp__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.54 => ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_less_imp_less
% 5.27/5.54 thf(fact_5109_less__imp__of__nat__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_imp_of_nat_less
% 5.27/5.54 thf(fact_5110_less__imp__of__nat__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_imp_of_nat_less
% 5.27/5.54 thf(fact_5111_less__imp__of__nat__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_imp_of_nat_less
% 5.27/5.54 thf(fact_5112_less__imp__of__nat__less,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( ord_less_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_imp_of_nat_less
% 5.27/5.54 thf(fact_5113_take__bit__tightened__less__eq__int,axiom,
% 5.27/5.54 ! [M: nat,N2: nat,K: int] :
% 5.27/5.54 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.54 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_tightened_less_eq_int
% 5.27/5.54 thf(fact_5114_of__nat__mono,axiom,
% 5.27/5.54 ! [I2: nat,J: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.54 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I2 ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mono
% 5.27/5.54 thf(fact_5115_of__nat__mono,axiom,
% 5.27/5.54 ! [I2: nat,J: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.54 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I2 ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mono
% 5.27/5.54 thf(fact_5116_of__nat__mono,axiom,
% 5.27/5.54 ! [I2: nat,J: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.54 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I2 ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mono
% 5.27/5.54 thf(fact_5117_of__nat__mono,axiom,
% 5.27/5.54 ! [I2: nat,J: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.54 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mono
% 5.27/5.54 thf(fact_5118_take__bit__int__less__eq__self__iff,axiom,
% 5.27/5.54 ! [N2: nat,K: int] :
% 5.27/5.54 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.27/5.54 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_int_less_eq_self_iff
% 5.27/5.54 thf(fact_5119_take__bit__nonnegative,axiom,
% 5.27/5.54 ! [N2: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_nonnegative
% 5.27/5.54 thf(fact_5120_take__bit__int__greater__self__iff,axiom,
% 5.27/5.54 ! [K: int,N2: nat] :
% 5.27/5.54 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.27/5.54 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_int_greater_self_iff
% 5.27/5.54 thf(fact_5121_not__take__bit__negative,axiom,
% 5.27/5.54 ! [N2: nat,K: int] :
% 5.27/5.54 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % not_take_bit_negative
% 5.27/5.54 thf(fact_5122_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,A: int,B: int] :
% 5.27/5.54 ( ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.27/5.54 = ( bit_ri631733984087533419it_int @ N2 @ B ) )
% 5.27/5.54 = ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % signed_take_bit_eq_iff_take_bit_eq
% 5.27/5.54 thf(fact_5123_signed__take__bit__take__bit,axiom,
% 5.27/5.54 ! [M: nat,N2: nat,A: int] :
% 5.27/5.54 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.27/5.54 = ( if_int_int @ ( ord_less_eq_nat @ N2 @ M ) @ ( bit_se2923211474154528505it_int @ N2 ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.27/5.54
% 5.27/5.54 % signed_take_bit_take_bit
% 5.27/5.54 thf(fact_5124_neg__numeral__le__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_numeral
% 5.27/5.54 thf(fact_5125_neg__numeral__le__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_numeral
% 5.27/5.54 thf(fact_5126_neg__numeral__le__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_numeral
% 5.27/5.54 thf(fact_5127_neg__numeral__le__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_numeral
% 5.27/5.54 thf(fact_5128_not__numeral__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_numeral
% 5.27/5.54 thf(fact_5129_not__numeral__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_numeral
% 5.27/5.54 thf(fact_5130_not__numeral__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_numeral
% 5.27/5.54 thf(fact_5131_not__numeral__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_numeral
% 5.27/5.54 thf(fact_5132_zero__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( zero_zero_real
% 5.27/5.54 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_numeral
% 5.27/5.54 thf(fact_5133_zero__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( zero_zero_int
% 5.27/5.54 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_numeral
% 5.27/5.54 thf(fact_5134_zero__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( zero_zero_complex
% 5.27/5.54 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_numeral
% 5.27/5.54 thf(fact_5135_zero__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( zero_z3403309356797280102nteger
% 5.27/5.54 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_numeral
% 5.27/5.54 thf(fact_5136_zero__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( zero_zero_rat
% 5.27/5.54 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_numeral
% 5.27/5.54 thf(fact_5137_not__numeral__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_numeral
% 5.27/5.54 thf(fact_5138_not__numeral__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_numeral
% 5.27/5.54 thf(fact_5139_not__numeral__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_numeral
% 5.27/5.54 thf(fact_5140_not__numeral__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] :
% 5.27/5.54 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_numeral
% 5.27/5.54 thf(fact_5141_neg__numeral__less__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_numeral
% 5.27/5.54 thf(fact_5142_neg__numeral__less__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_numeral
% 5.27/5.54 thf(fact_5143_neg__numeral__less__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_numeral
% 5.27/5.54 thf(fact_5144_neg__numeral__less__numeral,axiom,
% 5.27/5.54 ! [M: num,N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_numeral
% 5.27/5.54 thf(fact_5145_le__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(4)
% 5.27/5.54 thf(fact_5146_le__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(4)
% 5.27/5.54 thf(fact_5147_le__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(4)
% 5.27/5.54 thf(fact_5148_le__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(4)
% 5.27/5.54 thf(fact_5149_le__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(2)
% 5.27/5.54 thf(fact_5150_le__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(2)
% 5.27/5.54 thf(fact_5151_le__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(2)
% 5.27/5.54 thf(fact_5152_le__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(2)
% 5.27/5.54 thf(fact_5153_zero__neq__neg__one,axiom,
% 5.27/5.54 ( zero_zero_real
% 5.27/5.54 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_one
% 5.27/5.54 thf(fact_5154_zero__neq__neg__one,axiom,
% 5.27/5.54 ( zero_zero_int
% 5.27/5.54 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_one
% 5.27/5.54 thf(fact_5155_zero__neq__neg__one,axiom,
% 5.27/5.54 ( zero_zero_complex
% 5.27/5.54 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_one
% 5.27/5.54 thf(fact_5156_zero__neq__neg__one,axiom,
% 5.27/5.54 ( zero_z3403309356797280102nteger
% 5.27/5.54 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_one
% 5.27/5.54 thf(fact_5157_zero__neq__neg__one,axiom,
% 5.27/5.54 ( zero_zero_rat
% 5.27/5.54 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % zero_neq_neg_one
% 5.27/5.54 thf(fact_5158_neg__eq__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( uminus_uminus_real @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( plus_plus_real @ A @ B )
% 5.27/5.54 = zero_zero_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_eq_iff_add_eq_0
% 5.27/5.54 thf(fact_5159_neg__eq__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( uminus_uminus_int @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( plus_plus_int @ A @ B )
% 5.27/5.54 = zero_zero_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_eq_iff_add_eq_0
% 5.27/5.54 thf(fact_5160_neg__eq__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( plus_plus_complex @ A @ B )
% 5.27/5.54 = zero_zero_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_eq_iff_add_eq_0
% 5.27/5.54 thf(fact_5161_neg__eq__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.27/5.54 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_eq_iff_add_eq_0
% 5.27/5.54 thf(fact_5162_neg__eq__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( uminus_uminus_rat @ A )
% 5.27/5.54 = B )
% 5.27/5.54 = ( ( plus_plus_rat @ A @ B )
% 5.27/5.54 = zero_zero_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_eq_iff_add_eq_0
% 5.27/5.54 thf(fact_5163_eq__neg__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( ( plus_plus_real @ A @ B )
% 5.27/5.54 = zero_zero_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_neg_iff_add_eq_0
% 5.27/5.54 thf(fact_5164_eq__neg__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( ( plus_plus_int @ A @ B )
% 5.27/5.54 = zero_zero_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_neg_iff_add_eq_0
% 5.27/5.54 thf(fact_5165_eq__neg__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.54 = ( ( plus_plus_complex @ A @ B )
% 5.27/5.54 = zero_zero_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_neg_iff_add_eq_0
% 5.27/5.54 thf(fact_5166_eq__neg__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.27/5.54 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_neg_iff_add_eq_0
% 5.27/5.54 thf(fact_5167_eq__neg__iff__add__eq__0,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( ( plus_plus_rat @ A @ B )
% 5.27/5.54 = zero_zero_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_neg_iff_add_eq_0
% 5.27/5.54 thf(fact_5168_add_Oinverse__unique,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( plus_plus_real @ A @ B )
% 5.27/5.54 = zero_zero_real )
% 5.27/5.54 => ( ( uminus_uminus_real @ A )
% 5.27/5.54 = B ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_unique
% 5.27/5.54 thf(fact_5169_add_Oinverse__unique,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( plus_plus_int @ A @ B )
% 5.27/5.54 = zero_zero_int )
% 5.27/5.54 => ( ( uminus_uminus_int @ A )
% 5.27/5.54 = B ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_unique
% 5.27/5.54 thf(fact_5170_add_Oinverse__unique,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( plus_plus_complex @ A @ B )
% 5.27/5.54 = zero_zero_complex )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.54 = B ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_unique
% 5.27/5.54 thf(fact_5171_add_Oinverse__unique,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.27/5.54 = zero_z3403309356797280102nteger )
% 5.27/5.54 => ( ( uminus1351360451143612070nteger @ A )
% 5.27/5.54 = B ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_unique
% 5.27/5.54 thf(fact_5172_add_Oinverse__unique,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( plus_plus_rat @ A @ B )
% 5.27/5.54 = zero_zero_rat )
% 5.27/5.54 => ( ( uminus_uminus_rat @ A )
% 5.27/5.54 = B ) ) ).
% 5.27/5.54
% 5.27/5.54 % add.inverse_unique
% 5.27/5.54 thf(fact_5173_ab__group__add__class_Oab__left__minus,axiom,
% 5.27/5.54 ! [A: real] :
% 5.27/5.54 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.27/5.54 = zero_zero_real ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_left_minus
% 5.27/5.54 thf(fact_5174_ab__group__add__class_Oab__left__minus,axiom,
% 5.27/5.54 ! [A: int] :
% 5.27/5.54 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.27/5.54 = zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_left_minus
% 5.27/5.54 thf(fact_5175_ab__group__add__class_Oab__left__minus,axiom,
% 5.27/5.54 ! [A: complex] :
% 5.27/5.54 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.27/5.54 = zero_zero_complex ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_left_minus
% 5.27/5.54 thf(fact_5176_ab__group__add__class_Oab__left__minus,axiom,
% 5.27/5.54 ! [A: code_integer] :
% 5.27/5.54 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.27/5.54 = zero_z3403309356797280102nteger ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_left_minus
% 5.27/5.54 thf(fact_5177_ab__group__add__class_Oab__left__minus,axiom,
% 5.27/5.54 ! [A: rat] :
% 5.27/5.54 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.27/5.54 = zero_zero_rat ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_left_minus
% 5.27/5.54 thf(fact_5178_add__eq__0__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( plus_plus_real @ A @ B )
% 5.27/5.54 = zero_zero_real )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_eq_0_iff
% 5.27/5.54 thf(fact_5179_add__eq__0__iff,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( plus_plus_int @ A @ B )
% 5.27/5.54 = zero_zero_int )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_eq_0_iff
% 5.27/5.54 thf(fact_5180_add__eq__0__iff,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( plus_plus_complex @ A @ B )
% 5.27/5.54 = zero_zero_complex )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_eq_0_iff
% 5.27/5.54 thf(fact_5181_add__eq__0__iff,axiom,
% 5.27/5.54 ! [A: code_integer,B: code_integer] :
% 5.27/5.54 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.27/5.54 = zero_z3403309356797280102nteger )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_eq_0_iff
% 5.27/5.54 thf(fact_5182_add__eq__0__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( plus_plus_rat @ A @ B )
% 5.27/5.54 = zero_zero_rat )
% 5.27/5.54 = ( B
% 5.27/5.54 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_eq_0_iff
% 5.27/5.54 thf(fact_5183_xor__num_Ocases,axiom,
% 5.27/5.54 ! [X4: product_prod_num_num] :
% 5.27/5.54 ( ( X4
% 5.27/5.54 != ( product_Pair_num_num @ one @ one ) )
% 5.27/5.54 => ( ! [N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.27/5.54 => ( ! [N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.27/5.54 => ( ! [M5: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) )
% 5.27/5.54 => ( ! [M5: num,N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.27/5.54 => ( ! [M5: num,N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) )
% 5.27/5.54 => ( ! [M5: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) )
% 5.27/5.54 => ( ! [M5: num,N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) )
% 5.27/5.54 => ~ ! [M5: num,N3: num] :
% 5.27/5.54 ( X4
% 5.27/5.54 != ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % xor_num.cases
% 5.27/5.54 thf(fact_5184_num_Oexhaust,axiom,
% 5.27/5.54 ! [Y: num] :
% 5.27/5.54 ( ( Y != one )
% 5.27/5.54 => ( ! [X23: num] :
% 5.27/5.54 ( Y
% 5.27/5.54 != ( bit0 @ X23 ) )
% 5.27/5.54 => ~ ! [X33: num] :
% 5.27/5.54 ( Y
% 5.27/5.54 != ( bit1 @ X33 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % num.exhaust
% 5.27/5.54 thf(fact_5185_less__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(2)
% 5.27/5.54 thf(fact_5186_less__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(2)
% 5.27/5.54 thf(fact_5187_less__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(2)
% 5.27/5.54 thf(fact_5188_less__minus__one__simps_I2_J,axiom,
% 5.27/5.54 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(2)
% 5.27/5.54 thf(fact_5189_less__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(4)
% 5.27/5.54 thf(fact_5190_less__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(4)
% 5.27/5.54 thf(fact_5191_less__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(4)
% 5.27/5.54 thf(fact_5192_less__minus__one__simps_I4_J,axiom,
% 5.27/5.54 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(4)
% 5.27/5.54 thf(fact_5193_numeral__times__minus__swap,axiom,
% 5.27/5.54 ! [W: num,X4: real] :
% 5.27/5.54 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.54 = ( times_times_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_times_minus_swap
% 5.27/5.54 thf(fact_5194_numeral__times__minus__swap,axiom,
% 5.27/5.54 ! [W: num,X4: int] :
% 5.27/5.54 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X4 ) )
% 5.27/5.54 = ( times_times_int @ X4 @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_times_minus_swap
% 5.27/5.54 thf(fact_5195_numeral__times__minus__swap,axiom,
% 5.27/5.54 ! [W: num,X4: complex] :
% 5.27/5.54 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X4 ) )
% 5.27/5.54 = ( times_times_complex @ X4 @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_times_minus_swap
% 5.27/5.54 thf(fact_5196_numeral__times__minus__swap,axiom,
% 5.27/5.54 ! [W: num,X4: code_integer] :
% 5.27/5.54 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X4 ) )
% 5.27/5.54 = ( times_3573771949741848930nteger @ X4 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_times_minus_swap
% 5.27/5.54 thf(fact_5197_numeral__times__minus__swap,axiom,
% 5.27/5.54 ! [W: num,X4: rat] :
% 5.27/5.54 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X4 ) )
% 5.27/5.54 = ( times_times_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_times_minus_swap
% 5.27/5.54 thf(fact_5198_nonzero__minus__divide__divide,axiom,
% 5.27/5.54 ! [B: real,A: real] :
% 5.27/5.54 ( ( B != zero_zero_real )
% 5.27/5.54 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_divide
% 5.27/5.54 thf(fact_5199_nonzero__minus__divide__divide,axiom,
% 5.27/5.54 ! [B: complex,A: complex] :
% 5.27/5.54 ( ( B != zero_zero_complex )
% 5.27/5.54 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_divide
% 5.27/5.54 thf(fact_5200_nonzero__minus__divide__divide,axiom,
% 5.27/5.54 ! [B: rat,A: rat] :
% 5.27/5.54 ( ( B != zero_zero_rat )
% 5.27/5.54 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_divide
% 5.27/5.54 thf(fact_5201_nonzero__minus__divide__right,axiom,
% 5.27/5.54 ! [B: real,A: real] :
% 5.27/5.54 ( ( B != zero_zero_real )
% 5.27/5.54 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.54 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_right
% 5.27/5.54 thf(fact_5202_nonzero__minus__divide__right,axiom,
% 5.27/5.54 ! [B: complex,A: complex] :
% 5.27/5.54 ( ( B != zero_zero_complex )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_right
% 5.27/5.54 thf(fact_5203_nonzero__minus__divide__right,axiom,
% 5.27/5.54 ! [B: rat,A: rat] :
% 5.27/5.54 ( ( B != zero_zero_rat )
% 5.27/5.54 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.54 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_minus_divide_right
% 5.27/5.54 thf(fact_5204_one__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( one_one_real
% 5.27/5.54 != ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_numeral
% 5.27/5.54 thf(fact_5205_one__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( one_one_int
% 5.27/5.54 != ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_numeral
% 5.27/5.54 thf(fact_5206_one__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( one_one_complex
% 5.27/5.54 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_numeral
% 5.27/5.54 thf(fact_5207_one__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( one_one_Code_integer
% 5.27/5.54 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_numeral
% 5.27/5.54 thf(fact_5208_one__neq__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( one_one_rat
% 5.27/5.54 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % one_neq_neg_numeral
% 5.27/5.54 thf(fact_5209_numeral__neq__neg__one,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_real @ N2 )
% 5.27/5.54 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_one
% 5.27/5.54 thf(fact_5210_numeral__neq__neg__one,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_int @ N2 )
% 5.27/5.54 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_one
% 5.27/5.54 thf(fact_5211_numeral__neq__neg__one,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numera6690914467698888265omplex @ N2 )
% 5.27/5.54 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_one
% 5.27/5.54 thf(fact_5212_numeral__neq__neg__one,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numera6620942414471956472nteger @ N2 )
% 5.27/5.54 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_one
% 5.27/5.54 thf(fact_5213_numeral__neq__neg__one,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_rat @ N2 )
% 5.27/5.54 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_neq_neg_one
% 5.27/5.54 thf(fact_5214_square__eq__1__iff,axiom,
% 5.27/5.54 ! [X4: real] :
% 5.27/5.54 ( ( ( times_times_real @ X4 @ X4 )
% 5.27/5.54 = one_one_real )
% 5.27/5.54 = ( ( X4 = one_one_real )
% 5.27/5.54 | ( X4
% 5.27/5.54 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_1_iff
% 5.27/5.54 thf(fact_5215_square__eq__1__iff,axiom,
% 5.27/5.54 ! [X4: int] :
% 5.27/5.54 ( ( ( times_times_int @ X4 @ X4 )
% 5.27/5.54 = one_one_int )
% 5.27/5.54 = ( ( X4 = one_one_int )
% 5.27/5.54 | ( X4
% 5.27/5.54 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_1_iff
% 5.27/5.54 thf(fact_5216_square__eq__1__iff,axiom,
% 5.27/5.54 ! [X4: complex] :
% 5.27/5.54 ( ( ( times_times_complex @ X4 @ X4 )
% 5.27/5.54 = one_one_complex )
% 5.27/5.54 = ( ( X4 = one_one_complex )
% 5.27/5.54 | ( X4
% 5.27/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_1_iff
% 5.27/5.54 thf(fact_5217_square__eq__1__iff,axiom,
% 5.27/5.54 ! [X4: code_integer] :
% 5.27/5.54 ( ( ( times_3573771949741848930nteger @ X4 @ X4 )
% 5.27/5.54 = one_one_Code_integer )
% 5.27/5.54 = ( ( X4 = one_one_Code_integer )
% 5.27/5.54 | ( X4
% 5.27/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_1_iff
% 5.27/5.54 thf(fact_5218_square__eq__1__iff,axiom,
% 5.27/5.54 ! [X4: rat] :
% 5.27/5.54 ( ( ( times_times_rat @ X4 @ X4 )
% 5.27/5.54 = one_one_rat )
% 5.27/5.54 = ( ( X4 = one_one_rat )
% 5.27/5.54 | ( X4
% 5.27/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % square_eq_1_iff
% 5.27/5.54 thf(fact_5219_group__cancel_Osub2,axiom,
% 5.27/5.54 ! [B3: real,K: real,B: real,A: real] :
% 5.27/5.54 ( ( B3
% 5.27/5.54 = ( plus_plus_real @ K @ B ) )
% 5.27/5.54 => ( ( minus_minus_real @ A @ B3 )
% 5.27/5.54 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.sub2
% 5.27/5.54 thf(fact_5220_group__cancel_Osub2,axiom,
% 5.27/5.54 ! [B3: int,K: int,B: int,A: int] :
% 5.27/5.54 ( ( B3
% 5.27/5.54 = ( plus_plus_int @ K @ B ) )
% 5.27/5.54 => ( ( minus_minus_int @ A @ B3 )
% 5.27/5.54 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.sub2
% 5.27/5.54 thf(fact_5221_group__cancel_Osub2,axiom,
% 5.27/5.54 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.27/5.54 ( ( B3
% 5.27/5.54 = ( plus_plus_complex @ K @ B ) )
% 5.27/5.54 => ( ( minus_minus_complex @ A @ B3 )
% 5.27/5.54 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.sub2
% 5.27/5.54 thf(fact_5222_group__cancel_Osub2,axiom,
% 5.27/5.54 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.27/5.54 ( ( B3
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.27/5.54 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.sub2
% 5.27/5.54 thf(fact_5223_group__cancel_Osub2,axiom,
% 5.27/5.54 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.27/5.54 ( ( B3
% 5.27/5.54 = ( plus_plus_rat @ K @ B ) )
% 5.27/5.54 => ( ( minus_minus_rat @ A @ B3 )
% 5.27/5.54 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % group_cancel.sub2
% 5.27/5.54 thf(fact_5224_diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_real
% 5.27/5.54 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % diff_conv_add_uminus
% 5.27/5.54 thf(fact_5225_diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_int
% 5.27/5.54 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % diff_conv_add_uminus
% 5.27/5.54 thf(fact_5226_diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_complex
% 5.27/5.54 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % diff_conv_add_uminus
% 5.27/5.54 thf(fact_5227_diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_8373710615458151222nteger
% 5.27/5.54 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % diff_conv_add_uminus
% 5.27/5.54 thf(fact_5228_diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_rat
% 5.27/5.54 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % diff_conv_add_uminus
% 5.27/5.54 thf(fact_5229_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_real
% 5.27/5.54 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.27/5.54 thf(fact_5230_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_int
% 5.27/5.54 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.27/5.54 thf(fact_5231_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_complex
% 5.27/5.54 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.27/5.54 thf(fact_5232_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_8373710615458151222nteger
% 5.27/5.54 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.27/5.54 thf(fact_5233_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.27/5.54 ( minus_minus_rat
% 5.27/5.54 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.27/5.54 thf(fact_5234_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri4939895301339042750nteger @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.54 = ( divide6298287555418463151nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.27/5.54 thf(fact_5235_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.54 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.27/5.54 thf(fact_5236_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.54 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.27/5.54 thf(fact_5237_of__nat__dvd__iff,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.27/5.54 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_dvd_iff
% 5.27/5.54 thf(fact_5238_of__nat__dvd__iff,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.54 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_dvd_iff
% 5.27/5.54 thf(fact_5239_of__nat__dvd__iff,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) )
% 5.27/5.54 = ( dvd_dvd_nat @ M @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_dvd_iff
% 5.27/5.54 thf(fact_5240_take__bit__unset__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: int] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_unset_bit_eq
% 5.27/5.54 thf(fact_5241_take__bit__unset__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: nat] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_unset_bit_eq
% 5.27/5.54 thf(fact_5242_take__bit__set__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: int] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_set_bit_eq
% 5.27/5.54 thf(fact_5243_take__bit__set__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: nat] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_set_bit_eq
% 5.27/5.54 thf(fact_5244_take__bit__flip__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: int] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.27/5.54 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_flip_bit_eq
% 5.27/5.54 thf(fact_5245_take__bit__flip__bit__eq,axiom,
% 5.27/5.54 ! [N2: nat,M: nat,A: nat] :
% 5.27/5.54 ( ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se2925701944663578781it_nat @ N2 @ A ) ) )
% 5.27/5.54 & ( ~ ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.27/5.54 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_flip_bit_eq
% 5.27/5.54 thf(fact_5246_dvd__div__neg,axiom,
% 5.27/5.54 ! [B: real,A: real] :
% 5.27/5.54 ( ( dvd_dvd_real @ B @ A )
% 5.27/5.54 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.27/5.54 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_div_neg
% 5.27/5.54 thf(fact_5247_dvd__div__neg,axiom,
% 5.27/5.54 ! [B: int,A: int] :
% 5.27/5.54 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.54 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_div_neg
% 5.27/5.54 thf(fact_5248_dvd__div__neg,axiom,
% 5.27/5.54 ! [B: complex,A: complex] :
% 5.27/5.54 ( ( dvd_dvd_complex @ B @ A )
% 5.27/5.54 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_div_neg
% 5.27/5.54 thf(fact_5249_dvd__div__neg,axiom,
% 5.27/5.54 ! [B: code_integer,A: code_integer] :
% 5.27/5.54 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.27/5.54 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_div_neg
% 5.27/5.54 thf(fact_5250_dvd__div__neg,axiom,
% 5.27/5.54 ! [B: rat,A: rat] :
% 5.27/5.54 ( ( dvd_dvd_rat @ B @ A )
% 5.27/5.54 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.27/5.54 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_div_neg
% 5.27/5.54 thf(fact_5251_dvd__neg__div,axiom,
% 5.27/5.54 ! [B: real,A: real] :
% 5.27/5.54 ( ( dvd_dvd_real @ B @ A )
% 5.27/5.54 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.54 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_neg_div
% 5.27/5.54 thf(fact_5252_dvd__neg__div,axiom,
% 5.27/5.54 ! [B: int,A: int] :
% 5.27/5.54 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.54 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_neg_div
% 5.27/5.54 thf(fact_5253_dvd__neg__div,axiom,
% 5.27/5.54 ! [B: complex,A: complex] :
% 5.27/5.54 ( ( dvd_dvd_complex @ B @ A )
% 5.27/5.54 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_neg_div
% 5.27/5.54 thf(fact_5254_dvd__neg__div,axiom,
% 5.27/5.54 ! [B: code_integer,A: code_integer] :
% 5.27/5.54 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.27/5.54 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_neg_div
% 5.27/5.54 thf(fact_5255_dvd__neg__div,axiom,
% 5.27/5.54 ! [B: rat,A: rat] :
% 5.27/5.54 ( ( dvd_dvd_rat @ B @ A )
% 5.27/5.54 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.54 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % dvd_neg_div
% 5.27/5.54 thf(fact_5256_real__of__nat__div4,axiom,
% 5.27/5.54 ! [N2: nat,X4: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ X4 ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_of_nat_div4
% 5.27/5.54 thf(fact_5257_of__nat__mod,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.27/5.54 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mod
% 5.27/5.54 thf(fact_5258_of__nat__mod,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.27/5.54 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mod
% 5.27/5.54 thf(fact_5259_of__nat__mod,axiom,
% 5.27/5.54 ! [M: nat,N2: nat] :
% 5.27/5.54 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N2 ) )
% 5.27/5.54 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_mod
% 5.27/5.54 thf(fact_5260_real__minus__mult__self__le,axiom,
% 5.27/5.54 ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X4 @ X4 ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_minus_mult_self_le
% 5.27/5.54 thf(fact_5261_real__of__nat__div,axiom,
% 5.27/5.54 ! [D: nat,N2: nat] :
% 5.27/5.54 ( ( dvd_dvd_nat @ D @ N2 )
% 5.27/5.54 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ D ) )
% 5.27/5.54 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_of_nat_div
% 5.27/5.54 thf(fact_5262_zmod__zminus1__not__zero,axiom,
% 5.27/5.54 ! [K: int,L: int] :
% 5.27/5.54 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.27/5.54 != zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ K @ L )
% 5.27/5.54 != zero_zero_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % zmod_zminus1_not_zero
% 5.27/5.54 thf(fact_5263_zmod__zminus2__not__zero,axiom,
% 5.27/5.54 ! [K: int,L: int] :
% 5.27/5.54 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L ) )
% 5.27/5.54 != zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ K @ L )
% 5.27/5.54 != zero_zero_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % zmod_zminus2_not_zero
% 5.27/5.54 thf(fact_5264_take__bit__Suc__minus__bit0,axiom,
% 5.27/5.54 ! [N2: nat,K: num] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.54 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_Suc_minus_bit0
% 5.27/5.54 thf(fact_5265_Bernoulli__inequality,axiom,
% 5.27/5.54 ! [X4: real,N2: nat] :
% 5.27/5.54 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.54 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X4 ) @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % Bernoulli_inequality
% 5.27/5.54 thf(fact_5266_add__diff__assoc__enat,axiom,
% 5.27/5.54 ! [Z: extended_enat,Y: extended_enat,X4: extended_enat] :
% 5.27/5.54 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.27/5.54 => ( ( plus_p3455044024723400733d_enat @ X4 @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.27/5.54 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X4 @ Y ) @ Z ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % add_diff_assoc_enat
% 5.27/5.54 thf(fact_5267_take__bit__signed__take__bit,axiom,
% 5.27/5.54 ! [M: nat,N2: nat,A: int] :
% 5.27/5.54 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N2 @ A ) )
% 5.27/5.54 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_signed_take_bit
% 5.27/5.54 thf(fact_5268_neg__numeral__le__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_zero
% 5.27/5.54 thf(fact_5269_neg__numeral__le__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_zero
% 5.27/5.54 thf(fact_5270_neg__numeral__le__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_zero
% 5.27/5.54 thf(fact_5271_neg__numeral__le__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_zero
% 5.27/5.54 thf(fact_5272_not__zero__le__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_le_neg_numeral
% 5.27/5.54 thf(fact_5273_not__zero__le__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_le_neg_numeral
% 5.27/5.54 thf(fact_5274_not__zero__le__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_le_neg_numeral
% 5.27/5.54 thf(fact_5275_not__zero__le__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_le_neg_numeral
% 5.27/5.54 thf(fact_5276_not__zero__less__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_less_neg_numeral
% 5.27/5.54 thf(fact_5277_not__zero__less__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_less_neg_numeral
% 5.27/5.54 thf(fact_5278_not__zero__less__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_less_neg_numeral
% 5.27/5.54 thf(fact_5279_not__zero__less__neg__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_zero_less_neg_numeral
% 5.27/5.54 thf(fact_5280_neg__numeral__less__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) @ zero_zero_real ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_zero
% 5.27/5.54 thf(fact_5281_neg__numeral__less__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ zero_zero_int ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_zero
% 5.27/5.54 thf(fact_5282_neg__numeral__less__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) @ zero_z3403309356797280102nteger ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_zero
% 5.27/5.54 thf(fact_5283_neg__numeral__less__zero,axiom,
% 5.27/5.54 ! [N2: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) @ zero_zero_rat ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_zero
% 5.27/5.54 thf(fact_5284_le__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(3)
% 5.27/5.54 thf(fact_5285_le__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(3)
% 5.27/5.54 thf(fact_5286_le__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(3)
% 5.27/5.54 thf(fact_5287_le__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(3)
% 5.27/5.54 thf(fact_5288_le__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(1)
% 5.27/5.54 thf(fact_5289_le__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(1)
% 5.27/5.54 thf(fact_5290_le__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(1)
% 5.27/5.54 thf(fact_5291_le__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.27/5.54
% 5.27/5.54 % le_minus_one_simps(1)
% 5.27/5.54 thf(fact_5292_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5293_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5294_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5295_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5296_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5297_numeral__Bit1,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1
% 5.27/5.54 thf(fact_5298_take__bit__decr__eq,axiom,
% 5.27/5.54 ! [N2: nat,K: int] :
% 5.27/5.54 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.54 != zero_zero_int )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( minus_minus_int @ K @ one_one_int ) )
% 5.27/5.54 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ one_one_int ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_decr_eq
% 5.27/5.54 thf(fact_5299_less__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(1)
% 5.27/5.54 thf(fact_5300_less__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(1)
% 5.27/5.54 thf(fact_5301_less__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(1)
% 5.27/5.54 thf(fact_5302_less__minus__one__simps_I1_J,axiom,
% 5.27/5.54 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(1)
% 5.27/5.54 thf(fact_5303_less__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(3)
% 5.27/5.54 thf(fact_5304_less__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(3)
% 5.27/5.54 thf(fact_5305_less__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(3)
% 5.27/5.54 thf(fact_5306_less__minus__one__simps_I3_J,axiom,
% 5.27/5.54 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_one_simps(3)
% 5.27/5.54 thf(fact_5307_of__nat__diff,axiom,
% 5.27/5.54 ! [N2: nat,M: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.54 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_diff
% 5.27/5.54 thf(fact_5308_of__nat__diff,axiom,
% 5.27/5.54 ! [N2: nat,M: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.54 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_diff
% 5.27/5.54 thf(fact_5309_of__nat__diff,axiom,
% 5.27/5.54 ! [N2: nat,M: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.54 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_diff
% 5.27/5.54 thf(fact_5310_of__nat__diff,axiom,
% 5.27/5.54 ! [N2: nat,M: nat] :
% 5.27/5.54 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.54 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N2 ) )
% 5.27/5.54 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % of_nat_diff
% 5.27/5.54 thf(fact_5311_not__one__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_le_neg_numeral
% 5.27/5.54 thf(fact_5312_not__one__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_le_neg_numeral
% 5.27/5.54 thf(fact_5313_not__one__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_le_neg_numeral
% 5.27/5.54 thf(fact_5314_not__one__le__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_le_neg_numeral
% 5.27/5.54 thf(fact_5315_not__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_one
% 5.27/5.54 thf(fact_5316_not__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_one
% 5.27/5.54 thf(fact_5317_not__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_one
% 5.27/5.54 thf(fact_5318_not__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_le_neg_one
% 5.27/5.54 thf(fact_5319_neg__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_neg_one
% 5.27/5.54 thf(fact_5320_neg__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_neg_one
% 5.27/5.54 thf(fact_5321_neg__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_neg_one
% 5.27/5.54 thf(fact_5322_neg__numeral__le__neg__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_neg_one
% 5.27/5.54 thf(fact_5323_neg__one__le__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_le_numeral
% 5.27/5.54 thf(fact_5324_neg__one__le__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_le_numeral
% 5.27/5.54 thf(fact_5325_neg__one__le__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_le_numeral
% 5.27/5.54 thf(fact_5326_neg__one__le__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_le_numeral
% 5.27/5.54 thf(fact_5327_neg__numeral__le__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_one
% 5.27/5.54 thf(fact_5328_neg__numeral__le__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_one
% 5.27/5.54 thf(fact_5329_neg__numeral__le__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_one
% 5.27/5.54 thf(fact_5330_neg__numeral__le__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_le_one
% 5.27/5.54 thf(fact_5331_not__neg__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_neg_one_less_neg_numeral
% 5.27/5.54 thf(fact_5332_not__neg__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_neg_one_less_neg_numeral
% 5.27/5.54 thf(fact_5333_not__neg__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_neg_one_less_neg_numeral
% 5.27/5.54 thf(fact_5334_not__neg__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_neg_one_less_neg_numeral
% 5.27/5.54 thf(fact_5335_not__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_less_neg_numeral
% 5.27/5.54 thf(fact_5336_not__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_less_neg_numeral
% 5.27/5.54 thf(fact_5337_not__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_less_neg_numeral
% 5.27/5.54 thf(fact_5338_not__one__less__neg__numeral,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_one_less_neg_numeral
% 5.27/5.54 thf(fact_5339_not__numeral__less__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_one
% 5.27/5.54 thf(fact_5340_not__numeral__less__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_one
% 5.27/5.54 thf(fact_5341_not__numeral__less__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_one
% 5.27/5.54 thf(fact_5342_not__numeral__less__neg__one,axiom,
% 5.27/5.54 ! [M: num] :
% 5.27/5.54 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % not_numeral_less_neg_one
% 5.27/5.54 thf(fact_5343_neg__one__less__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_less_numeral
% 5.27/5.54 thf(fact_5344_neg__one__less__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_less_numeral
% 5.27/5.54 thf(fact_5345_neg__one__less__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_less_numeral
% 5.27/5.54 thf(fact_5346_neg__one__less__numeral,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_one_less_numeral
% 5.27/5.54 thf(fact_5347_neg__numeral__less__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_one
% 5.27/5.54 thf(fact_5348_neg__numeral__less__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_one
% 5.27/5.54 thf(fact_5349_neg__numeral__less__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_one
% 5.27/5.54 thf(fact_5350_neg__numeral__less__one,axiom,
% 5.27/5.54 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.27/5.54
% 5.27/5.54 % neg_numeral_less_one
% 5.27/5.54 thf(fact_5351_eq__minus__divide__eq,axiom,
% 5.27/5.54 ! [A: real,B: real,C: real] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_real )
% 5.27/5.54 => ( ( times_times_real @ A @ C )
% 5.27/5.54 = ( uminus_uminus_real @ B ) ) )
% 5.27/5.54 & ( ( C = zero_zero_real )
% 5.27/5.54 => ( A = zero_zero_real ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_minus_divide_eq
% 5.27/5.54 thf(fact_5352_eq__minus__divide__eq,axiom,
% 5.27/5.54 ! [A: complex,B: complex,C: complex] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_complex )
% 5.27/5.54 => ( ( times_times_complex @ A @ C )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.27/5.54 & ( ( C = zero_zero_complex )
% 5.27/5.54 => ( A = zero_zero_complex ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_minus_divide_eq
% 5.27/5.54 thf(fact_5353_eq__minus__divide__eq,axiom,
% 5.27/5.54 ! [A: rat,B: rat,C: rat] :
% 5.27/5.54 ( ( A
% 5.27/5.54 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_rat )
% 5.27/5.54 => ( ( times_times_rat @ A @ C )
% 5.27/5.54 = ( uminus_uminus_rat @ B ) ) )
% 5.27/5.54 & ( ( C = zero_zero_rat )
% 5.27/5.54 => ( A = zero_zero_rat ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_minus_divide_eq
% 5.27/5.54 thf(fact_5354_minus__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: real,C: real,A: real] :
% 5.27/5.54 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.27/5.54 = A )
% 5.27/5.54 = ( ( ( C != zero_zero_real )
% 5.27/5.54 => ( ( uminus_uminus_real @ B )
% 5.27/5.54 = ( times_times_real @ A @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_real )
% 5.27/5.54 => ( A = zero_zero_real ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_eq_eq
% 5.27/5.54 thf(fact_5355_minus__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: complex,C: complex,A: complex] :
% 5.27/5.54 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.27/5.54 = A )
% 5.27/5.54 = ( ( ( C != zero_zero_complex )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ B )
% 5.27/5.54 = ( times_times_complex @ A @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_complex )
% 5.27/5.54 => ( A = zero_zero_complex ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_eq_eq
% 5.27/5.54 thf(fact_5356_minus__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: rat,C: rat,A: rat] :
% 5.27/5.54 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.54 = A )
% 5.27/5.54 = ( ( ( C != zero_zero_rat )
% 5.27/5.54 => ( ( uminus_uminus_rat @ B )
% 5.27/5.54 = ( times_times_rat @ A @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_rat )
% 5.27/5.54 => ( A = zero_zero_rat ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_eq_eq
% 5.27/5.54 thf(fact_5357_nonzero__neg__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: real,A: real,C: real] :
% 5.27/5.54 ( ( B != zero_zero_real )
% 5.27/5.54 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.54 = C )
% 5.27/5.54 = ( ( uminus_uminus_real @ A )
% 5.27/5.54 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq
% 5.27/5.54 thf(fact_5358_nonzero__neg__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: complex,A: complex,C: complex] :
% 5.27/5.54 ( ( B != zero_zero_complex )
% 5.27/5.54 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.54 = C )
% 5.27/5.54 = ( ( uminus1482373934393186551omplex @ A )
% 5.27/5.54 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq
% 5.27/5.54 thf(fact_5359_nonzero__neg__divide__eq__eq,axiom,
% 5.27/5.54 ! [B: rat,A: rat,C: rat] :
% 5.27/5.54 ( ( B != zero_zero_rat )
% 5.27/5.54 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.54 = C )
% 5.27/5.54 = ( ( uminus_uminus_rat @ A )
% 5.27/5.54 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq
% 5.27/5.54 thf(fact_5360_nonzero__neg__divide__eq__eq2,axiom,
% 5.27/5.54 ! [B: real,C: real,A: real] :
% 5.27/5.54 ( ( B != zero_zero_real )
% 5.27/5.54 => ( ( C
% 5.27/5.54 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.27/5.54 = ( ( times_times_real @ C @ B )
% 5.27/5.54 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq2
% 5.27/5.54 thf(fact_5361_nonzero__neg__divide__eq__eq2,axiom,
% 5.27/5.54 ! [B: complex,C: complex,A: complex] :
% 5.27/5.54 ( ( B != zero_zero_complex )
% 5.27/5.54 => ( ( C
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.54 = ( ( times_times_complex @ C @ B )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq2
% 5.27/5.54 thf(fact_5362_nonzero__neg__divide__eq__eq2,axiom,
% 5.27/5.54 ! [B: rat,C: rat,A: rat] :
% 5.27/5.54 ( ( B != zero_zero_rat )
% 5.27/5.54 => ( ( C
% 5.27/5.54 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.27/5.54 = ( ( times_times_rat @ C @ B )
% 5.27/5.54 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % nonzero_neg_divide_eq_eq2
% 5.27/5.54 thf(fact_5363_divide__eq__minus__1__iff,axiom,
% 5.27/5.54 ! [A: real,B: real] :
% 5.27/5.54 ( ( ( divide_divide_real @ A @ B )
% 5.27/5.54 = ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.54 = ( ( B != zero_zero_real )
% 5.27/5.54 & ( A
% 5.27/5.54 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_minus_1_iff
% 5.27/5.54 thf(fact_5364_divide__eq__minus__1__iff,axiom,
% 5.27/5.54 ! [A: complex,B: complex] :
% 5.27/5.54 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.54 = ( ( B != zero_zero_complex )
% 5.27/5.54 & ( A
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_minus_1_iff
% 5.27/5.54 thf(fact_5365_divide__eq__minus__1__iff,axiom,
% 5.27/5.54 ! [A: rat,B: rat] :
% 5.27/5.54 ( ( ( divide_divide_rat @ A @ B )
% 5.27/5.54 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.54 = ( ( B != zero_zero_rat )
% 5.27/5.54 & ( A
% 5.27/5.54 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_minus_1_iff
% 5.27/5.54 thf(fact_5366_mult__1s__ring__1_I1_J,axiom,
% 5.27/5.54 ! [B: real] :
% 5.27/5.54 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.27/5.54 = ( uminus_uminus_real @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(1)
% 5.27/5.54 thf(fact_5367_mult__1s__ring__1_I1_J,axiom,
% 5.27/5.54 ! [B: int] :
% 5.27/5.54 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.27/5.54 = ( uminus_uminus_int @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(1)
% 5.27/5.54 thf(fact_5368_mult__1s__ring__1_I1_J,axiom,
% 5.27/5.54 ! [B: complex] :
% 5.27/5.54 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(1)
% 5.27/5.54 thf(fact_5369_mult__1s__ring__1_I1_J,axiom,
% 5.27/5.54 ! [B: code_integer] :
% 5.27/5.54 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(1)
% 5.27/5.54 thf(fact_5370_mult__1s__ring__1_I1_J,axiom,
% 5.27/5.54 ! [B: rat] :
% 5.27/5.54 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.27/5.54 = ( uminus_uminus_rat @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(1)
% 5.27/5.54 thf(fact_5371_mult__1s__ring__1_I2_J,axiom,
% 5.27/5.54 ! [B: real] :
% 5.27/5.54 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.27/5.54 = ( uminus_uminus_real @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(2)
% 5.27/5.54 thf(fact_5372_mult__1s__ring__1_I2_J,axiom,
% 5.27/5.54 ! [B: int] :
% 5.27/5.54 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.27/5.54 = ( uminus_uminus_int @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(2)
% 5.27/5.54 thf(fact_5373_mult__1s__ring__1_I2_J,axiom,
% 5.27/5.54 ! [B: complex] :
% 5.27/5.54 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(2)
% 5.27/5.54 thf(fact_5374_mult__1s__ring__1_I2_J,axiom,
% 5.27/5.54 ! [B: code_integer] :
% 5.27/5.54 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(2)
% 5.27/5.54 thf(fact_5375_mult__1s__ring__1_I2_J,axiom,
% 5.27/5.54 ! [B: rat] :
% 5.27/5.54 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.27/5.54 = ( uminus_uminus_rat @ B ) ) ).
% 5.27/5.54
% 5.27/5.54 % mult_1s_ring_1(2)
% 5.27/5.54 thf(fact_5376_uminus__numeral__One,axiom,
% 5.27/5.54 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.27/5.54 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.54
% 5.27/5.54 % uminus_numeral_One
% 5.27/5.54 thf(fact_5377_uminus__numeral__One,axiom,
% 5.27/5.54 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.27/5.54 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % uminus_numeral_One
% 5.27/5.54 thf(fact_5378_uminus__numeral__One,axiom,
% 5.27/5.54 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.54
% 5.27/5.54 % uminus_numeral_One
% 5.27/5.54 thf(fact_5379_uminus__numeral__One,axiom,
% 5.27/5.54 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.27/5.54 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % uminus_numeral_One
% 5.27/5.54 thf(fact_5380_uminus__numeral__One,axiom,
% 5.27/5.54 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.27/5.54 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.54
% 5.27/5.54 % uminus_numeral_One
% 5.27/5.54 thf(fact_5381_power__minus,axiom,
% 5.27/5.54 ! [A: real,N2: nat] :
% 5.27/5.54 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.27/5.54 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus
% 5.27/5.54 thf(fact_5382_power__minus,axiom,
% 5.27/5.54 ! [A: int,N2: nat] :
% 5.27/5.54 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.27/5.54 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus
% 5.27/5.54 thf(fact_5383_power__minus,axiom,
% 5.27/5.54 ! [A: complex,N2: nat] :
% 5.27/5.54 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.27/5.54 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus
% 5.27/5.54 thf(fact_5384_power__minus,axiom,
% 5.27/5.54 ! [A: code_integer,N2: nat] :
% 5.27/5.54 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.27/5.54 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus
% 5.27/5.54 thf(fact_5385_power__minus,axiom,
% 5.27/5.54 ! [A: rat,N2: nat] :
% 5.27/5.54 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.27/5.54 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus
% 5.27/5.54 thf(fact_5386_eval__nat__numeral_I3_J,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.27/5.54 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eval_nat_numeral(3)
% 5.27/5.54 thf(fact_5387_cong__exp__iff__simps_I10_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(10)
% 5.27/5.54 thf(fact_5388_cong__exp__iff__simps_I10_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(10)
% 5.27/5.54 thf(fact_5389_cong__exp__iff__simps_I10_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(10)
% 5.27/5.54 thf(fact_5390_cong__exp__iff__simps_I12_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(12)
% 5.27/5.54 thf(fact_5391_cong__exp__iff__simps_I12_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(12)
% 5.27/5.54 thf(fact_5392_cong__exp__iff__simps_I12_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(12)
% 5.27/5.54 thf(fact_5393_cong__exp__iff__simps_I13_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.54 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.27/5.54 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(13)
% 5.27/5.54 thf(fact_5394_cong__exp__iff__simps_I13_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.54 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.27/5.54 = ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(13)
% 5.27/5.54 thf(fact_5395_cong__exp__iff__simps_I13_J,axiom,
% 5.27/5.54 ! [M: num,Q3: num,N2: num] :
% 5.27/5.54 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.54 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.27/5.54 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % cong_exp_iff_simps(13)
% 5.27/5.54 thf(fact_5396_power__minus__Bit0,axiom,
% 5.27/5.54 ! [X4: real,K: num] :
% 5.27/5.54 ( ( power_power_real @ ( uminus_uminus_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.54 = ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit0
% 5.27/5.54 thf(fact_5397_power__minus__Bit0,axiom,
% 5.27/5.54 ! [X4: int,K: num] :
% 5.27/5.54 ( ( power_power_int @ ( uminus_uminus_int @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.54 = ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit0
% 5.27/5.54 thf(fact_5398_power__minus__Bit0,axiom,
% 5.27/5.54 ! [X4: complex,K: num] :
% 5.27/5.54 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.54 = ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit0
% 5.27/5.54 thf(fact_5399_power__minus__Bit0,axiom,
% 5.27/5.54 ! [X4: code_integer,K: num] :
% 5.27/5.54 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.54 = ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit0
% 5.27/5.54 thf(fact_5400_power__minus__Bit0,axiom,
% 5.27/5.54 ! [X4: rat,K: num] :
% 5.27/5.54 ( ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.54 = ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % power_minus_Bit0
% 5.27/5.54 thf(fact_5401_reals__Archimedean3,axiom,
% 5.27/5.54 ! [X4: real] :
% 5.27/5.54 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.54 => ! [Y4: real] :
% 5.27/5.54 ? [N3: nat] : ( ord_less_real @ Y4 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % reals_Archimedean3
% 5.27/5.54 thf(fact_5402_take__bit__Suc__bit1,axiom,
% 5.27/5.54 ! [N2: nat,K: num] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_Suc_bit1
% 5.27/5.54 thf(fact_5403_take__bit__Suc__bit1,axiom,
% 5.27/5.54 ! [N2: nat,K: num] :
% 5.27/5.54 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_Suc_bit1
% 5.27/5.54 thf(fact_5404_take__bit__Suc__minus__1__eq,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.54 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_Suc_minus_1_eq
% 5.27/5.54 thf(fact_5405_take__bit__Suc__minus__1__eq,axiom,
% 5.27/5.54 ! [N2: nat] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_Suc_minus_1_eq
% 5.27/5.54 thf(fact_5406_take__bit__numeral__minus__1__eq,axiom,
% 5.27/5.54 ! [K: num] :
% 5.27/5.54 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.54 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_numeral_minus_1_eq
% 5.27/5.54 thf(fact_5407_take__bit__numeral__minus__1__eq,axiom,
% 5.27/5.54 ! [K: num] :
% 5.27/5.54 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_numeral_minus_1_eq
% 5.27/5.54 thf(fact_5408_real__0__less__add__iff,axiom,
% 5.27/5.54 ! [X4: real,Y: real] :
% 5.27/5.54 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.54 = ( ord_less_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_0_less_add_iff
% 5.27/5.54 thf(fact_5409_real__add__less__0__iff,axiom,
% 5.27/5.54 ! [X4: real,Y: real] :
% 5.27/5.54 ( ( ord_less_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 5.27/5.54 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_add_less_0_iff
% 5.27/5.54 thf(fact_5410_real__0__le__add__iff,axiom,
% 5.27/5.54 ! [X4: real,Y: real] :
% 5.27/5.54 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.54 = ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ Y ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_0_le_add_iff
% 5.27/5.54 thf(fact_5411_real__add__le__0__iff,axiom,
% 5.27/5.54 ! [X4: real,Y: real] :
% 5.27/5.54 ( ( ord_less_eq_real @ ( plus_plus_real @ X4 @ Y ) @ zero_zero_real )
% 5.27/5.54 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X4 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_add_le_0_iff
% 5.27/5.54 thf(fact_5412_real__of__nat__div__aux,axiom,
% 5.27/5.54 ! [X4: nat,D: nat] :
% 5.27/5.54 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X4 ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.27/5.54 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X4 @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X4 @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % real_of_nat_div_aux
% 5.27/5.54 thf(fact_5413_zmod__zminus1__eq__if,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.54 = zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = zero_zero_int ) )
% 5.27/5.54 & ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.54 != zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.54 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zmod_zminus1_eq_if
% 5.27/5.54 thf(fact_5414_zmod__zminus2__eq__if,axiom,
% 5.27/5.54 ! [A: int,B: int] :
% 5.27/5.54 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.54 = zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = zero_zero_int ) )
% 5.27/5.54 & ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.54 != zero_zero_int )
% 5.27/5.54 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.54 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % zmod_zminus2_eq_if
% 5.27/5.54 thf(fact_5415_mod__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: code_integer,M: nat,N2: nat] :
% 5.27/5.54 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N2 ) ) )
% 5.27/5.54 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N2 ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_mult2_eq'
% 5.27/5.54 thf(fact_5416_mod__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: int,M: nat,N2: nat] :
% 5.27/5.54 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.54 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_mult2_eq'
% 5.27/5.54 thf(fact_5417_mod__mult2__eq_H,axiom,
% 5.27/5.54 ! [A: nat,M: nat,N2: nat] :
% 5.27/5.54 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) )
% 5.27/5.54 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % mod_mult2_eq'
% 5.27/5.54 thf(fact_5418_take__bit__minus__small__eq,axiom,
% 5.27/5.54 ! [K: int,N2: nat] :
% 5.27/5.54 ( ( ord_less_int @ zero_zero_int @ K )
% 5.27/5.54 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.54 => ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) )
% 5.27/5.54 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % take_bit_minus_small_eq
% 5.27/5.54 thf(fact_5419_numeral__Bit1__div__2,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.54 = ( numeral_numeral_nat @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1_div_2
% 5.27/5.54 thf(fact_5420_numeral__Bit1__div__2,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.54 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1_div_2
% 5.27/5.54 thf(fact_5421_numeral__Bit1__div__2,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ( ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.54 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.54
% 5.27/5.54 % numeral_Bit1_div_2
% 5.27/5.54 thf(fact_5422_pos__minus__divide__less__eq,axiom,
% 5.27/5.54 ! [C: real,B: real,A: real] :
% 5.27/5.54 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.54 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % pos_minus_divide_less_eq
% 5.27/5.54 thf(fact_5423_pos__minus__divide__less__eq,axiom,
% 5.27/5.54 ! [C: rat,B: rat,A: rat] :
% 5.27/5.54 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.54 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % pos_minus_divide_less_eq
% 5.27/5.54 thf(fact_5424_pos__less__minus__divide__eq,axiom,
% 5.27/5.54 ! [C: real,A: real,B: real] :
% 5.27/5.54 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.54 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % pos_less_minus_divide_eq
% 5.27/5.54 thf(fact_5425_pos__less__minus__divide__eq,axiom,
% 5.27/5.54 ! [C: rat,A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.54 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % pos_less_minus_divide_eq
% 5.27/5.54 thf(fact_5426_neg__minus__divide__less__eq,axiom,
% 5.27/5.54 ! [C: real,B: real,A: real] :
% 5.27/5.54 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.54 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_minus_divide_less_eq
% 5.27/5.54 thf(fact_5427_neg__minus__divide__less__eq,axiom,
% 5.27/5.54 ! [C: rat,B: rat,A: rat] :
% 5.27/5.54 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.54 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_minus_divide_less_eq
% 5.27/5.54 thf(fact_5428_neg__less__minus__divide__eq,axiom,
% 5.27/5.54 ! [C: real,A: real,B: real] :
% 5.27/5.54 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.54 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_less_minus_divide_eq
% 5.27/5.54 thf(fact_5429_neg__less__minus__divide__eq,axiom,
% 5.27/5.54 ! [C: rat,A: rat,B: rat] :
% 5.27/5.54 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.54 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % neg_less_minus_divide_eq
% 5.27/5.54 thf(fact_5430_minus__divide__less__eq,axiom,
% 5.27/5.54 ! [B: real,C: real,A: real] :
% 5.27/5.54 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.54 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.27/5.54 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.27/5.54 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_less_eq
% 5.27/5.54 thf(fact_5431_minus__divide__less__eq,axiom,
% 5.27/5.54 ! [B: rat,C: rat,A: rat] :
% 5.27/5.54 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.54 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.27/5.54 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_less_eq
% 5.27/5.54 thf(fact_5432_less__minus__divide__eq,axiom,
% 5.27/5.54 ! [A: real,B: real,C: real] :
% 5.27/5.54 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.54 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.27/5.54 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.54 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.27/5.54 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.54 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_divide_eq
% 5.27/5.54 thf(fact_5433_less__minus__divide__eq,axiom,
% 5.27/5.54 ! [A: rat,B: rat,C: rat] :
% 5.27/5.54 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.54 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.27/5.54 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.54 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.54 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.54 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % less_minus_divide_eq
% 5.27/5.54 thf(fact_5434_eq__divide__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [W: num,B: real,C: real] :
% 5.27/5.54 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.54 = ( divide_divide_real @ B @ C ) )
% 5.27/5.54 = ( ( ( C != zero_zero_real )
% 5.27/5.54 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.27/5.54 = B ) )
% 5.27/5.54 & ( ( C = zero_zero_real )
% 5.27/5.54 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.54 = zero_zero_real ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_divide_eq_numeral(2)
% 5.27/5.54 thf(fact_5435_eq__divide__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [W: num,B: complex,C: complex] :
% 5.27/5.54 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.54 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.27/5.54 = ( ( ( C != zero_zero_complex )
% 5.27/5.54 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.27/5.54 = B ) )
% 5.27/5.54 & ( ( C = zero_zero_complex )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.54 = zero_zero_complex ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_divide_eq_numeral(2)
% 5.27/5.54 thf(fact_5436_eq__divide__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [W: num,B: rat,C: rat] :
% 5.27/5.54 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.54 = ( divide_divide_rat @ B @ C ) )
% 5.27/5.54 = ( ( ( C != zero_zero_rat )
% 5.27/5.54 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.27/5.54 = B ) )
% 5.27/5.54 & ( ( C = zero_zero_rat )
% 5.27/5.54 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.54 = zero_zero_rat ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % eq_divide_eq_numeral(2)
% 5.27/5.54 thf(fact_5437_divide__eq__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [B: real,C: real,W: num] :
% 5.27/5.54 ( ( ( divide_divide_real @ B @ C )
% 5.27/5.54 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_real )
% 5.27/5.54 => ( B
% 5.27/5.54 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_real )
% 5.27/5.54 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.54 = zero_zero_real ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_eq_numeral(2)
% 5.27/5.54 thf(fact_5438_divide__eq__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [B: complex,C: complex,W: num] :
% 5.27/5.54 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.27/5.54 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_complex )
% 5.27/5.54 => ( B
% 5.27/5.54 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_complex )
% 5.27/5.54 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.54 = zero_zero_complex ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_eq_numeral(2)
% 5.27/5.54 thf(fact_5439_divide__eq__eq__numeral_I2_J,axiom,
% 5.27/5.54 ! [B: rat,C: rat,W: num] :
% 5.27/5.54 ( ( ( divide_divide_rat @ B @ C )
% 5.27/5.54 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.54 = ( ( ( C != zero_zero_rat )
% 5.27/5.54 => ( B
% 5.27/5.54 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.27/5.54 & ( ( C = zero_zero_rat )
% 5.27/5.54 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.54 = zero_zero_rat ) ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % divide_eq_eq_numeral(2)
% 5.27/5.54 thf(fact_5440_odd__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % odd_numeral
% 5.27/5.54 thf(fact_5441_odd__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % odd_numeral
% 5.27/5.54 thf(fact_5442_odd__numeral,axiom,
% 5.27/5.54 ! [N2: num] :
% 5.27/5.54 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % odd_numeral
% 5.27/5.54 thf(fact_5443_minus__divide__add__eq__iff,axiom,
% 5.27/5.54 ! [Z: real,X4: real,Y: real] :
% 5.27/5.54 ( ( Z != zero_zero_real )
% 5.27/5.54 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 5.27/5.54 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.54
% 5.27/5.54 % minus_divide_add_eq_iff
% 5.27/5.54 thf(fact_5444_minus__divide__add__eq__iff,axiom,
% 5.27/5.54 ! [Z: complex,X4: complex,Y: complex] :
% 5.27/5.55 ( ( Z != zero_zero_complex )
% 5.27/5.55 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_add_eq_iff
% 5.27/5.55 thf(fact_5445_minus__divide__add__eq__iff,axiom,
% 5.27/5.55 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.55 ( ( Z != zero_zero_rat )
% 5.27/5.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 5.27/5.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_add_eq_iff
% 5.27/5.55 thf(fact_5446_add__divide__eq__if__simps_I3_J,axiom,
% 5.27/5.55 ! [Z: real,A: real,B: real] :
% 5.27/5.55 ( ( ( Z = zero_zero_real )
% 5.27/5.55 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.27/5.55 = B ) )
% 5.27/5.55 & ( ( Z != zero_zero_real )
% 5.27/5.55 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(3)
% 5.27/5.55 thf(fact_5447_add__divide__eq__if__simps_I3_J,axiom,
% 5.27/5.55 ! [Z: complex,A: complex,B: complex] :
% 5.27/5.55 ( ( ( Z = zero_zero_complex )
% 5.27/5.55 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.27/5.55 = B ) )
% 5.27/5.55 & ( ( Z != zero_zero_complex )
% 5.27/5.55 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(3)
% 5.27/5.55 thf(fact_5448_add__divide__eq__if__simps_I3_J,axiom,
% 5.27/5.55 ! [Z: rat,A: rat,B: rat] :
% 5.27/5.55 ( ( ( Z = zero_zero_rat )
% 5.27/5.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.27/5.55 = B ) )
% 5.27/5.55 & ( ( Z != zero_zero_rat )
% 5.27/5.55 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(3)
% 5.27/5.55 thf(fact_5449_cong__exp__iff__simps_I3_J,axiom,
% 5.27/5.55 ! [N2: num,Q3: num] :
% 5.27/5.55 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 != zero_zero_nat ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(3)
% 5.27/5.55 thf(fact_5450_cong__exp__iff__simps_I3_J,axiom,
% 5.27/5.55 ! [N2: num,Q3: num] :
% 5.27/5.55 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 != zero_zero_int ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(3)
% 5.27/5.55 thf(fact_5451_cong__exp__iff__simps_I3_J,axiom,
% 5.27/5.55 ! [N2: num,Q3: num] :
% 5.27/5.55 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 != zero_z3403309356797280102nteger ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(3)
% 5.27/5.55 thf(fact_5452_add__divide__eq__if__simps_I6_J,axiom,
% 5.27/5.55 ! [Z: real,A: real,B: real] :
% 5.27/5.55 ( ( ( Z = zero_zero_real )
% 5.27/5.55 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.27/5.55 = ( uminus_uminus_real @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_real )
% 5.27/5.55 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(6)
% 5.27/5.55 thf(fact_5453_add__divide__eq__if__simps_I6_J,axiom,
% 5.27/5.55 ! [Z: complex,A: complex,B: complex] :
% 5.27/5.55 ( ( ( Z = zero_zero_complex )
% 5.27/5.55 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_complex )
% 5.27/5.55 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(6)
% 5.27/5.55 thf(fact_5454_add__divide__eq__if__simps_I6_J,axiom,
% 5.27/5.55 ! [Z: rat,A: rat,B: rat] :
% 5.27/5.55 ( ( ( Z = zero_zero_rat )
% 5.27/5.55 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.27/5.55 = ( uminus_uminus_rat @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_rat )
% 5.27/5.55 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.27/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(6)
% 5.27/5.55 thf(fact_5455_add__divide__eq__if__simps_I5_J,axiom,
% 5.27/5.55 ! [Z: real,A: real,B: real] :
% 5.27/5.55 ( ( ( Z = zero_zero_real )
% 5.27/5.55 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.27/5.55 = ( uminus_uminus_real @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_real )
% 5.27/5.55 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(5)
% 5.27/5.55 thf(fact_5456_add__divide__eq__if__simps_I5_J,axiom,
% 5.27/5.55 ! [Z: complex,A: complex,B: complex] :
% 5.27/5.55 ( ( ( Z = zero_zero_complex )
% 5.27/5.55 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_complex )
% 5.27/5.55 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(5)
% 5.27/5.55 thf(fact_5457_add__divide__eq__if__simps_I5_J,axiom,
% 5.27/5.55 ! [Z: rat,A: rat,B: rat] :
% 5.27/5.55 ( ( ( Z = zero_zero_rat )
% 5.27/5.55 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.27/5.55 = ( uminus_uminus_rat @ B ) ) )
% 5.27/5.55 & ( ( Z != zero_zero_rat )
% 5.27/5.55 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.27/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_divide_eq_if_simps(5)
% 5.27/5.55 thf(fact_5458_minus__divide__diff__eq__iff,axiom,
% 5.27/5.55 ! [Z: real,X4: real,Y: real] :
% 5.27/5.55 ( ( Z != zero_zero_real )
% 5.27/5.55 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X4 @ Z ) ) @ Y )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_diff_eq_iff
% 5.27/5.55 thf(fact_5459_minus__divide__diff__eq__iff,axiom,
% 5.27/5.55 ! [Z: complex,X4: complex,Y: complex] :
% 5.27/5.55 ( ( Z != zero_zero_complex )
% 5.27/5.55 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X4 @ Z ) ) @ Y )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_diff_eq_iff
% 5.27/5.55 thf(fact_5460_minus__divide__diff__eq__iff,axiom,
% 5.27/5.55 ! [Z: rat,X4: rat,Y: rat] :
% 5.27/5.55 ( ( Z != zero_zero_rat )
% 5.27/5.55 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X4 @ Z ) ) @ Y )
% 5.27/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X4 ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_diff_eq_iff
% 5.27/5.55 thf(fact_5461_power3__eq__cube,axiom,
% 5.27/5.55 ! [A: complex] :
% 5.27/5.55 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.27/5.55 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % power3_eq_cube
% 5.27/5.55 thf(fact_5462_power3__eq__cube,axiom,
% 5.27/5.55 ! [A: real] :
% 5.27/5.55 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.27/5.55 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % power3_eq_cube
% 5.27/5.55 thf(fact_5463_power3__eq__cube,axiom,
% 5.27/5.55 ! [A: nat] :
% 5.27/5.55 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.27/5.55 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % power3_eq_cube
% 5.27/5.55 thf(fact_5464_power3__eq__cube,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.27/5.55 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % power3_eq_cube
% 5.27/5.55 thf(fact_5465_even__minus,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.27/5.55 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % even_minus
% 5.27/5.55 thf(fact_5466_even__minus,axiom,
% 5.27/5.55 ! [A: code_integer] :
% 5.27/5.55 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.55 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % even_minus
% 5.27/5.55 thf(fact_5467_numeral__3__eq__3,axiom,
% 5.27/5.55 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.27/5.55 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_3_eq_3
% 5.27/5.55 thf(fact_5468_even__xor__iff,axiom,
% 5.27/5.55 ! [A: code_integer,B: code_integer] :
% 5.27/5.55 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3222712562003087583nteger @ A @ B ) )
% 5.27/5.55 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % even_xor_iff
% 5.27/5.55 thf(fact_5469_even__xor__iff,axiom,
% 5.27/5.55 ! [A: nat,B: nat] :
% 5.27/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.27/5.55 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % even_xor_iff
% 5.27/5.55 thf(fact_5470_even__xor__iff,axiom,
% 5.27/5.55 ! [A: int,B: int] :
% 5.27/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.27/5.55 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % even_xor_iff
% 5.27/5.55 thf(fact_5471_power2__eq__iff,axiom,
% 5.27/5.55 ! [X4: real,Y: real] :
% 5.27/5.55 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( ( X4 = Y )
% 5.27/5.55 | ( X4
% 5.27/5.55 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_iff
% 5.27/5.55 thf(fact_5472_power2__eq__iff,axiom,
% 5.27/5.55 ! [X4: int,Y: int] :
% 5.27/5.55 ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( ( X4 = Y )
% 5.27/5.55 | ( X4
% 5.27/5.55 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_iff
% 5.27/5.55 thf(fact_5473_power2__eq__iff,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex] :
% 5.27/5.55 ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( ( X4 = Y )
% 5.27/5.55 | ( X4
% 5.27/5.55 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_iff
% 5.27/5.55 thf(fact_5474_power2__eq__iff,axiom,
% 5.27/5.55 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.55 ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( ( X4 = Y )
% 5.27/5.55 | ( X4
% 5.27/5.55 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_iff
% 5.27/5.55 thf(fact_5475_power2__eq__iff,axiom,
% 5.27/5.55 ! [X4: rat,Y: rat] :
% 5.27/5.55 ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( ( X4 = Y )
% 5.27/5.55 | ( X4
% 5.27/5.55 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_iff
% 5.27/5.55 thf(fact_5476_Suc3__eq__add__3,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( suc @ ( suc @ ( suc @ N2 ) ) )
% 5.27/5.55 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % Suc3_eq_add_3
% 5.27/5.55 thf(fact_5477_field__char__0__class_Oof__nat__div,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.55 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri681578069525770553at_rat @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % field_char_0_class.of_nat_div
% 5.27/5.55 thf(fact_5478_field__char__0__class_Oof__nat__div,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.55 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri8010041392384452111omplex @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % field_char_0_class.of_nat_div
% 5.27/5.55 thf(fact_5479_field__char__0__class_Oof__nat__div,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N2 ) )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % field_char_0_class.of_nat_div
% 5.27/5.55 thf(fact_5480_nat__less__real__le,axiom,
% 5.27/5.55 ( ord_less_nat
% 5.27/5.55 = ( ^ [N: nat,M6: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M6 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_less_real_le
% 5.27/5.55 thf(fact_5481_nat__le__real__less,axiom,
% 5.27/5.55 ( ord_less_eq_nat
% 5.27/5.55 = ( ^ [N: nat,M6: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_le_real_less
% 5.27/5.55 thf(fact_5482_verit__less__mono__div__int2,axiom,
% 5.27/5.55 ! [A2: int,B3: int,N2: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.27/5.55 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N2 ) )
% 5.27/5.55 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N2 ) @ ( divide_divide_int @ A2 @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % verit_less_mono_div_int2
% 5.27/5.55 thf(fact_5483_div__eq__minus1,axiom,
% 5.27/5.55 ! [B: int] :
% 5.27/5.55 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.55 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % div_eq_minus1
% 5.27/5.55 thf(fact_5484_take__bit__Suc__bit0,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.27/5.55 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc_bit0
% 5.27/5.55 thf(fact_5485_take__bit__Suc__bit0,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.55 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc_bit0
% 5.27/5.55 thf(fact_5486_take__bit__eq__mod,axiom,
% 5.27/5.55 ( bit_se1745604003318907178nteger
% 5.27/5.55 = ( ^ [N: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_mod
% 5.27/5.55 thf(fact_5487_take__bit__eq__mod,axiom,
% 5.27/5.55 ( bit_se2923211474154528505it_int
% 5.27/5.55 = ( ^ [N: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_mod
% 5.27/5.55 thf(fact_5488_take__bit__eq__mod,axiom,
% 5.27/5.55 ( bit_se2925701944663578781it_nat
% 5.27/5.55 = ( ^ [N: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_mod
% 5.27/5.55 thf(fact_5489_take__bit__nat__eq__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.27/5.55 = M )
% 5.27/5.55 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_nat_eq_self_iff
% 5.27/5.55 thf(fact_5490_take__bit__nat__less__exp,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_nat_less_exp
% 5.27/5.55 thf(fact_5491_take__bit__nat__eq__self,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 => ( ( bit_se2925701944663578781it_nat @ N2 @ M )
% 5.27/5.55 = M ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_nat_eq_self
% 5.27/5.55 thf(fact_5492_num_Osize__gen_I3_J,axiom,
% 5.27/5.55 ! [X32: num] :
% 5.27/5.55 ( ( size_num @ ( bit1 @ X32 ) )
% 5.27/5.55 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % num.size_gen(3)
% 5.27/5.55 thf(fact_5493_num_Osize_I6_J,axiom,
% 5.27/5.55 ! [X32: num] :
% 5.27/5.55 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.27/5.55 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % num.size(6)
% 5.27/5.55 thf(fact_5494_take__bit__nat__def,axiom,
% 5.27/5.55 ( bit_se2925701944663578781it_nat
% 5.27/5.55 = ( ^ [N: nat,M6: nat] : ( modulo_modulo_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_nat_def
% 5.27/5.55 thf(fact_5495_of__nat__less__two__power,axiom,
% 5.27/5.55 ! [N2: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % of_nat_less_two_power
% 5.27/5.55 thf(fact_5496_of__nat__less__two__power,axiom,
% 5.27/5.55 ! [N2: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % of_nat_less_two_power
% 5.27/5.55 thf(fact_5497_of__nat__less__two__power,axiom,
% 5.27/5.55 ! [N2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % of_nat_less_two_power
% 5.27/5.55 thf(fact_5498_inverse__of__nat__le,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.55 => ( ( N2 != zero_zero_nat )
% 5.27/5.55 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % inverse_of_nat_le
% 5.27/5.55 thf(fact_5499_inverse__of__nat__le,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.55 => ( ( N2 != zero_zero_nat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % inverse_of_nat_le
% 5.27/5.55 thf(fact_5500_take__bit__int__less__exp,axiom,
% 5.27/5.55 ! [N2: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_less_exp
% 5.27/5.55 thf(fact_5501_le__minus__divide__eq,axiom,
% 5.27/5.55 ! [A: real,B: real,C: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_minus_divide_eq
% 5.27/5.55 thf(fact_5502_le__minus__divide__eq,axiom,
% 5.27/5.55 ! [A: rat,B: rat,C: rat] :
% 5.27/5.55 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_minus_divide_eq
% 5.27/5.55 thf(fact_5503_minus__divide__le__eq,axiom,
% 5.27/5.55 ! [B: real,C: real,A: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_le_eq
% 5.27/5.55 thf(fact_5504_minus__divide__le__eq,axiom,
% 5.27/5.55 ! [B: rat,C: rat,A: rat] :
% 5.27/5.55 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_divide_le_eq
% 5.27/5.55 thf(fact_5505_neg__le__minus__divide__eq,axiom,
% 5.27/5.55 ! [C: real,A: real,B: real] :
% 5.27/5.55 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.55 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_le_minus_divide_eq
% 5.27/5.55 thf(fact_5506_neg__le__minus__divide__eq,axiom,
% 5.27/5.55 ! [C: rat,A: rat,B: rat] :
% 5.27/5.55 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.55 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_le_minus_divide_eq
% 5.27/5.55 thf(fact_5507_neg__minus__divide__le__eq,axiom,
% 5.27/5.55 ! [C: real,B: real,A: real] :
% 5.27/5.55 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.55 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_minus_divide_le_eq
% 5.27/5.55 thf(fact_5508_neg__minus__divide__le__eq,axiom,
% 5.27/5.55 ! [C: rat,B: rat,A: rat] :
% 5.27/5.55 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.55 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_minus_divide_le_eq
% 5.27/5.55 thf(fact_5509_pos__le__minus__divide__eq,axiom,
% 5.27/5.55 ! [C: real,A: real,B: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.27/5.55 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pos_le_minus_divide_eq
% 5.27/5.55 thf(fact_5510_pos__le__minus__divide__eq,axiom,
% 5.27/5.55 ! [C: rat,A: rat,B: rat] :
% 5.27/5.55 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.27/5.55 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pos_le_minus_divide_eq
% 5.27/5.55 thf(fact_5511_pos__minus__divide__le__eq,axiom,
% 5.27/5.55 ! [C: real,B: real,A: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.27/5.55 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pos_minus_divide_le_eq
% 5.27/5.55 thf(fact_5512_pos__minus__divide__le__eq,axiom,
% 5.27/5.55 ! [C: rat,B: rat,A: rat] :
% 5.27/5.55 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.27/5.55 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pos_minus_divide_le_eq
% 5.27/5.55 thf(fact_5513_less__divide__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [W: num,B: real,C: real] :
% 5.27/5.55 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % less_divide_eq_numeral(2)
% 5.27/5.55 thf(fact_5514_less__divide__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [W: num,B: rat,C: rat] :
% 5.27/5.55 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % less_divide_eq_numeral(2)
% 5.27/5.55 thf(fact_5515_divide__less__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [B: real,C: real,W: num] :
% 5.27/5.55 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divide_less_eq_numeral(2)
% 5.27/5.55 thf(fact_5516_divide__less__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [B: rat,C: rat,W: num] :
% 5.27/5.55 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divide_less_eq_numeral(2)
% 5.27/5.55 thf(fact_5517_take__bit__int__def,axiom,
% 5.27/5.55 ( bit_se2923211474154528505it_int
% 5.27/5.55 = ( ^ [N: nat,K3: int] : ( modulo_modulo_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_def
% 5.27/5.55 thf(fact_5518_cong__exp__iff__simps_I7_J,axiom,
% 5.27/5.55 ! [Q3: num,N2: num] :
% 5.27/5.55 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.27/5.55 = zero_zero_nat ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(7)
% 5.27/5.55 thf(fact_5519_cong__exp__iff__simps_I7_J,axiom,
% 5.27/5.55 ! [Q3: num,N2: num] :
% 5.27/5.55 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ Q3 ) )
% 5.27/5.55 = zero_zero_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(7)
% 5.27/5.55 thf(fact_5520_cong__exp__iff__simps_I7_J,axiom,
% 5.27/5.55 ! [Q3: num,N2: num] :
% 5.27/5.55 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N2 ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.27/5.55 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(7)
% 5.27/5.55 thf(fact_5521_cong__exp__iff__simps_I11_J,axiom,
% 5.27/5.55 ! [M: num,Q3: num] :
% 5.27/5.55 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q3 ) )
% 5.27/5.55 = zero_zero_nat ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(11)
% 5.27/5.55 thf(fact_5522_cong__exp__iff__simps_I11_J,axiom,
% 5.27/5.55 ! [M: num,Q3: num] :
% 5.27/5.55 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q3 ) )
% 5.27/5.55 = zero_zero_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(11)
% 5.27/5.55 thf(fact_5523_cong__exp__iff__simps_I11_J,axiom,
% 5.27/5.55 ! [M: num,Q3: num] :
% 5.27/5.55 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) )
% 5.27/5.55 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q3 ) ) ) )
% 5.27/5.55 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q3 ) )
% 5.27/5.55 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.55
% 5.27/5.55 % cong_exp_iff_simps(11)
% 5.27/5.55 thf(fact_5524_power2__eq__1__iff,axiom,
% 5.27/5.55 ! [A: real] :
% 5.27/5.55 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_real )
% 5.27/5.55 = ( ( A = one_one_real )
% 5.27/5.55 | ( A
% 5.27/5.55 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_1_iff
% 5.27/5.55 thf(fact_5525_power2__eq__1__iff,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_int )
% 5.27/5.55 = ( ( A = one_one_int )
% 5.27/5.55 | ( A
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_1_iff
% 5.27/5.55 thf(fact_5526_power2__eq__1__iff,axiom,
% 5.27/5.55 ! [A: complex] :
% 5.27/5.55 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_complex )
% 5.27/5.55 = ( ( A = one_one_complex )
% 5.27/5.55 | ( A
% 5.27/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_1_iff
% 5.27/5.55 thf(fact_5527_power2__eq__1__iff,axiom,
% 5.27/5.55 ! [A: code_integer] :
% 5.27/5.55 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_Code_integer )
% 5.27/5.55 = ( ( A = one_one_Code_integer )
% 5.27/5.55 | ( A
% 5.27/5.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_1_iff
% 5.27/5.55 thf(fact_5528_power2__eq__1__iff,axiom,
% 5.27/5.55 ! [A: rat] :
% 5.27/5.55 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_rat )
% 5.27/5.55 = ( ( A = one_one_rat )
% 5.27/5.55 | ( A
% 5.27/5.55 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power2_eq_1_iff
% 5.27/5.55 thf(fact_5529_real__archimedian__rdiv__eq__0,axiom,
% 5.27/5.55 ! [X4: real,C: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ! [M5: nat] :
% 5.27/5.55 ( ( ord_less_nat @ zero_zero_nat @ M5 )
% 5.27/5.55 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M5 ) @ X4 ) @ C ) )
% 5.27/5.55 => ( X4 = zero_zero_real ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % real_archimedian_rdiv_eq_0
% 5.27/5.55 thf(fact_5530_uminus__power__if,axiom,
% 5.27/5.55 ! [N2: nat,A: real] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.27/5.55 = ( power_power_real @ A @ N2 ) ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_real @ ( power_power_real @ A @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % uminus_power_if
% 5.27/5.55 thf(fact_5531_uminus__power__if,axiom,
% 5.27/5.55 ! [N2: nat,A: int] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.27/5.55 = ( power_power_int @ A @ N2 ) ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_int @ ( power_power_int @ A @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % uminus_power_if
% 5.27/5.55 thf(fact_5532_uminus__power__if,axiom,
% 5.27/5.55 ! [N2: nat,A: complex] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.27/5.55 = ( power_power_complex @ A @ N2 ) ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % uminus_power_if
% 5.27/5.55 thf(fact_5533_uminus__power__if,axiom,
% 5.27/5.55 ! [N2: nat,A: code_integer] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.27/5.55 = ( power_8256067586552552935nteger @ A @ N2 ) ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % uminus_power_if
% 5.27/5.55 thf(fact_5534_uminus__power__if,axiom,
% 5.27/5.55 ! [N2: nat,A: rat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.27/5.55 = ( power_power_rat @ A @ N2 ) ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % uminus_power_if
% 5.27/5.55 thf(fact_5535_Suc__div__eq__add3__div,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.27/5.55 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % Suc_div_eq_add3_div
% 5.27/5.55 thf(fact_5536_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.27/5.55 ! [K: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.55 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.55 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_one_power_add_eq_neg_one_power_diff
% 5.27/5.55 thf(fact_5537_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.27/5.55 ! [K: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.55 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.55 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_one_power_add_eq_neg_one_power_diff
% 5.27/5.55 thf(fact_5538_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.27/5.55 ! [K: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.55 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.55 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_one_power_add_eq_neg_one_power_diff
% 5.27/5.55 thf(fact_5539_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.27/5.55 ! [K: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.55 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.55 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_one_power_add_eq_neg_one_power_diff
% 5.27/5.55 thf(fact_5540_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.27/5.55 ! [K: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.55 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N2 @ K ) )
% 5.27/5.55 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_one_power_add_eq_neg_one_power_diff
% 5.27/5.55 thf(fact_5541_Suc__mod__eq__add3__mod,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N2 )
% 5.27/5.55 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % Suc_mod_eq_add3_mod
% 5.27/5.55 thf(fact_5542_realpow__square__minus__le,axiom,
% 5.27/5.55 ! [U: real,X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % realpow_square_minus_le
% 5.27/5.55 thf(fact_5543_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ K )
% 5.27/5.55 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_less_eq_self_iff
% 5.27/5.55 thf(fact_5544_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.27/5.55 ! [N2: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_greater_eq_minus_exp
% 5.27/5.55 thf(fact_5545_signed__take__bit__int__greater__self__iff,axiom,
% 5.27/5.55 ! [K: int,N2: nat] :
% 5.27/5.55 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.27/5.55 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_greater_self_iff
% 5.27/5.55 thf(fact_5546_take__bit__eq__0__iff,axiom,
% 5.27/5.55 ! [N2: nat,A: code_integer] :
% 5.27/5.55 ( ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.27/5.55 = zero_z3403309356797280102nteger )
% 5.27/5.55 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_0_iff
% 5.27/5.55 thf(fact_5547_take__bit__eq__0__iff,axiom,
% 5.27/5.55 ! [N2: nat,A: int] :
% 5.27/5.55 ( ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.27/5.55 = zero_zero_int )
% 5.27/5.55 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_0_iff
% 5.27/5.55 thf(fact_5548_take__bit__eq__0__iff,axiom,
% 5.27/5.55 ! [N2: nat,A: nat] :
% 5.27/5.55 ( ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.27/5.55 = zero_zero_nat )
% 5.27/5.55 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_eq_0_iff
% 5.27/5.55 thf(fact_5549_minus__mod__int__eq,axiom,
% 5.27/5.55 ! [L: int,K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.27/5.55 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L )
% 5.27/5.55 = ( minus_minus_int @ ( minus_minus_int @ L @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_mod_int_eq
% 5.27/5.55 thf(fact_5550_zmod__minus1,axiom,
% 5.27/5.55 ! [B: int] :
% 5.27/5.55 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.55 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.27/5.55 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zmod_minus1
% 5.27/5.55 thf(fact_5551_zdiv__zminus1__eq__if,axiom,
% 5.27/5.55 ! [B: int,A: int] :
% 5.27/5.55 ( ( B != zero_zero_int )
% 5.27/5.55 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.55 = zero_zero_int )
% 5.27/5.55 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.55 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.27/5.55 & ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.55 != zero_zero_int )
% 5.27/5.55 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.55 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zdiv_zminus1_eq_if
% 5.27/5.55 thf(fact_5552_zdiv__zminus2__eq__if,axiom,
% 5.27/5.55 ! [B: int,A: int] :
% 5.27/5.55 ( ( B != zero_zero_int )
% 5.27/5.55 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.55 = zero_zero_int )
% 5.27/5.55 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.27/5.55 & ( ( ( modulo_modulo_int @ A @ B )
% 5.27/5.55 != zero_zero_int )
% 5.27/5.55 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.27/5.55 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zdiv_zminus2_eq_if
% 5.27/5.55 thf(fact_5553_take__bit__nat__less__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N2 @ M ) @ M )
% 5.27/5.55 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_nat_less_self_iff
% 5.27/5.55 thf(fact_5554_zminus1__lemma,axiom,
% 5.27/5.55 ! [A: int,B: int,Q3: int,R3: int] :
% 5.27/5.55 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q3 @ R3 ) )
% 5.27/5.55 => ( ( B != zero_zero_int )
% 5.27/5.55 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R3 = zero_zero_int ) @ ( uminus_uminus_int @ Q3 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q3 ) @ one_one_int ) ) @ ( if_int @ ( R3 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R3 ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zminus1_lemma
% 5.27/5.55 thf(fact_5555_take__bit__int__less__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ K )
% 5.27/5.55 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_less_self_iff
% 5.27/5.55 thf(fact_5556_take__bit__int__greater__eq__self__iff,axiom,
% 5.27/5.55 ! [K: int,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.27/5.55 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_greater_eq_self_iff
% 5.27/5.55 thf(fact_5557_le__divide__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [W: num,B: real,C: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_divide_eq_numeral(2)
% 5.27/5.55 thf(fact_5558_le__divide__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [W: num,B: rat,C: rat] :
% 5.27/5.55 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_divide_eq_numeral(2)
% 5.27/5.55 thf(fact_5559_divide__le__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [B: real,C: real,W: num] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.55 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.55 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.55 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divide_le_eq_numeral(2)
% 5.27/5.55 thf(fact_5560_divide__le__eq__numeral_I2_J,axiom,
% 5.27/5.55 ! [B: rat,C: rat,W: num] :
% 5.27/5.55 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.55 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.27/5.55 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.27/5.55 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divide_le_eq_numeral(2)
% 5.27/5.55 thf(fact_5561_square__le__1,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.55 => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_le_1
% 5.27/5.55 thf(fact_5562_square__le__1,axiom,
% 5.27/5.55 ! [X4: code_integer] :
% 5.27/5.55 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 5.27/5.55 => ( ( ord_le3102999989581377725nteger @ X4 @ one_one_Code_integer )
% 5.27/5.55 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_le_1
% 5.27/5.55 thf(fact_5563_square__le__1,axiom,
% 5.27/5.55 ! [X4: rat] :
% 5.27/5.55 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_rat @ X4 @ one_one_rat )
% 5.27/5.55 => ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_le_1
% 5.27/5.55 thf(fact_5564_square__le__1,axiom,
% 5.27/5.55 ! [X4: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_int @ X4 @ one_one_int )
% 5.27/5.55 => ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_le_1
% 5.27/5.55 thf(fact_5565_minus__power__mult__self,axiom,
% 5.27/5.55 ! [A: real,N2: nat] :
% 5.27/5.55 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.27/5.55 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_power_mult_self
% 5.27/5.55 thf(fact_5566_minus__power__mult__self,axiom,
% 5.27/5.55 ! [A: int,N2: nat] :
% 5.27/5.55 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.27/5.55 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_power_mult_self
% 5.27/5.55 thf(fact_5567_minus__power__mult__self,axiom,
% 5.27/5.55 ! [A: complex,N2: nat] :
% 5.27/5.55 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N2 ) )
% 5.27/5.55 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_power_mult_self
% 5.27/5.55 thf(fact_5568_minus__power__mult__self,axiom,
% 5.27/5.55 ! [A: code_integer,N2: nat] :
% 5.27/5.55 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.27/5.55 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_power_mult_self
% 5.27/5.55 thf(fact_5569_minus__power__mult__self,axiom,
% 5.27/5.55 ! [A: rat,N2: nat] :
% 5.27/5.55 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.27/5.55 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_power_mult_self
% 5.27/5.55 thf(fact_5570_minus__one__power__iff,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.27/5.55 = one_one_real ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_power_iff
% 5.27/5.55 thf(fact_5571_minus__one__power__iff,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.27/5.55 = one_one_int ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_power_iff
% 5.27/5.55 thf(fact_5572_minus__one__power__iff,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.27/5.55 = one_one_complex ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_power_iff
% 5.27/5.55 thf(fact_5573_minus__one__power__iff,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.27/5.55 = one_one_Code_integer ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_power_iff
% 5.27/5.55 thf(fact_5574_minus__one__power__iff,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.27/5.55 = one_one_rat ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.55 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 )
% 5.27/5.55 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_power_iff
% 5.27/5.55 thf(fact_5575_signed__take__bit__int__eq__self,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.27/5.55 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 => ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.27/5.55 = K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_eq_self
% 5.27/5.55 thf(fact_5576_signed__take__bit__int__eq__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ( bit_ri631733984087533419it_int @ N2 @ K )
% 5.27/5.55 = K )
% 5.27/5.55 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ K )
% 5.27/5.55 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_eq_self_iff
% 5.27/5.55 thf(fact_5577_minus__1__div__exp__eq__int,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_1_div_exp_eq_int
% 5.27/5.55 thf(fact_5578_div__pos__neg__trivial,axiom,
% 5.27/5.55 ! [K: int,L: int] :
% 5.27/5.55 ( ( ord_less_int @ zero_zero_int @ K )
% 5.27/5.55 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L ) @ zero_zero_int )
% 5.27/5.55 => ( ( divide_divide_int @ K @ L )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % div_pos_neg_trivial
% 5.27/5.55 thf(fact_5579_take__bit__int__eq__self,axiom,
% 5.27/5.55 ! [K: int,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.55 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 => ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.55 = K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_eq_self
% 5.27/5.55 thf(fact_5580_take__bit__int__eq__self__iff,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.55 = K )
% 5.27/5.55 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.55 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_eq_self_iff
% 5.27/5.55 thf(fact_5581_signed__take__bit__eq__take__bit__shift,axiom,
% 5.27/5.55 ( bit_ri631733984087533419it_int
% 5.27/5.55 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( plus_plus_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_eq_take_bit_shift
% 5.27/5.55 thf(fact_5582_take__bit__incr__eq,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.55 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) )
% 5.27/5.55 => ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.27/5.55 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_incr_eq
% 5.27/5.55 thf(fact_5583_power__minus1__odd,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_minus1_odd
% 5.27/5.55 thf(fact_5584_power__minus1__odd,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_minus1_odd
% 5.27/5.55 thf(fact_5585_power__minus1__odd,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_minus1_odd
% 5.27/5.55 thf(fact_5586_power__minus1__odd,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_minus1_odd
% 5.27/5.55 thf(fact_5587_power__minus1__odd,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_minus1_odd
% 5.27/5.55 thf(fact_5588_take__bit__Suc,axiom,
% 5.27/5.55 ! [N2: nat,A: code_integer] :
% 5.27/5.55 ( ( bit_se1745604003318907178nteger @ ( suc @ N2 ) @ A )
% 5.27/5.55 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N2 @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc
% 5.27/5.55 thf(fact_5589_take__bit__Suc,axiom,
% 5.27/5.55 ! [N2: nat,A: int] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ A )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc
% 5.27/5.55 thf(fact_5590_take__bit__Suc,axiom,
% 5.27/5.55 ! [N2: nat,A: nat] :
% 5.27/5.55 ( ( bit_se2925701944663578781it_nat @ ( suc @ N2 ) @ A )
% 5.27/5.55 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc
% 5.27/5.55 thf(fact_5591_int__bit__induct,axiom,
% 5.27/5.55 ! [P: int > $o,K: int] :
% 5.27/5.55 ( ( P @ zero_zero_int )
% 5.27/5.55 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 => ( ! [K2: int] :
% 5.27/5.55 ( ( P @ K2 )
% 5.27/5.55 => ( ( K2 != zero_zero_int )
% 5.27/5.55 => ( P @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.55 => ( ! [K2: int] :
% 5.27/5.55 ( ( P @ K2 )
% 5.27/5.55 => ( ( K2
% 5.27/5.55 != ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.27/5.55 => ( P @ K ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_bit_induct
% 5.27/5.55 thf(fact_5592_take__bit__int__less__eq,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ K )
% 5.27/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.55 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_less_eq
% 5.27/5.55 thf(fact_5593_xor__nat__unfold,axiom,
% 5.27/5.55 ( bit_se6528837805403552850or_nat
% 5.27/5.55 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_nat_unfold
% 5.27/5.55 thf(fact_5594_take__bit__int__greater__eq,axiom,
% 5.27/5.55 ! [K: int,N2: nat] :
% 5.27/5.55 ( ( ord_less_int @ K @ zero_zero_int )
% 5.27/5.55 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_int_greater_eq
% 5.27/5.55 thf(fact_5595_xor__nat__rec,axiom,
% 5.27/5.55 ( bit_se6528837805403552850or_nat
% 5.27/5.55 = ( ^ [M6: nat,N: nat] :
% 5.27/5.55 ( plus_plus_nat
% 5.27/5.55 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.55 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 ) )
% 5.27/5.55 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.27/5.55 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_nat_rec
% 5.27/5.55 thf(fact_5596_stable__imp__take__bit__eq,axiom,
% 5.27/5.55 ! [A: code_integer,N2: nat] :
% 5.27/5.55 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.55 = A )
% 5.27/5.55 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.27/5.55 = zero_z3403309356797280102nteger ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se1745604003318907178nteger @ N2 @ A )
% 5.27/5.55 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % stable_imp_take_bit_eq
% 5.27/5.55 thf(fact_5597_stable__imp__take__bit__eq,axiom,
% 5.27/5.55 ! [A: int,N2: nat] :
% 5.27/5.55 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.55 = A )
% 5.27/5.55 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.27/5.55 = zero_zero_int ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.27/5.55 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % stable_imp_take_bit_eq
% 5.27/5.55 thf(fact_5598_stable__imp__take__bit__eq,axiom,
% 5.27/5.55 ! [A: nat,N2: nat] :
% 5.27/5.55 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = A )
% 5.27/5.55 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.27/5.55 = zero_zero_nat ) )
% 5.27/5.55 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.55 => ( ( bit_se2925701944663578781it_nat @ N2 @ A )
% 5.27/5.55 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % stable_imp_take_bit_eq
% 5.27/5.55 thf(fact_5599_xor__one__eq,axiom,
% 5.27/5.55 ! [A: code_integer] :
% 5.27/5.55 ( ( bit_se3222712562003087583nteger @ A @ one_one_Code_integer )
% 5.27/5.55 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n356916108424825756nteger
% 5.27/5.55 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_one_eq
% 5.27/5.55 thf(fact_5600_xor__one__eq,axiom,
% 5.27/5.55 ! [A: nat] :
% 5.27/5.55 ( ( bit_se6528837805403552850or_nat @ A @ one_one_nat )
% 5.27/5.55 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.55 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_one_eq
% 5.27/5.55 thf(fact_5601_xor__one__eq,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( bit_se6526347334894502574or_int @ A @ one_one_int )
% 5.27/5.55 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n2684676970156552555ol_int
% 5.27/5.55 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_one_eq
% 5.27/5.55 thf(fact_5602_one__xor__eq,axiom,
% 5.27/5.55 ! [A: code_integer] :
% 5.27/5.55 ( ( bit_se3222712562003087583nteger @ one_one_Code_integer @ A )
% 5.27/5.55 = ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n356916108424825756nteger
% 5.27/5.55 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % one_xor_eq
% 5.27/5.55 thf(fact_5603_one__xor__eq,axiom,
% 5.27/5.55 ! [A: nat] :
% 5.27/5.55 ( ( bit_se6528837805403552850or_nat @ one_one_nat @ A )
% 5.27/5.55 = ( minus_minus_nat @ ( plus_plus_nat @ A @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.55 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % one_xor_eq
% 5.27/5.55 thf(fact_5604_one__xor__eq,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( bit_se6526347334894502574or_int @ one_one_int @ A )
% 5.27/5.55 = ( minus_minus_int @ ( plus_plus_int @ A @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.55 @ ( zero_n2684676970156552555ol_int
% 5.27/5.55 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % one_xor_eq
% 5.27/5.55 thf(fact_5605_signed__take__bit__int__greater__eq,axiom,
% 5.27/5.55 ! [K: int,N2: nat] :
% 5.27/5.55 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) ) @ ( bit_ri631733984087533419it_int @ N2 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_int_greater_eq
% 5.27/5.55 thf(fact_5606_xor__Suc__0__eq,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( bit_se6528837805403552850or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.55 = ( minus_minus_nat @ ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.55 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.55 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_Suc_0_eq
% 5.27/5.55 thf(fact_5607_real__average__minus__first,axiom,
% 5.27/5.55 ! [A: real,B: real] :
% 5.27/5.55 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % real_average_minus_first
% 5.27/5.55 thf(fact_5608_real__average__minus__second,axiom,
% 5.27/5.55 ! [B: real,A: real] :
% 5.27/5.55 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.27/5.55 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % real_average_minus_second
% 5.27/5.55 thf(fact_5609_linear__plus__1__le__power,axiom,
% 5.27/5.55 ! [X4: real,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X4 @ one_one_real ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % linear_plus_1_le_power
% 5.27/5.55 thf(fact_5610_mod__exhaust__less__4,axiom,
% 5.27/5.55 ! [M: nat] :
% 5.27/5.55 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = zero_zero_nat )
% 5.27/5.55 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = one_one_nat )
% 5.27/5.55 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.55 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % mod_exhaust_less_4
% 5.27/5.55 thf(fact_5611_nat__approx__posE,axiom,
% 5.27/5.55 ! [E2: rat] :
% 5.27/5.55 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_approx_posE
% 5.27/5.55 thf(fact_5612_nat__approx__posE,axiom,
% 5.27/5.55 ! [E2: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_approx_posE
% 5.27/5.55 thf(fact_5613_compl__le__compl__iff,axiom,
% 5.27/5.55 ! [X4: set_int,Y: set_int] :
% 5.27/5.55 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ ( uminus1532241313380277803et_int @ Y ) )
% 5.27/5.55 = ( ord_less_eq_set_int @ Y @ X4 ) ) ).
% 5.27/5.55
% 5.27/5.55 % compl_le_compl_iff
% 5.27/5.55 thf(fact_5614_dbl__dec__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(4)
% 5.27/5.55 thf(fact_5615_dbl__dec__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(4)
% 5.27/5.55 thf(fact_5616_dbl__dec__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(4)
% 5.27/5.55 thf(fact_5617_dbl__dec__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(4)
% 5.27/5.55 thf(fact_5618_dbl__dec__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(4)
% 5.27/5.55 thf(fact_5619_int__eq__iff__numeral,axiom,
% 5.27/5.55 ! [M: nat,V: num] :
% 5.27/5.55 ( ( ( semiri1314217659103216013at_int @ M )
% 5.27/5.55 = ( numeral_numeral_int @ V ) )
% 5.27/5.55 = ( M
% 5.27/5.55 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_eq_iff_numeral
% 5.27/5.55 thf(fact_5620_xor__nonnegative__int__iff,axiom,
% 5.27/5.55 ! [K: int,L: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.27/5.55 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.55 = ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_nonnegative_int_iff
% 5.27/5.55 thf(fact_5621_xor__negative__int__iff,axiom,
% 5.27/5.55 ! [K: int,L: int] :
% 5.27/5.55 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ zero_zero_int )
% 5.27/5.55 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.27/5.55 != ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_negative_int_iff
% 5.27/5.55 thf(fact_5622_negative__zle,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.27/5.55
% 5.27/5.55 % negative_zle
% 5.27/5.55 thf(fact_5623_dbl__dec__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.27/5.55 = one_one_complex ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(3)
% 5.27/5.55 thf(fact_5624_dbl__dec__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.27/5.55 = one_one_real ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(3)
% 5.27/5.55 thf(fact_5625_dbl__dec__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.27/5.55 = one_one_rat ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(3)
% 5.27/5.55 thf(fact_5626_dbl__dec__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.27/5.55 = one_one_int ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(3)
% 5.27/5.55 thf(fact_5627_negative__zless,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.27/5.55
% 5.27/5.55 % negative_zless
% 5.27/5.55 thf(fact_5628_dbl__dec__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.27/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(2)
% 5.27/5.55 thf(fact_5629_dbl__dec__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(2)
% 5.27/5.55 thf(fact_5630_dbl__dec__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(2)
% 5.27/5.55 thf(fact_5631_dbl__dec__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(2)
% 5.27/5.55 thf(fact_5632_dbl__dec__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.27/5.55 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(2)
% 5.27/5.55 thf(fact_5633_take__bit__minus,axiom,
% 5.27/5.55 ! [N2: nat,K: int] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.27/5.55 = ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_minus
% 5.27/5.55 thf(fact_5634_int__cases,axiom,
% 5.27/5.55 ! [Z: int] :
% 5.27/5.55 ( ! [N3: nat] :
% 5.27/5.55 ( Z
% 5.27/5.55 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( Z
% 5.27/5.55 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_cases
% 5.27/5.55 thf(fact_5635_int__of__nat__induct,axiom,
% 5.27/5.55 ! [P: int > $o,Z: int] :
% 5.27/5.55 ( ! [N3: nat] : ( P @ ( semiri1314217659103216013at_int @ N3 ) )
% 5.27/5.55 => ( ! [N3: nat] : ( P @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) )
% 5.27/5.55 => ( P @ Z ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_of_nat_induct
% 5.27/5.55 thf(fact_5636_not__int__zless__negative,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % not_int_zless_negative
% 5.27/5.55 thf(fact_5637_XOR__lower,axiom,
% 5.27/5.55 ! [X4: int,Y: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.55 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % XOR_lower
% 5.27/5.55 thf(fact_5638_int__cases4,axiom,
% 5.27/5.55 ! [M: int] :
% 5.27/5.55 ( ! [N3: nat] :
% 5.27/5.55 ( M
% 5.27/5.55 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.55 => ( M
% 5.27/5.55 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_cases4
% 5.27/5.55 thf(fact_5639_int__ops_I3_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.55 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_ops(3)
% 5.27/5.55 thf(fact_5640_int__zle__neg,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.27/5.55 = ( ( N2 = zero_zero_nat )
% 5.27/5.55 & ( M = zero_zero_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_zle_neg
% 5.27/5.55 thf(fact_5641_nat__int__comparison_I2_J,axiom,
% 5.27/5.55 ( ord_less_nat
% 5.27/5.55 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_int_comparison(2)
% 5.27/5.55 thf(fact_5642_zle__int,axiom,
% 5.27/5.55 ! [M: nat,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.55 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % zle_int
% 5.27/5.55 thf(fact_5643_nat__int__comparison_I3_J,axiom,
% 5.27/5.55 ( ord_less_eq_nat
% 5.27/5.55 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nat_int_comparison(3)
% 5.27/5.55 thf(fact_5644_nonneg__int__cases,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( K
% 5.27/5.55 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nonneg_int_cases
% 5.27/5.55 thf(fact_5645_zero__le__imp__eq__int,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.55 => ? [N3: nat] :
% 5.27/5.55 ( K
% 5.27/5.55 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zero_le_imp_eq_int
% 5.27/5.55 thf(fact_5646_negative__zle__0,axiom,
% 5.27/5.55 ! [N2: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ zero_zero_int ) ).
% 5.27/5.55
% 5.27/5.55 % negative_zle_0
% 5.27/5.55 thf(fact_5647_nonpos__int__cases,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( K
% 5.27/5.55 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nonpos_int_cases
% 5.27/5.55 thf(fact_5648_zadd__int__left,axiom,
% 5.27/5.55 ! [M: nat,N2: nat,Z: int] :
% 5.27/5.55 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ Z ) )
% 5.27/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N2 ) ) @ Z ) ) ).
% 5.27/5.55
% 5.27/5.55 % zadd_int_left
% 5.27/5.55 thf(fact_5649_int__plus,axiom,
% 5.27/5.55 ! [N2: nat,M: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_plus
% 5.27/5.55 thf(fact_5650_int__ops_I5_J,axiom,
% 5.27/5.55 ! [A: nat,B: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.27/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_ops(5)
% 5.27/5.55 thf(fact_5651_int__ops_I2_J,axiom,
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.27/5.55 = one_one_int ) ).
% 5.27/5.55
% 5.27/5.55 % int_ops(2)
% 5.27/5.55 thf(fact_5652_zle__iff__zadd,axiom,
% 5.27/5.55 ( ord_less_eq_int
% 5.27/5.55 = ( ^ [W3: int,Z5: int] :
% 5.27/5.55 ? [N: nat] :
% 5.27/5.55 ( Z5
% 5.27/5.55 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zle_iff_zadd
% 5.27/5.55 thf(fact_5653_zdiv__int,axiom,
% 5.27/5.55 ! [A: nat,B: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.27/5.55 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zdiv_int
% 5.27/5.55 thf(fact_5654_zmod__int,axiom,
% 5.27/5.55 ! [A: nat,B: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.27/5.55 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zmod_int
% 5.27/5.55 thf(fact_5655_int__cases3,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( K != zero_zero_int )
% 5.27/5.55 => ( ! [N3: nat] :
% 5.27/5.55 ( ( K
% 5.27/5.55 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.27/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( ( K
% 5.27/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.27/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_cases3
% 5.27/5.55 thf(fact_5656_not__zle__0__negative,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % not_zle_0_negative
% 5.27/5.55 thf(fact_5657_negD,axiom,
% 5.27/5.55 ! [X4: int] :
% 5.27/5.55 ( ( ord_less_int @ X4 @ zero_zero_int )
% 5.27/5.55 => ? [N3: nat] :
% 5.27/5.55 ( X4
% 5.27/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % negD
% 5.27/5.55 thf(fact_5658_negative__zless__0,axiom,
% 5.27/5.55 ! [N2: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) @ zero_zero_int ) ).
% 5.27/5.55
% 5.27/5.55 % negative_zless_0
% 5.27/5.55 thf(fact_5659_int__Suc,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ N2 ) )
% 5.27/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_Suc
% 5.27/5.55 thf(fact_5660_int__ops_I4_J,axiom,
% 5.27/5.55 ! [A: nat] :
% 5.27/5.55 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.27/5.55 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_ops(4)
% 5.27/5.55 thf(fact_5661_zless__iff__Suc__zadd,axiom,
% 5.27/5.55 ( ord_less_int
% 5.27/5.55 = ( ^ [W3: int,Z5: int] :
% 5.27/5.55 ? [N: nat] :
% 5.27/5.55 ( Z5
% 5.27/5.55 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zless_iff_Suc_zadd
% 5.27/5.55 thf(fact_5662_pos__int__cases,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_int @ zero_zero_int @ K )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( ( K
% 5.27/5.55 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.27/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pos_int_cases
% 5.27/5.55 thf(fact_5663_zero__less__imp__eq__int,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_int @ zero_zero_int @ K )
% 5.27/5.55 => ? [N3: nat] :
% 5.27/5.55 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.55 & ( K
% 5.27/5.55 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zero_less_imp_eq_int
% 5.27/5.55 thf(fact_5664_neg__int__cases,axiom,
% 5.27/5.55 ! [K: int] :
% 5.27/5.55 ( ( ord_less_int @ K @ zero_zero_int )
% 5.27/5.55 => ~ ! [N3: nat] :
% 5.27/5.55 ( ( K
% 5.27/5.55 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.27/5.55 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % neg_int_cases
% 5.27/5.55 thf(fact_5665_zmult__zless__mono2__lemma,axiom,
% 5.27/5.55 ! [I2: int,J: int,K: nat] :
% 5.27/5.55 ( ( ord_less_int @ I2 @ J )
% 5.27/5.55 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.55 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I2 ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zmult_zless_mono2_lemma
% 5.27/5.55 thf(fact_5666_int__ops_I6_J,axiom,
% 5.27/5.55 ! [A: nat,B: nat] :
% 5.27/5.55 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.27/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.55 = zero_zero_int ) )
% 5.27/5.55 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.27/5.55 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.27/5.55 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % int_ops(6)
% 5.27/5.55 thf(fact_5667_zdiff__int__split,axiom,
% 5.27/5.55 ! [P: int > $o,X4: nat,Y: nat] :
% 5.27/5.55 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X4 @ Y ) ) )
% 5.27/5.55 = ( ( ( ord_less_eq_nat @ Y @ X4 )
% 5.27/5.55 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X4 ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.27/5.55 & ( ( ord_less_nat @ X4 @ Y )
% 5.27/5.55 => ( P @ zero_zero_int ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % zdiff_int_split
% 5.27/5.55 thf(fact_5668_dbl__dec__def,axiom,
% 5.27/5.55 ( neg_nu6511756317524482435omplex
% 5.27/5.55 = ( ^ [X: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_def
% 5.27/5.55 thf(fact_5669_dbl__dec__def,axiom,
% 5.27/5.55 ( neg_nu6075765906172075777c_real
% 5.27/5.55 = ( ^ [X: real] : ( minus_minus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_def
% 5.27/5.55 thf(fact_5670_dbl__dec__def,axiom,
% 5.27/5.55 ( neg_nu3179335615603231917ec_rat
% 5.27/5.55 = ( ^ [X: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_def
% 5.27/5.55 thf(fact_5671_dbl__dec__def,axiom,
% 5.27/5.55 ( neg_nu3811975205180677377ec_int
% 5.27/5.55 = ( ^ [X: int] : ( minus_minus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_def
% 5.27/5.55 thf(fact_5672_compl__le__swap2,axiom,
% 5.27/5.55 ! [Y: set_int,X4: set_int] :
% 5.27/5.55 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X4 )
% 5.27/5.55 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X4 ) @ Y ) ) ).
% 5.27/5.55
% 5.27/5.55 % compl_le_swap2
% 5.27/5.55 thf(fact_5673_compl__le__swap1,axiom,
% 5.27/5.55 ! [Y: set_int,X4: set_int] :
% 5.27/5.55 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X4 ) )
% 5.27/5.55 => ( ord_less_eq_set_int @ X4 @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % compl_le_swap1
% 5.27/5.55 thf(fact_5674_compl__mono,axiom,
% 5.27/5.55 ! [X4: set_int,Y: set_int] :
% 5.27/5.55 ( ( ord_less_eq_set_int @ X4 @ Y )
% 5.27/5.55 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X4 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % compl_mono
% 5.27/5.55 thf(fact_5675_XOR__upper,axiom,
% 5.27/5.55 ! [X4: int,N2: nat,Y: int] :
% 5.27/5.55 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.55 => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % XOR_upper
% 5.27/5.55 thf(fact_5676_real__arch__simple,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ? [N3: nat] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.27/5.55
% 5.27/5.55 % real_arch_simple
% 5.27/5.55 thf(fact_5677_real__arch__simple,axiom,
% 5.27/5.55 ! [X4: rat] :
% 5.27/5.55 ? [N3: nat] : ( ord_less_eq_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.27/5.55
% 5.27/5.55 % real_arch_simple
% 5.27/5.55 thf(fact_5678_reals__Archimedean2,axiom,
% 5.27/5.55 ! [X4: rat] :
% 5.27/5.55 ? [N3: nat] : ( ord_less_rat @ X4 @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.27/5.55
% 5.27/5.55 % reals_Archimedean2
% 5.27/5.55 thf(fact_5679_reals__Archimedean2,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ? [N3: nat] : ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.27/5.55
% 5.27/5.55 % reals_Archimedean2
% 5.27/5.55 thf(fact_5680_exists__least__lemma,axiom,
% 5.27/5.55 ! [P: nat > $o] :
% 5.27/5.55 ( ~ ( P @ zero_zero_nat )
% 5.27/5.55 => ( ? [X_1: nat] : ( P @ X_1 )
% 5.27/5.55 => ? [N3: nat] :
% 5.27/5.55 ( ~ ( P @ N3 )
% 5.27/5.55 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % exists_least_lemma
% 5.27/5.55 thf(fact_5681_xor__int__rec,axiom,
% 5.27/5.55 ( bit_se6526347334894502574or_int
% 5.27/5.55 = ( ^ [K3: int,L2: int] :
% 5.27/5.55 ( plus_plus_int
% 5.27/5.55 @ ( zero_n2684676970156552555ol_int
% 5.27/5.55 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 ) )
% 5.27/5.55 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.27/5.55 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % xor_int_rec
% 5.27/5.55 thf(fact_5682_Bolzano,axiom,
% 5.27/5.55 ! [A: real,B: real,P: real > real > $o] :
% 5.27/5.55 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.55 => ( ! [A5: real,B5: real,C3: real] :
% 5.27/5.55 ( ( P @ A5 @ B5 )
% 5.27/5.55 => ( ( P @ B5 @ C3 )
% 5.27/5.55 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.27/5.55 => ( ( ord_less_eq_real @ B5 @ C3 )
% 5.27/5.55 => ( P @ A5 @ C3 ) ) ) ) )
% 5.27/5.55 => ( ! [X5: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.55 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.55 => ? [D6: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ D6 )
% 5.27/5.55 & ! [A5: real,B5: real] :
% 5.27/5.55 ( ( ( ord_less_eq_real @ A5 @ X5 )
% 5.27/5.55 & ( ord_less_eq_real @ X5 @ B5 )
% 5.27/5.55 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D6 ) )
% 5.27/5.55 => ( P @ A5 @ B5 ) ) ) ) )
% 5.27/5.55 => ( P @ A @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % Bolzano
% 5.27/5.55 thf(fact_5683_ex__less__of__nat__mult,axiom,
% 5.27/5.55 ! [X4: rat,Y: rat] :
% 5.27/5.55 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.55 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X4 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % ex_less_of_nat_mult
% 5.27/5.55 thf(fact_5684_ex__less__of__nat__mult,axiom,
% 5.27/5.55 ! [X4: real,Y: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X4 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % ex_less_of_nat_mult
% 5.27/5.55 thf(fact_5685_signed__take__bit__numeral__minus__bit1,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_numeral_minus_bit1
% 5.27/5.55 thf(fact_5686_divmod__algorithm__code_I7_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(7)
% 5.27/5.55 thf(fact_5687_divmod__algorithm__code_I7_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(7)
% 5.27/5.55 thf(fact_5688_divmod__algorithm__code_I7_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_eq_num @ M @ N2 )
% 5.27/5.55 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(7)
% 5.27/5.55 thf(fact_5689_divmod__algorithm__code_I8_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique5026877609467782581ep_nat @ ( bit1 @ N2 ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(8)
% 5.27/5.55 thf(fact_5690_divmod__algorithm__code_I8_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique5024387138958732305ep_int @ ( bit1 @ N2 ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(8)
% 5.27/5.55 thf(fact_5691_divmod__algorithm__code_I8_J,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.27/5.55 & ( ~ ( ord_less_num @ M @ N2 )
% 5.27/5.55 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( unique4921790084139445826nteger @ ( bit1 @ N2 ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(8)
% 5.27/5.55 thf(fact_5692_take__bit__Suc__minus__bit1,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_Suc_minus_bit1
% 5.27/5.55 thf(fact_5693_lemma__termdiff3,axiom,
% 5.27/5.55 ! [H: real,Z: real,K5: real,N2: nat] :
% 5.27/5.55 ( ( H != zero_zero_real )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H ) ) @ K5 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % lemma_termdiff3
% 5.27/5.55 thf(fact_5694_lemma__termdiff3,axiom,
% 5.27/5.55 ! [H: complex,Z: complex,K5: real,N2: nat] :
% 5.27/5.55 ( ( H != zero_zero_complex )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H ) ) @ K5 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % lemma_termdiff3
% 5.27/5.55 thf(fact_5695_signed__take__bit__numeral__bit1,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_numeral_bit1
% 5.27/5.55 thf(fact_5696_dbl__inc__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.27/5.55 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(3)
% 5.27/5.55 thf(fact_5697_dbl__inc__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.27/5.55 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(3)
% 5.27/5.55 thf(fact_5698_dbl__inc__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.27/5.55 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(3)
% 5.27/5.55 thf(fact_5699_dbl__inc__simps_I3_J,axiom,
% 5.27/5.55 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.27/5.55 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(3)
% 5.27/5.55 thf(fact_5700_pred__numeral__simps_I1_J,axiom,
% 5.27/5.55 ( ( pred_numeral @ one )
% 5.27/5.55 = zero_zero_nat ) ).
% 5.27/5.55
% 5.27/5.55 % pred_numeral_simps(1)
% 5.27/5.55 thf(fact_5701_Suc__eq__numeral,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( ( suc @ N2 )
% 5.27/5.55 = ( numeral_numeral_nat @ K ) )
% 5.27/5.55 = ( N2
% 5.27/5.55 = ( pred_numeral @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % Suc_eq_numeral
% 5.27/5.55 thf(fact_5702_eq__numeral__Suc,axiom,
% 5.27/5.55 ! [K: num,N2: nat] :
% 5.27/5.55 ( ( ( numeral_numeral_nat @ K )
% 5.27/5.55 = ( suc @ N2 ) )
% 5.27/5.55 = ( ( pred_numeral @ K )
% 5.27/5.55 = N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % eq_numeral_Suc
% 5.27/5.55 thf(fact_5703_dbl__inc__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.27/5.55 = one_one_complex ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(2)
% 5.27/5.55 thf(fact_5704_dbl__inc__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.27/5.55 = one_one_real ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(2)
% 5.27/5.55 thf(fact_5705_dbl__inc__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.27/5.55 = one_one_rat ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(2)
% 5.27/5.55 thf(fact_5706_dbl__inc__simps_I2_J,axiom,
% 5.27/5.55 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.27/5.55 = one_one_int ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(2)
% 5.27/5.55 thf(fact_5707_pred__numeral__inc,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( pred_numeral @ ( inc @ K ) )
% 5.27/5.55 = ( numeral_numeral_nat @ K ) ) ).
% 5.27/5.55
% 5.27/5.55 % pred_numeral_inc
% 5.27/5.55 thf(fact_5708_dbl__inc__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.55 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(4)
% 5.27/5.55 thf(fact_5709_dbl__inc__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(4)
% 5.27/5.55 thf(fact_5710_dbl__inc__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(4)
% 5.27/5.55 thf(fact_5711_dbl__inc__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(4)
% 5.27/5.55 thf(fact_5712_dbl__inc__simps_I4_J,axiom,
% 5.27/5.55 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.55 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(4)
% 5.27/5.55 thf(fact_5713_dbl__inc__simps_I5_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.27/5.55 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(5)
% 5.27/5.55 thf(fact_5714_dbl__inc__simps_I5_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.27/5.55 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(5)
% 5.27/5.55 thf(fact_5715_dbl__inc__simps_I5_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.27/5.55 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(5)
% 5.27/5.55 thf(fact_5716_pred__numeral__simps_I3_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.27/5.55 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pred_numeral_simps(3)
% 5.27/5.55 thf(fact_5717_less__numeral__Suc,axiom,
% 5.27/5.55 ! [K: num,N2: nat] :
% 5.27/5.55 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.27/5.55 = ( ord_less_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % less_numeral_Suc
% 5.27/5.55 thf(fact_5718_less__Suc__numeral,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( ord_less_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.55 = ( ord_less_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % less_Suc_numeral
% 5.27/5.55 thf(fact_5719_le__Suc__numeral,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( ord_less_eq_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.55 = ( ord_less_eq_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_Suc_numeral
% 5.27/5.55 thf(fact_5720_le__numeral__Suc,axiom,
% 5.27/5.55 ! [K: num,N2: nat] :
% 5.27/5.55 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.27/5.55 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % le_numeral_Suc
% 5.27/5.55 thf(fact_5721_diff__Suc__numeral,axiom,
% 5.27/5.55 ! [N2: nat,K: num] :
% 5.27/5.55 ( ( minus_minus_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.55 = ( minus_minus_nat @ N2 @ ( pred_numeral @ K ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_Suc_numeral
% 5.27/5.55 thf(fact_5722_diff__numeral__Suc,axiom,
% 5.27/5.55 ! [K: num,N2: nat] :
% 5.27/5.55 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.27/5.55 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_Suc
% 5.27/5.55 thf(fact_5723_minus__numeral__div__numeral,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_numeral_div_numeral
% 5.27/5.55 thf(fact_5724_numeral__div__minus__numeral,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_div_minus_numeral
% 5.27/5.55 thf(fact_5725_dbl__inc__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(1)
% 5.27/5.55 thf(fact_5726_dbl__inc__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(1)
% 5.27/5.55 thf(fact_5727_dbl__inc__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(1)
% 5.27/5.55 thf(fact_5728_dbl__inc__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(1)
% 5.27/5.55 thf(fact_5729_dbl__inc__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_simps(1)
% 5.27/5.55 thf(fact_5730_dbl__dec__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(1)
% 5.27/5.55 thf(fact_5731_dbl__dec__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(1)
% 5.27/5.55 thf(fact_5732_dbl__dec__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(1)
% 5.27/5.55 thf(fact_5733_dbl__dec__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(1)
% 5.27/5.55 thf(fact_5734_dbl__dec__simps_I1_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_dec_simps(1)
% 5.27/5.55 thf(fact_5735_dvd__numeral__simp,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.55 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N2 @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dvd_numeral_simp
% 5.27/5.55 thf(fact_5736_dvd__numeral__simp,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.55 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N2 @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dvd_numeral_simp
% 5.27/5.55 thf(fact_5737_dvd__numeral__simp,axiom,
% 5.27/5.55 ! [M: num,N2: num] :
% 5.27/5.55 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.55 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N2 @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dvd_numeral_simp
% 5.27/5.55 thf(fact_5738_divmod__algorithm__code_I2_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( unique5052692396658037445od_int @ M @ one )
% 5.27/5.55 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(2)
% 5.27/5.55 thf(fact_5739_divmod__algorithm__code_I2_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.27/5.55 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(2)
% 5.27/5.55 thf(fact_5740_divmod__algorithm__code_I2_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( unique3479559517661332726nteger @ M @ one )
% 5.27/5.55 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(2)
% 5.27/5.55 thf(fact_5741_add__neg__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(5)
% 5.27/5.55 thf(fact_5742_add__neg__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(5)
% 5.27/5.55 thf(fact_5743_add__neg__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N2 ) ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(5)
% 5.27/5.55 thf(fact_5744_add__neg__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(5)
% 5.27/5.55 thf(fact_5745_add__neg__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(5)
% 5.27/5.55 thf(fact_5746_add__neg__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(6)
% 5.27/5.55 thf(fact_5747_add__neg__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(6)
% 5.27/5.55 thf(fact_5748_add__neg__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(6)
% 5.27/5.55 thf(fact_5749_add__neg__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(6)
% 5.27/5.55 thf(fact_5750_add__neg__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_neg_numeral_special(6)
% 5.27/5.55 thf(fact_5751_diff__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.55 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(6)
% 5.27/5.55 thf(fact_5752_diff__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.55 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(6)
% 5.27/5.55 thf(fact_5753_diff__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.55 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(6)
% 5.27/5.55 thf(fact_5754_diff__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.55 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(6)
% 5.27/5.55 thf(fact_5755_diff__numeral__special_I6_J,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.55 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(6)
% 5.27/5.55 thf(fact_5756_diff__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(5)
% 5.27/5.55 thf(fact_5757_diff__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(5)
% 5.27/5.55 thf(fact_5758_diff__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N2 ) )
% 5.27/5.55 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(5)
% 5.27/5.55 thf(fact_5759_diff__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.55 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(5)
% 5.27/5.55 thf(fact_5760_diff__numeral__special_I5_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % diff_numeral_special(5)
% 5.27/5.55 thf(fact_5761_divmod__algorithm__code_I3_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N2 ) )
% 5.27/5.55 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(3)
% 5.27/5.55 thf(fact_5762_divmod__algorithm__code_I3_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N2 ) )
% 5.27/5.55 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(3)
% 5.27/5.55 thf(fact_5763_divmod__algorithm__code_I3_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N2 ) )
% 5.27/5.55 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(3)
% 5.27/5.55 thf(fact_5764_divmod__algorithm__code_I4_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(4)
% 5.27/5.55 thf(fact_5765_divmod__algorithm__code_I4_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(4)
% 5.27/5.55 thf(fact_5766_divmod__algorithm__code_I4_J,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N2 ) )
% 5.27/5.55 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_algorithm_code(4)
% 5.27/5.55 thf(fact_5767_one__div__minus__numeral,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % one_div_minus_numeral
% 5.27/5.55 thf(fact_5768_minus__one__div__numeral,axiom,
% 5.27/5.55 ! [N2: num] :
% 5.27/5.55 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.55 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % minus_one_div_numeral
% 5.27/5.55 thf(fact_5769_signed__take__bit__numeral__bit0,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.27/5.55 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_numeral_bit0
% 5.27/5.55 thf(fact_5770_signed__take__bit__numeral__minus__bit0,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.55 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % signed_take_bit_numeral_minus_bit0
% 5.27/5.55 thf(fact_5771_num__induct,axiom,
% 5.27/5.55 ! [P: num > $o,X4: num] :
% 5.27/5.55 ( ( P @ one )
% 5.27/5.55 => ( ! [X5: num] :
% 5.27/5.55 ( ( P @ X5 )
% 5.27/5.55 => ( P @ ( inc @ X5 ) ) )
% 5.27/5.55 => ( P @ X4 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % num_induct
% 5.27/5.55 thf(fact_5772_add__inc,axiom,
% 5.27/5.55 ! [X4: num,Y: num] :
% 5.27/5.55 ( ( plus_plus_num @ X4 @ ( inc @ Y ) )
% 5.27/5.55 = ( inc @ ( plus_plus_num @ X4 @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_inc
% 5.27/5.55 thf(fact_5773_numeral__eq__Suc,axiom,
% 5.27/5.55 ( numeral_numeral_nat
% 5.27/5.55 = ( ^ [K3: num] : ( suc @ ( pred_numeral @ K3 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_eq_Suc
% 5.27/5.55 thf(fact_5774_inc_Osimps_I1_J,axiom,
% 5.27/5.55 ( ( inc @ one )
% 5.27/5.55 = ( bit0 @ one ) ) ).
% 5.27/5.55
% 5.27/5.55 % inc.simps(1)
% 5.27/5.55 thf(fact_5775_inc_Osimps_I2_J,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( inc @ ( bit0 @ X4 ) )
% 5.27/5.55 = ( bit1 @ X4 ) ) ).
% 5.27/5.55
% 5.27/5.55 % inc.simps(2)
% 5.27/5.55 thf(fact_5776_inc_Osimps_I3_J,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( inc @ ( bit1 @ X4 ) )
% 5.27/5.55 = ( bit0 @ ( inc @ X4 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % inc.simps(3)
% 5.27/5.55 thf(fact_5777_add__One,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( plus_plus_num @ X4 @ one )
% 5.27/5.55 = ( inc @ X4 ) ) ).
% 5.27/5.55
% 5.27/5.55 % add_One
% 5.27/5.55 thf(fact_5778_mult__inc,axiom,
% 5.27/5.55 ! [X4: num,Y: num] :
% 5.27/5.55 ( ( times_times_num @ X4 @ ( inc @ Y ) )
% 5.27/5.55 = ( plus_plus_num @ ( times_times_num @ X4 @ Y ) @ X4 ) ) ).
% 5.27/5.55
% 5.27/5.55 % mult_inc
% 5.27/5.55 thf(fact_5779_pred__numeral__def,axiom,
% 5.27/5.55 ( pred_numeral
% 5.27/5.55 = ( ^ [K3: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K3 ) @ one_one_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pred_numeral_def
% 5.27/5.55 thf(fact_5780_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numeral_numeral_rat @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_plus_rat @ ( numeral_numeral_rat @ X4 ) @ one_one_rat ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5781_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numera1916890842035813515d_enat @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ X4 ) @ one_on7984719198319812577d_enat ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5782_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numera6690914467698888265omplex @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X4 ) @ one_one_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5783_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numeral_numeral_real @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_plus_real @ ( numeral_numeral_real @ X4 ) @ one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5784_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numeral_numeral_nat @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_plus_nat @ ( numeral_numeral_nat @ X4 ) @ one_one_nat ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5785_numeral__inc,axiom,
% 5.27/5.55 ! [X4: num] :
% 5.27/5.55 ( ( numeral_numeral_int @ ( inc @ X4 ) )
% 5.27/5.55 = ( plus_plus_int @ ( numeral_numeral_int @ X4 ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % numeral_inc
% 5.27/5.55 thf(fact_5786_dbl__inc__def,axiom,
% 5.27/5.55 ( neg_nu8557863876264182079omplex
% 5.27/5.55 = ( ^ [X: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X @ X ) @ one_one_complex ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_def
% 5.27/5.55 thf(fact_5787_dbl__inc__def,axiom,
% 5.27/5.55 ( neg_nu8295874005876285629c_real
% 5.27/5.55 = ( ^ [X: real] : ( plus_plus_real @ ( plus_plus_real @ X @ X ) @ one_one_real ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_def
% 5.27/5.55 thf(fact_5788_dbl__inc__def,axiom,
% 5.27/5.55 ( neg_nu5219082963157363817nc_rat
% 5.27/5.55 = ( ^ [X: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X @ X ) @ one_one_rat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_def
% 5.27/5.55 thf(fact_5789_dbl__inc__def,axiom,
% 5.27/5.55 ( neg_nu5851722552734809277nc_int
% 5.27/5.55 = ( ^ [X: int] : ( plus_plus_int @ ( plus_plus_int @ X @ X ) @ one_one_int ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % dbl_inc_def
% 5.27/5.55 thf(fact_5790_divmod__int__def,axiom,
% 5.27/5.55 ( unique5052692396658037445od_int
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_int_def
% 5.27/5.55 thf(fact_5791_divmod__def,axiom,
% 5.27/5.55 ( unique5052692396658037445od_int
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M6 ) @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_def
% 5.27/5.55 thf(fact_5792_divmod__def,axiom,
% 5.27/5.55 ( unique5055182867167087721od_nat
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_def
% 5.27/5.55 thf(fact_5793_divmod__def,axiom,
% 5.27/5.55 ( unique3479559517661332726nteger
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_def
% 5.27/5.55 thf(fact_5794_divmod_H__nat__def,axiom,
% 5.27/5.55 ( unique5055182867167087721od_nat
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M6 ) @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod'_nat_def
% 5.27/5.55 thf(fact_5795_take__bit__numeral__minus__bit1,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_minus_bit1
% 5.27/5.55 thf(fact_5796_take__bit__numeral__bit0,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.27/5.55 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_bit0
% 5.27/5.55 thf(fact_5797_take__bit__numeral__bit0,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.27/5.55 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_bit0
% 5.27/5.55 thf(fact_5798_take__bit__numeral__minus__bit0,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.55 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_minus_bit0
% 5.27/5.55 thf(fact_5799_divmod__divmod__step,axiom,
% 5.27/5.55 ( unique5055182867167087721od_nat
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M6 ) ) @ ( unique5026877609467782581ep_nat @ N @ ( unique5055182867167087721od_nat @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_divmod_step
% 5.27/5.55 thf(fact_5800_divmod__divmod__step,axiom,
% 5.27/5.55 ( unique5052692396658037445od_int
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M6 @ N ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M6 ) ) @ ( unique5024387138958732305ep_int @ N @ ( unique5052692396658037445od_int @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_divmod_step
% 5.27/5.55 thf(fact_5801_divmod__divmod__step,axiom,
% 5.27/5.55 ( unique3479559517661332726nteger
% 5.27/5.55 = ( ^ [M6: num,N: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M6 @ N ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M6 ) ) @ ( unique4921790084139445826nteger @ N @ ( unique3479559517661332726nteger @ M6 @ ( bit0 @ N ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_divmod_step
% 5.27/5.55 thf(fact_5802_take__bit__numeral__bit1,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.27/5.55 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_bit1
% 5.27/5.55 thf(fact_5803_take__bit__numeral__bit1,axiom,
% 5.27/5.55 ! [L: num,K: num] :
% 5.27/5.55 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.27/5.55 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.27/5.55
% 5.27/5.55 % take_bit_numeral_bit1
% 5.27/5.55 thf(fact_5804_norm__divide__numeral,axiom,
% 5.27/5.55 ! [A: real,W: num] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_divide_numeral
% 5.27/5.55 thf(fact_5805_norm__divide__numeral,axiom,
% 5.27/5.55 ! [A: complex,W: num] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_divide_numeral
% 5.27/5.55 thf(fact_5806_norm__mult__numeral2,axiom,
% 5.27/5.55 ! [A: real,W: num] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.55 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_numeral2
% 5.27/5.55 thf(fact_5807_norm__mult__numeral2,axiom,
% 5.27/5.55 ! [A: complex,W: num] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.55 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_numeral2
% 5.27/5.55 thf(fact_5808_norm__mult__numeral1,axiom,
% 5.27/5.55 ! [W: num,A: real] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.27/5.55 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_numeral1
% 5.27/5.55 thf(fact_5809_norm__mult__numeral1,axiom,
% 5.27/5.55 ! [W: num,A: complex] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.27/5.55 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_numeral1
% 5.27/5.55 thf(fact_5810_norm__neg__numeral,axiom,
% 5.27/5.55 ! [W: num] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_neg_numeral
% 5.27/5.55 thf(fact_5811_norm__neg__numeral,axiom,
% 5.27/5.55 ! [W: num] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_neg_numeral
% 5.27/5.55 thf(fact_5812_norm__le__zero__iff,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ zero_zero_real )
% 5.27/5.55 = ( X4 = zero_zero_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_le_zero_iff
% 5.27/5.55 thf(fact_5813_norm__le__zero__iff,axiom,
% 5.27/5.55 ! [X4: complex] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real )
% 5.27/5.55 = ( X4 = zero_zero_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_le_zero_iff
% 5.27/5.55 thf(fact_5814_zero__less__norm__iff,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.27/5.55 = ( X4 != zero_zero_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % zero_less_norm_iff
% 5.27/5.55 thf(fact_5815_zero__less__norm__iff,axiom,
% 5.27/5.55 ! [X4: complex] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.27/5.55 = ( X4 != zero_zero_complex ) ) ).
% 5.27/5.55
% 5.27/5.55 % zero_less_norm_iff
% 5.27/5.55 thf(fact_5816_norm__numeral,axiom,
% 5.27/5.55 ! [W: num] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_numeral
% 5.27/5.55 thf(fact_5817_norm__numeral,axiom,
% 5.27/5.55 ! [W: num] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.55 = ( numeral_numeral_real @ W ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_numeral
% 5.27/5.55 thf(fact_5818_norm__one,axiom,
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.27/5.55 = one_one_real ) ).
% 5.27/5.55
% 5.27/5.55 % norm_one
% 5.27/5.55 thf(fact_5819_norm__one,axiom,
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.27/5.55 = one_one_real ) ).
% 5.27/5.55
% 5.27/5.55 % norm_one
% 5.27/5.55 thf(fact_5820_norm__not__less__zero,axiom,
% 5.27/5.55 ! [X4: complex] :
% 5.27/5.55 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ zero_zero_real ) ).
% 5.27/5.55
% 5.27/5.55 % norm_not_less_zero
% 5.27/5.55 thf(fact_5821_norm__ge__zero,axiom,
% 5.27/5.55 ! [X4: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_ge_zero
% 5.27/5.55 thf(fact_5822_norm__divide,axiom,
% 5.27/5.55 ! [A: real,B: real] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_divide
% 5.27/5.55 thf(fact_5823_norm__divide,axiom,
% 5.27/5.55 ! [A: complex,B: complex] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_divide
% 5.27/5.55 thf(fact_5824_norm__power,axiom,
% 5.27/5.55 ! [X4: real,N2: nat] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.55 = ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power
% 5.27/5.55 thf(fact_5825_norm__power,axiom,
% 5.27/5.55 ! [X4: complex,N2: nat] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) )
% 5.27/5.55 = ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power
% 5.27/5.55 thf(fact_5826_norm__uminus__minus,axiom,
% 5.27/5.55 ! [X4: real,Y: real] :
% 5.27/5.55 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ Y ) )
% 5.27/5.55 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_uminus_minus
% 5.27/5.55 thf(fact_5827_norm__uminus__minus,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex] :
% 5.27/5.55 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X4 ) @ Y ) )
% 5.27/5.55 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_uminus_minus
% 5.27/5.55 thf(fact_5828_nonzero__norm__divide,axiom,
% 5.27/5.55 ! [B: real,A: real] :
% 5.27/5.55 ( ( B != zero_zero_real )
% 5.27/5.55 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nonzero_norm_divide
% 5.27/5.55 thf(fact_5829_nonzero__norm__divide,axiom,
% 5.27/5.55 ! [B: complex,A: complex] :
% 5.27/5.55 ( ( B != zero_zero_complex )
% 5.27/5.55 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.55 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % nonzero_norm_divide
% 5.27/5.55 thf(fact_5830_power__eq__imp__eq__norm,axiom,
% 5.27/5.55 ! [W: real,N2: nat,Z: real] :
% 5.27/5.55 ( ( ( power_power_real @ W @ N2 )
% 5.27/5.55 = ( power_power_real @ Z @ N2 ) )
% 5.27/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.55 => ( ( real_V7735802525324610683m_real @ W )
% 5.27/5.55 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_eq_imp_eq_norm
% 5.27/5.55 thf(fact_5831_power__eq__imp__eq__norm,axiom,
% 5.27/5.55 ! [W: complex,N2: nat,Z: complex] :
% 5.27/5.55 ( ( ( power_power_complex @ W @ N2 )
% 5.27/5.55 = ( power_power_complex @ Z @ N2 ) )
% 5.27/5.55 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.55 => ( ( real_V1022390504157884413omplex @ W )
% 5.27/5.55 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_eq_imp_eq_norm
% 5.27/5.55 thf(fact_5832_norm__mult__less,axiom,
% 5.27/5.55 ! [X4: real,R3: real,Y: real,S: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.27/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_less
% 5.27/5.55 thf(fact_5833_norm__mult__less,axiom,
% 5.27/5.55 ! [X4: complex,R3: real,Y: complex,S: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.27/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_less
% 5.27/5.55 thf(fact_5834_norm__mult__ineq,axiom,
% 5.27/5.55 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X4 @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_ineq
% 5.27/5.55 thf(fact_5835_norm__mult__ineq,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X4 @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_mult_ineq
% 5.27/5.55 thf(fact_5836_norm__triangle__lt,axiom,
% 5.27/5.55 ! [X4: real,Y: real,E2: real] :
% 5.27/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_lt
% 5.27/5.55 thf(fact_5837_norm__triangle__lt,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex,E2: real] :
% 5.27/5.55 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_lt
% 5.27/5.55 thf(fact_5838_norm__add__less,axiom,
% 5.27/5.55 ! [X4: real,R3: real,Y: real,S: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ R3 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.27/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_add_less
% 5.27/5.55 thf(fact_5839_norm__add__less,axiom,
% 5.27/5.55 ! [X4: complex,R3: real,Y: complex,S: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ R3 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.27/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_add_less
% 5.27/5.55 thf(fact_5840_norm__add__leD,axiom,
% 5.27/5.55 ! [A: real,B: real,C: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_add_leD
% 5.27/5.55 thf(fact_5841_norm__add__leD,axiom,
% 5.27/5.55 ! [A: complex,B: complex,C: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_add_leD
% 5.27/5.55 thf(fact_5842_norm__triangle__le,axiom,
% 5.27/5.55 ! [X4: real,Y: real,E2: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_le
% 5.27/5.55 thf(fact_5843_norm__triangle__le,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex,E2: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_le
% 5.27/5.55 thf(fact_5844_norm__triangle__ineq,axiom,
% 5.27/5.55 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq
% 5.27/5.55 thf(fact_5845_norm__triangle__ineq,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq
% 5.27/5.55 thf(fact_5846_norm__triangle__mono,axiom,
% 5.27/5.55 ! [A: real,R3: real,B: real,S: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R3 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_mono
% 5.27/5.55 thf(fact_5847_norm__triangle__mono,axiom,
% 5.27/5.55 ! [A: complex,R3: real,B: complex,S: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R3 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R3 @ S ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_mono
% 5.27/5.55 thf(fact_5848_norm__diff__triangle__less,axiom,
% 5.27/5.55 ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.27/5.55 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_less
% 5.27/5.55 thf(fact_5849_norm__diff__triangle__less,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.27/5.55 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 5.27/5.55 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.27/5.55 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_less
% 5.27/5.55 thf(fact_5850_norm__power__ineq,axiom,
% 5.27/5.55 ! [X4: real,N2: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X4 ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power_ineq
% 5.27/5.55 thf(fact_5851_norm__power__ineq,axiom,
% 5.27/5.55 ! [X4: complex,N2: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X4 @ N2 ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X4 ) @ N2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power_ineq
% 5.27/5.55 thf(fact_5852_norm__triangle__sub,axiom,
% 5.27/5.55 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_sub
% 5.27/5.55 thf(fact_5853_norm__triangle__sub,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_sub
% 5.27/5.55 thf(fact_5854_norm__triangle__ineq4,axiom,
% 5.27/5.55 ! [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 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq4
% 5.27/5.55 thf(fact_5855_norm__triangle__ineq4,axiom,
% 5.27/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq4
% 5.27/5.55 thf(fact_5856_norm__diff__triangle__le,axiom,
% 5.27/5.55 ! [X4: real,Y: real,E1: real,Z: real,E22: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E1 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_le
% 5.27/5.55 thf(fact_5857_norm__diff__triangle__le,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E1 )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_le
% 5.27/5.55 thf(fact_5858_norm__triangle__le__diff,axiom,
% 5.27/5.55 ! [X4: real,Y: real,E2: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_le_diff
% 5.27/5.55 thf(fact_5859_norm__triangle__le__diff,axiom,
% 5.27/5.55 ! [X4: complex,Y: complex,E2: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E2 )
% 5.27/5.55 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X4 @ Y ) ) @ E2 ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_le_diff
% 5.27/5.55 thf(fact_5860_norm__diff__ineq,axiom,
% 5.27/5.55 ! [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 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_ineq
% 5.27/5.55 thf(fact_5861_norm__diff__ineq,axiom,
% 5.27/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_ineq
% 5.27/5.55 thf(fact_5862_norm__triangle__ineq2,axiom,
% 5.27/5.55 ! [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 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq2
% 5.27/5.55 thf(fact_5863_norm__triangle__ineq2,axiom,
% 5.27/5.55 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_triangle_ineq2
% 5.27/5.55 thf(fact_5864_power__eq__1__iff,axiom,
% 5.27/5.55 ! [W: real,N2: nat] :
% 5.27/5.55 ( ( ( power_power_real @ W @ N2 )
% 5.27/5.55 = one_one_real )
% 5.27/5.55 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.27/5.55 = one_one_real )
% 5.27/5.55 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_eq_1_iff
% 5.27/5.55 thf(fact_5865_power__eq__1__iff,axiom,
% 5.27/5.55 ! [W: complex,N2: nat] :
% 5.27/5.55 ( ( ( power_power_complex @ W @ N2 )
% 5.27/5.55 = one_one_complex )
% 5.27/5.55 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.27/5.55 = one_one_real )
% 5.27/5.55 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % power_eq_1_iff
% 5.27/5.55 thf(fact_5866_norm__diff__triangle__ineq,axiom,
% 5.27/5.55 ! [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 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_ineq
% 5.27/5.55 thf(fact_5867_norm__diff__triangle__ineq,axiom,
% 5.27/5.55 ! [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 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_diff_triangle_ineq
% 5.27/5.55 thf(fact_5868_square__norm__one,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_real )
% 5.27/5.55 => ( ( real_V7735802525324610683m_real @ X4 )
% 5.27/5.55 = one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_norm_one
% 5.27/5.55 thf(fact_5869_square__norm__one,axiom,
% 5.27/5.55 ! [X4: complex] :
% 5.27/5.55 ( ( ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.55 = one_one_complex )
% 5.27/5.55 => ( ( real_V1022390504157884413omplex @ X4 )
% 5.27/5.55 = one_one_real ) ) ).
% 5.27/5.55
% 5.27/5.55 % square_norm_one
% 5.27/5.55 thf(fact_5870_norm__power__diff,axiom,
% 5.27/5.55 ! [Z: real,W: real,M: nat] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ W ) @ one_one_real )
% 5.27/5.55 => ( 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 ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power_diff
% 5.27/5.55 thf(fact_5871_norm__power__diff,axiom,
% 5.27/5.55 ! [Z: complex,W: complex,M: nat] :
% 5.27/5.55 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.27/5.55 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.27/5.55 => ( 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 ) ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % norm_power_diff
% 5.27/5.55 thf(fact_5872_arcosh__1,axiom,
% 5.27/5.55 ( ( arcosh_real @ one_one_real )
% 5.27/5.55 = zero_zero_real ) ).
% 5.27/5.55
% 5.27/5.55 % arcosh_1
% 5.27/5.55 thf(fact_5873_pochhammer__double,axiom,
% 5.27/5.55 ! [Z: rat,N2: nat] :
% 5.27/5.55 ( ( comm_s4028243227959126397er_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 = ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_double
% 5.27/5.55 thf(fact_5874_pochhammer__double,axiom,
% 5.27/5.55 ! [Z: complex,N2: nat] :
% 5.27/5.55 ( ( comm_s2602460028002588243omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 = ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_double
% 5.27/5.55 thf(fact_5875_pochhammer__double,axiom,
% 5.27/5.55 ! [Z: real,N2: nat] :
% 5.27/5.55 ( ( comm_s7457072308508201937r_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.55 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ N2 ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_double
% 5.27/5.55 thf(fact_5876_ln__one__minus__pos__lower__bound,axiom,
% 5.27/5.55 ! [X4: real] :
% 5.27/5.55 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.55 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X4 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % ln_one_minus_pos_lower_bound
% 5.27/5.55 thf(fact_5877_central__binomial__lower__bound,axiom,
% 5.27/5.55 ! [N2: nat] :
% 5.27/5.55 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.55 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N2 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % central_binomial_lower_bound
% 5.27/5.55 thf(fact_5878_divmod__BitM__2__eq,axiom,
% 5.27/5.55 ! [M: num] :
% 5.27/5.55 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.27/5.55 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.27/5.55
% 5.27/5.55 % divmod_BitM_2_eq
% 5.27/5.55 thf(fact_5879_ln__one,axiom,
% 5.27/5.55 ( ( ln_ln_real @ one_one_real )
% 5.27/5.55 = zero_zero_real ) ).
% 5.27/5.55
% 5.27/5.55 % ln_one
% 5.27/5.55 thf(fact_5880_ln__inj__iff,axiom,
% 5.27/5.55 ! [X4: real,Y: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.55 => ( ( ( ln_ln_real @ X4 )
% 5.27/5.55 = ( ln_ln_real @ Y ) )
% 5.27/5.55 = ( X4 = Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % ln_inj_iff
% 5.27/5.55 thf(fact_5881_ln__less__cancel__iff,axiom,
% 5.27/5.55 ! [X4: real,Y: real] :
% 5.27/5.55 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.55 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.55 => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 5.27/5.55 = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.55
% 5.27/5.55 % ln_less_cancel_iff
% 5.27/5.55 thf(fact_5882_pochhammer__0,axiom,
% 5.27/5.55 ! [A: complex] :
% 5.27/5.55 ( ( comm_s2602460028002588243omplex @ A @ zero_zero_nat )
% 5.27/5.55 = one_one_complex ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_0
% 5.27/5.55 thf(fact_5883_pochhammer__0,axiom,
% 5.27/5.55 ! [A: real] :
% 5.27/5.55 ( ( comm_s7457072308508201937r_real @ A @ zero_zero_nat )
% 5.27/5.55 = one_one_real ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_0
% 5.27/5.55 thf(fact_5884_pochhammer__0,axiom,
% 5.27/5.55 ! [A: rat] :
% 5.27/5.55 ( ( comm_s4028243227959126397er_rat @ A @ zero_zero_nat )
% 5.27/5.55 = one_one_rat ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_0
% 5.27/5.55 thf(fact_5885_pochhammer__0,axiom,
% 5.27/5.55 ! [A: nat] :
% 5.27/5.55 ( ( comm_s4663373288045622133er_nat @ A @ zero_zero_nat )
% 5.27/5.55 = one_one_nat ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_0
% 5.27/5.55 thf(fact_5886_pochhammer__0,axiom,
% 5.27/5.55 ! [A: int] :
% 5.27/5.55 ( ( comm_s4660882817536571857er_int @ A @ zero_zero_nat )
% 5.27/5.55 = one_one_int ) ).
% 5.27/5.55
% 5.27/5.55 % pochhammer_0
% 5.27/5.55 thf(fact_5887_dbl__dec__simps_I5_J,axiom,
% 5.27/5.55 ! [K: num] :
% 5.27/5.55 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.27/5.55 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % dbl_dec_simps(5)
% 5.27/5.56 thf(fact_5888_dbl__dec__simps_I5_J,axiom,
% 5.27/5.56 ! [K: num] :
% 5.27/5.56 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.27/5.56 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % dbl_dec_simps(5)
% 5.27/5.56 thf(fact_5889_dbl__dec__simps_I5_J,axiom,
% 5.27/5.56 ! [K: num] :
% 5.27/5.56 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.27/5.56 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % dbl_dec_simps(5)
% 5.27/5.56 thf(fact_5890_ln__le__cancel__iff,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.56 => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) )
% 5.27/5.56 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_le_cancel_iff
% 5.27/5.56 thf(fact_5891_ln__less__zero__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 5.27/5.56 = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_less_zero_iff
% 5.27/5.56 thf(fact_5892_ln__gt__zero__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.56 = ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_gt_zero_iff
% 5.27/5.56 thf(fact_5893_ln__eq__zero__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ( ln_ln_real @ X4 )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 = ( X4 = one_one_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_eq_zero_iff
% 5.27/5.56 thf(fact_5894_pred__numeral__simps_I2_J,axiom,
% 5.27/5.56 ! [K: num] :
% 5.27/5.56 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.27/5.56 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pred_numeral_simps(2)
% 5.27/5.56 thf(fact_5895_ln__ge__zero__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.56 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_ge_zero_iff
% 5.27/5.56 thf(fact_5896_ln__le__zero__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ zero_zero_real )
% 5.27/5.56 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_le_zero_iff
% 5.27/5.56 thf(fact_5897_semiring__norm_I26_J,axiom,
% 5.27/5.56 ( ( bitM @ one )
% 5.27/5.56 = one ) ).
% 5.27/5.56
% 5.27/5.56 % semiring_norm(26)
% 5.27/5.56 thf(fact_5898_ln__less__self,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_less_self
% 5.27/5.56 thf(fact_5899_pochhammer__pos,axiom,
% 5.27/5.56 ! [X4: real,N2: nat] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_pos
% 5.27/5.56 thf(fact_5900_pochhammer__pos,axiom,
% 5.27/5.56 ! [X4: rat,N2: nat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.56 => ( ord_less_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_pos
% 5.27/5.56 thf(fact_5901_pochhammer__pos,axiom,
% 5.27/5.56 ! [X4: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.56 => ( ord_less_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_pos
% 5.27/5.56 thf(fact_5902_pochhammer__pos,axiom,
% 5.27/5.56 ! [X4: int,N2: nat] :
% 5.27/5.56 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.27/5.56 => ( ord_less_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_pos
% 5.27/5.56 thf(fact_5903_pochhammer__neq__0__mono,axiom,
% 5.27/5.56 ! [A: complex,M: nat,N2: nat] :
% 5.27/5.56 ( ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.27/5.56 != zero_zero_complex )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.27/5.56 != zero_zero_complex ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_neq_0_mono
% 5.27/5.56 thf(fact_5904_pochhammer__neq__0__mono,axiom,
% 5.27/5.56 ! [A: real,M: nat,N2: nat] :
% 5.27/5.56 ( ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.27/5.56 != zero_zero_real )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.27/5.56 != zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_neq_0_mono
% 5.27/5.56 thf(fact_5905_pochhammer__neq__0__mono,axiom,
% 5.27/5.56 ! [A: rat,M: nat,N2: nat] :
% 5.27/5.56 ( ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.27/5.56 != zero_zero_rat )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.27/5.56 != zero_zero_rat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_neq_0_mono
% 5.27/5.56 thf(fact_5906_pochhammer__eq__0__mono,axiom,
% 5.27/5.56 ! [A: complex,N2: nat,M: nat] :
% 5.27/5.56 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.27/5.56 = zero_zero_complex )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ A @ M )
% 5.27/5.56 = zero_zero_complex ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_mono
% 5.27/5.56 thf(fact_5907_pochhammer__eq__0__mono,axiom,
% 5.27/5.56 ! [A: real,N2: nat,M: nat] :
% 5.27/5.56 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ A @ M )
% 5.27/5.56 = zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_mono
% 5.27/5.56 thf(fact_5908_pochhammer__eq__0__mono,axiom,
% 5.27/5.56 ! [A: rat,N2: nat,M: nat] :
% 5.27/5.56 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.27/5.56 = zero_zero_rat )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ A @ M )
% 5.27/5.56 = zero_zero_rat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_mono
% 5.27/5.56 thf(fact_5909_semiring__norm_I27_J,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( bitM @ ( bit0 @ N2 ) )
% 5.27/5.56 = ( bit1 @ ( bitM @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % semiring_norm(27)
% 5.27/5.56 thf(fact_5910_semiring__norm_I28_J,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( bitM @ ( bit1 @ N2 ) )
% 5.27/5.56 = ( bit1 @ ( bit0 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % semiring_norm(28)
% 5.27/5.56 thf(fact_5911_inc__BitM__eq,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( inc @ ( bitM @ N2 ) )
% 5.27/5.56 = ( bit0 @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % inc_BitM_eq
% 5.27/5.56 thf(fact_5912_BitM__inc__eq,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( bitM @ ( inc @ N2 ) )
% 5.27/5.56 = ( bit1 @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % BitM_inc_eq
% 5.27/5.56 thf(fact_5913_ln__bound,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_bound
% 5.27/5.56 thf(fact_5914_ln__gt__zero__imp__gt__one,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_gt_zero_imp_gt_one
% 5.27/5.56 thf(fact_5915_ln__less__zero,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.56 => ( ord_less_real @ ( ln_ln_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_less_zero
% 5.27/5.56 thf(fact_5916_ln__gt__zero,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.56 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_gt_zero
% 5.27/5.56 thf(fact_5917_ln__ge__zero,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_ge_zero
% 5.27/5.56 thf(fact_5918_pochhammer__nonneg,axiom,
% 5.27/5.56 ! [X4: real,N2: nat] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ zero_zero_real @ ( comm_s7457072308508201937r_real @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_nonneg
% 5.27/5.56 thf(fact_5919_pochhammer__nonneg,axiom,
% 5.27/5.56 ! [X4: rat,N2: nat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.56 => ( ord_less_eq_rat @ zero_zero_rat @ ( comm_s4028243227959126397er_rat @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_nonneg
% 5.27/5.56 thf(fact_5920_pochhammer__nonneg,axiom,
% 5.27/5.56 ! [X4: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ X4 )
% 5.27/5.56 => ( ord_less_eq_nat @ zero_zero_nat @ ( comm_s4663373288045622133er_nat @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_nonneg
% 5.27/5.56 thf(fact_5921_pochhammer__nonneg,axiom,
% 5.27/5.56 ! [X4: int,N2: nat] :
% 5.27/5.56 ( ( ord_less_int @ zero_zero_int @ X4 )
% 5.27/5.56 => ( ord_less_eq_int @ zero_zero_int @ ( comm_s4660882817536571857er_int @ X4 @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_nonneg
% 5.27/5.56 thf(fact_5922_pochhammer__0__left,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( ( N2 = zero_zero_nat )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.27/5.56 = one_one_complex ) )
% 5.27/5.56 & ( ( N2 != zero_zero_nat )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ zero_zero_complex @ N2 )
% 5.27/5.56 = zero_zero_complex ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_0_left
% 5.27/5.56 thf(fact_5923_pochhammer__0__left,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( ( N2 = zero_zero_nat )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.27/5.56 = one_one_real ) )
% 5.27/5.56 & ( ( N2 != zero_zero_nat )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ zero_zero_real @ N2 )
% 5.27/5.56 = zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_0_left
% 5.27/5.56 thf(fact_5924_pochhammer__0__left,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( ( N2 = zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.27/5.56 = one_one_rat ) )
% 5.27/5.56 & ( ( N2 != zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ zero_zero_rat @ N2 )
% 5.27/5.56 = zero_zero_rat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_0_left
% 5.27/5.56 thf(fact_5925_pochhammer__0__left,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( ( N2 = zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.27/5.56 = one_one_nat ) )
% 5.27/5.56 & ( ( N2 != zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4663373288045622133er_nat @ zero_zero_nat @ N2 )
% 5.27/5.56 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_0_left
% 5.27/5.56 thf(fact_5926_pochhammer__0__left,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( ( N2 = zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.27/5.56 = one_one_int ) )
% 5.27/5.56 & ( ( N2 != zero_zero_nat )
% 5.27/5.56 => ( ( comm_s4660882817536571857er_int @ zero_zero_int @ N2 )
% 5.27/5.56 = zero_zero_int ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_0_left
% 5.27/5.56 thf(fact_5927_eval__nat__numeral_I2_J,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.27/5.56 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % eval_nat_numeral(2)
% 5.27/5.56 thf(fact_5928_ln__ge__zero__imp__ge__one,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_ge_zero_imp_ge_one
% 5.27/5.56 thf(fact_5929_one__plus__BitM,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( plus_plus_num @ one @ ( bitM @ N2 ) )
% 5.27/5.56 = ( bit0 @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % one_plus_BitM
% 5.27/5.56 thf(fact_5930_BitM__plus__one,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( plus_plus_num @ ( bitM @ N2 ) @ one )
% 5.27/5.56 = ( bit0 @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % BitM_plus_one
% 5.27/5.56 thf(fact_5931_ln__add__one__self__le__self,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_add_one_self_le_self
% 5.27/5.56 thf(fact_5932_ln__mult,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.56 => ( ( ln_ln_real @ ( times_times_real @ X4 @ Y ) )
% 5.27/5.56 = ( plus_plus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_mult
% 5.27/5.56 thf(fact_5933_ln__eq__minus__one,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ( ln_ln_real @ X4 )
% 5.27/5.56 = ( minus_minus_real @ X4 @ one_one_real ) )
% 5.27/5.56 => ( X4 = one_one_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_eq_minus_one
% 5.27/5.56 thf(fact_5934_ln__div,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.56 => ( ( ln_ln_real @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.56 = ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_div
% 5.27/5.56 thf(fact_5935_pochhammer__rec,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_rat @ A @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec
% 5.27/5.56 thf(fact_5936_pochhammer__rec,axiom,
% 5.27/5.56 ! [A: complex,N2: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_complex @ A @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec
% 5.27/5.56 thf(fact_5937_pochhammer__rec,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_real @ A @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ one_one_real ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec
% 5.27/5.56 thf(fact_5938_pochhammer__rec,axiom,
% 5.27/5.56 ! [A: nat,N2: nat] :
% 5.27/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_nat @ A @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec
% 5.27/5.56 thf(fact_5939_pochhammer__rec,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_int @ A @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ one_one_int ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec
% 5.27/5.56 thf(fact_5940_pochhammer__rec_H,axiom,
% 5.27/5.56 ! [Z: rat,N2: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec'
% 5.27/5.56 thf(fact_5941_pochhammer__rec_H,axiom,
% 5.27/5.56 ! [Z: complex,N2: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_complex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ ( comm_s2602460028002588243omplex @ Z @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec'
% 5.27/5.56 thf(fact_5942_pochhammer__rec_H,axiom,
% 5.27/5.56 ! [Z: real,N2: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( comm_s7457072308508201937r_real @ Z @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec'
% 5.27/5.56 thf(fact_5943_pochhammer__rec_H,axiom,
% 5.27/5.56 ! [Z: int,N2: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ Z @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ ( comm_s4660882817536571857er_int @ Z @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec'
% 5.27/5.56 thf(fact_5944_pochhammer__rec_H,axiom,
% 5.27/5.56 ! [Z: nat,N2: nat] :
% 5.27/5.56 ( ( comm_s4663373288045622133er_nat @ Z @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_rec'
% 5.27/5.56 thf(fact_5945_pochhammer__Suc,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ A @ N2 ) @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_Suc
% 5.27/5.56 thf(fact_5946_pochhammer__Suc,axiom,
% 5.27/5.56 ! [A: complex,N2: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ A @ N2 ) @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_Suc
% 5.27/5.56 thf(fact_5947_pochhammer__Suc,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ A @ N2 ) @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_Suc
% 5.27/5.56 thf(fact_5948_pochhammer__Suc,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ A @ N2 ) @ ( plus_plus_int @ A @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_Suc
% 5.27/5.56 thf(fact_5949_pochhammer__Suc,axiom,
% 5.27/5.56 ! [A: nat,N2: nat] :
% 5.27/5.56 ( ( comm_s4663373288045622133er_nat @ A @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ A @ N2 ) @ ( plus_plus_nat @ A @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_Suc
% 5.27/5.56 thf(fact_5950_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_complex ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.27/5.56 thf(fact_5951_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.27/5.56 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.27/5.56 thf(fact_5952_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.27/5.56 thf(fact_5953_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.27/5.56 thf(fact_5954_pochhammer__of__nat__eq__0__lemma,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma
% 5.27/5.56 thf(fact_5955_pochhammer__of__nat__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_complex )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_iff
% 5.27/5.56 thf(fact_5956_pochhammer__of__nat__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.27/5.56 = zero_z3403309356797280102nteger )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_iff
% 5.27/5.56 thf(fact_5957_pochhammer__of__nat__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_rat )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_iff
% 5.27/5.56 thf(fact_5958_pochhammer__of__nat__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_iff
% 5.27/5.56 thf(fact_5959_pochhammer__of__nat__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.27/5.56 = zero_zero_int )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_iff
% 5.27/5.56 thf(fact_5960_pochhammer__eq__0__iff,axiom,
% 5.27/5.56 ! [A: complex,N2: nat] :
% 5.27/5.56 ( ( ( comm_s2602460028002588243omplex @ A @ N2 )
% 5.27/5.56 = zero_zero_complex )
% 5.27/5.56 = ( ? [K3: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K3 @ N2 )
% 5.27/5.56 & ( A
% 5.27/5.56 = ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K3 ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_iff
% 5.27/5.56 thf(fact_5961_pochhammer__eq__0__iff,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( ( comm_s4028243227959126397er_rat @ A @ N2 )
% 5.27/5.56 = zero_zero_rat )
% 5.27/5.56 = ( ? [K3: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K3 @ N2 )
% 5.27/5.56 & ( A
% 5.27/5.56 = ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K3 ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_iff
% 5.27/5.56 thf(fact_5962_pochhammer__eq__0__iff,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( ( comm_s7457072308508201937r_real @ A @ N2 )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 = ( ? [K3: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K3 @ N2 )
% 5.27/5.56 & ( A
% 5.27/5.56 = ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K3 ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_eq_0_iff
% 5.27/5.56 thf(fact_5963_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ K )
% 5.27/5.56 != zero_zero_complex ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.27/5.56 thf(fact_5964_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ K )
% 5.27/5.56 != zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.27/5.56 thf(fact_5965_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ K )
% 5.27/5.56 != zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.27/5.56 thf(fact_5966_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ K )
% 5.27/5.56 != zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.27/5.56 thf(fact_5967_pochhammer__of__nat__eq__0__lemma_H,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ K )
% 5.27/5.56 != zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_of_nat_eq_0_lemma'
% 5.27/5.56 thf(fact_5968_pochhammer__product_H,axiom,
% 5.27/5.56 ! [Z: rat,N2: nat,M: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ N2 ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ N2 ) ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product'
% 5.27/5.56 thf(fact_5969_pochhammer__product_H,axiom,
% 5.27/5.56 ! [Z: complex,N2: nat,M: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.56 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ N2 ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ N2 ) ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product'
% 5.27/5.56 thf(fact_5970_pochhammer__product_H,axiom,
% 5.27/5.56 ! [Z: real,N2: nat,M: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ N2 ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ N2 ) ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product'
% 5.27/5.56 thf(fact_5971_pochhammer__product_H,axiom,
% 5.27/5.56 ! [Z: int,N2: nat,M: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ N2 ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ N2 ) ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product'
% 5.27/5.56 thf(fact_5972_pochhammer__product_H,axiom,
% 5.27/5.56 ! [Z: nat,N2: nat,M: nat] :
% 5.27/5.56 ( ( comm_s4663373288045622133er_nat @ Z @ ( plus_plus_nat @ N2 @ M ) )
% 5.27/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ N2 ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ N2 ) ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product'
% 5.27/5.56 thf(fact_5973_binomial__maximum_H,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_maximum'
% 5.27/5.56 thf(fact_5974_binomial__mono,axiom,
% 5.27/5.56 ! [K: nat,K6: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.27/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.27/5.56 => ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_mono
% 5.27/5.56 thf(fact_5975_ln__2__less__1,axiom,
% 5.27/5.56 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.27/5.56
% 5.27/5.56 % ln_2_less_1
% 5.27/5.56 thf(fact_5976_numeral__BitM,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( numeral_numeral_rat @ ( bitM @ N2 ) )
% 5.27/5.56 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N2 ) ) @ one_one_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % numeral_BitM
% 5.27/5.56 thf(fact_5977_numeral__BitM,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( numera6690914467698888265omplex @ ( bitM @ N2 ) )
% 5.27/5.56 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N2 ) ) @ one_one_complex ) ) ).
% 5.27/5.56
% 5.27/5.56 % numeral_BitM
% 5.27/5.56 thf(fact_5978_numeral__BitM,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( numeral_numeral_real @ ( bitM @ N2 ) )
% 5.27/5.56 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N2 ) ) @ one_one_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % numeral_BitM
% 5.27/5.56 thf(fact_5979_numeral__BitM,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( numeral_numeral_int @ ( bitM @ N2 ) )
% 5.27/5.56 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) @ one_one_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % numeral_BitM
% 5.27/5.56 thf(fact_5980_binomial__antimono,axiom,
% 5.27/5.56 ! [K: nat,K6: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ K6 )
% 5.27/5.56 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.27/5.56 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.27/5.56 => ( ord_less_eq_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_antimono
% 5.27/5.56 thf(fact_5981_binomial__maximum,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_maximum
% 5.27/5.56 thf(fact_5982_odd__numeral__BitM,axiom,
% 5.27/5.56 ! [W: num] :
% 5.27/5.56 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % odd_numeral_BitM
% 5.27/5.56 thf(fact_5983_odd__numeral__BitM,axiom,
% 5.27/5.56 ! [W: num] :
% 5.27/5.56 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % odd_numeral_BitM
% 5.27/5.56 thf(fact_5984_odd__numeral__BitM,axiom,
% 5.27/5.56 ! [W: num] :
% 5.27/5.56 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % odd_numeral_BitM
% 5.27/5.56 thf(fact_5985_ln__le__minus__one,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_le_minus_one
% 5.27/5.56 thf(fact_5986_ln__diff__le,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.56 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X4 ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X4 @ Y ) @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_diff_le
% 5.27/5.56 thf(fact_5987_ln__add__one__self__le__self2,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_add_one_self_le_self2
% 5.27/5.56 thf(fact_5988_ln__realpow,axiom,
% 5.27/5.56 ! [X4: real,N2: nat] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ln_ln_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.56 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_realpow
% 5.27/5.56 thf(fact_5989_pochhammer__product,axiom,
% 5.27/5.56 ! [M: nat,N2: nat,Z: rat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( comm_s4028243227959126397er_rat @ Z @ N2 )
% 5.27/5.56 = ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ M ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( semiri681578069525770553at_rat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product
% 5.27/5.56 thf(fact_5990_pochhammer__product,axiom,
% 5.27/5.56 ! [M: nat,N2: nat,Z: complex] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( comm_s2602460028002588243omplex @ Z @ N2 )
% 5.27/5.56 = ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ M ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( semiri8010041392384452111omplex @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product
% 5.27/5.56 thf(fact_5991_pochhammer__product,axiom,
% 5.27/5.56 ! [M: nat,N2: nat,Z: real] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( comm_s7457072308508201937r_real @ Z @ N2 )
% 5.27/5.56 = ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ M ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( semiri5074537144036343181t_real @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product
% 5.27/5.56 thf(fact_5992_pochhammer__product,axiom,
% 5.27/5.56 ! [M: nat,N2: nat,Z: int] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( comm_s4660882817536571857er_int @ Z @ N2 )
% 5.27/5.56 = ( times_times_int @ ( comm_s4660882817536571857er_int @ Z @ M ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product
% 5.27/5.56 thf(fact_5993_pochhammer__product,axiom,
% 5.27/5.56 ! [M: nat,N2: nat,Z: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( comm_s4663373288045622133er_nat @ Z @ N2 )
% 5.27/5.56 = ( times_times_nat @ ( comm_s4663373288045622133er_nat @ Z @ M ) @ ( comm_s4663373288045622133er_nat @ ( plus_plus_nat @ Z @ ( semiri1316708129612266289at_nat @ M ) ) @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_product
% 5.27/5.56 thf(fact_5994_binomial__strict__antimono,axiom,
% 5.27/5.56 ! [K: nat,K6: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.27/5.56 => ( ( ord_less_eq_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.27/5.56 => ( ( ord_less_eq_nat @ K6 @ N2 )
% 5.27/5.56 => ( ord_less_nat @ ( binomial @ N2 @ K6 ) @ ( binomial @ N2 @ K ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_strict_antimono
% 5.27/5.56 thf(fact_5995_binomial__strict__mono,axiom,
% 5.27/5.56 ! [K: nat,K6: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K @ K6 )
% 5.27/5.56 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N2 )
% 5.27/5.56 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ K6 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_strict_mono
% 5.27/5.56 thf(fact_5996_binomial__less__binomial__Suc,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.56 => ( ord_less_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_less_binomial_Suc
% 5.27/5.56 thf(fact_5997_central__binomial__odd,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.56 => ( ( binomial @ N2 @ ( suc @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.56 = ( binomial @ N2 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % central_binomial_odd
% 5.27/5.56 thf(fact_5998_ln__one__minus__pos__upper__bound,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.56 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X4 ) ) @ ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_one_minus_pos_upper_bound
% 5.27/5.56 thf(fact_5999_pochhammer__absorb__comp,axiom,
% 5.27/5.56 ! [R3: complex,K: nat] :
% 5.27/5.56 ( ( times_times_complex @ ( minus_minus_complex @ R3 @ ( semiri8010041392384452111omplex @ K ) ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ R3 ) @ K ) )
% 5.27/5.56 = ( times_times_complex @ R3 @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ R3 ) @ one_one_complex ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_absorb_comp
% 5.27/5.56 thf(fact_6000_pochhammer__absorb__comp,axiom,
% 5.27/5.56 ! [R3: code_integer,K: nat] :
% 5.27/5.56 ( ( times_3573771949741848930nteger @ ( minus_8373710615458151222nteger @ R3 @ ( semiri4939895301339042750nteger @ K ) ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ R3 ) @ K ) )
% 5.27/5.56 = ( times_3573771949741848930nteger @ R3 @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ R3 ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_absorb_comp
% 5.27/5.56 thf(fact_6001_pochhammer__absorb__comp,axiom,
% 5.27/5.56 ! [R3: rat,K: nat] :
% 5.27/5.56 ( ( times_times_rat @ ( minus_minus_rat @ R3 @ ( semiri681578069525770553at_rat @ K ) ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ R3 ) @ K ) )
% 5.27/5.56 = ( times_times_rat @ R3 @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ R3 ) @ one_one_rat ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_absorb_comp
% 5.27/5.56 thf(fact_6002_pochhammer__absorb__comp,axiom,
% 5.27/5.56 ! [R3: real,K: nat] :
% 5.27/5.56 ( ( times_times_real @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ K ) ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ R3 ) @ K ) )
% 5.27/5.56 = ( times_times_real @ R3 @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( uminus_uminus_real @ R3 ) @ one_one_real ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_absorb_comp
% 5.27/5.56 thf(fact_6003_pochhammer__absorb__comp,axiom,
% 5.27/5.56 ! [R3: int,K: nat] :
% 5.27/5.56 ( ( times_times_int @ ( minus_minus_int @ R3 @ ( semiri1314217659103216013at_int @ K ) ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ R3 ) @ K ) )
% 5.27/5.56 = ( times_times_int @ R3 @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( uminus_uminus_int @ R3 ) @ one_one_int ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_absorb_comp
% 5.27/5.56 thf(fact_6004_pochhammer__minus,axiom,
% 5.27/5.56 ! [B: complex,K: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K )
% 5.27/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus
% 5.27/5.56 thf(fact_6005_pochhammer__minus,axiom,
% 5.27/5.56 ! [B: code_integer,K: nat] :
% 5.27/5.56 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K )
% 5.27/5.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus
% 5.27/5.56 thf(fact_6006_pochhammer__minus,axiom,
% 5.27/5.56 ! [B: rat,K: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K )
% 5.27/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus
% 5.27/5.56 thf(fact_6007_pochhammer__minus,axiom,
% 5.27/5.56 ! [B: real,K: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K )
% 5.27/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus
% 5.27/5.56 thf(fact_6008_pochhammer__minus,axiom,
% 5.27/5.56 ! [B: int,K: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K )
% 5.27/5.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus
% 5.27/5.56 thf(fact_6009_pochhammer__minus_H,axiom,
% 5.27/5.56 ! [B: complex,K: nat] :
% 5.27/5.56 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ B @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ K )
% 5.27/5.56 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ B ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus'
% 5.27/5.56 thf(fact_6010_pochhammer__minus_H,axiom,
% 5.27/5.56 ! [B: code_integer,K: nat] :
% 5.27/5.56 ( ( comm_s8582702949713902594nteger @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ B @ ( semiri4939895301339042750nteger @ K ) ) @ one_one_Code_integer ) @ K )
% 5.27/5.56 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ K ) @ ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ B ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus'
% 5.27/5.56 thf(fact_6011_pochhammer__minus_H,axiom,
% 5.27/5.56 ! [B: rat,K: nat] :
% 5.27/5.56 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ ( minus_minus_rat @ B @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ K )
% 5.27/5.56 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ B ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus'
% 5.27/5.56 thf(fact_6012_pochhammer__minus_H,axiom,
% 5.27/5.56 ! [B: real,K: nat] :
% 5.27/5.56 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ ( minus_minus_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ K )
% 5.27/5.56 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ B ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus'
% 5.27/5.56 thf(fact_6013_pochhammer__minus_H,axiom,
% 5.27/5.56 ! [B: int,K: nat] :
% 5.27/5.56 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ ( minus_minus_int @ B @ ( semiri1314217659103216013at_int @ K ) ) @ one_one_int ) @ K )
% 5.27/5.56 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ K ) @ ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ B ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_minus'
% 5.27/5.56 thf(fact_6014_ln__one__plus__pos__lower__bound,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.56 => ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % ln_one_plus_pos_lower_bound
% 5.27/5.56 thf(fact_6015_zero__less__binomial__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) )
% 5.27/5.56 = ( ord_less_eq_nat @ K @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_binomial_iff
% 5.27/5.56 thf(fact_6016_artanh__def,axiom,
% 5.27/5.56 ( artanh_real
% 5.27/5.56 = ( ^ [X: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X ) @ ( minus_minus_real @ one_one_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % artanh_def
% 5.27/5.56 thf(fact_6017_choose__two,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % choose_two
% 5.27/5.56 thf(fact_6018_binomial__n__0,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ N2 @ zero_zero_nat )
% 5.27/5.56 = one_one_nat ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_n_0
% 5.27/5.56 thf(fact_6019_binomial__Suc__Suc,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.27/5.56 = ( plus_plus_nat @ ( binomial @ N2 @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_Suc_Suc
% 5.27/5.56 thf(fact_6020_binomial__eq__0__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ( binomial @ N2 @ K )
% 5.27/5.56 = zero_zero_nat )
% 5.27/5.56 = ( ord_less_nat @ N2 @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_eq_0_iff
% 5.27/5.56 thf(fact_6021_binomial__Suc__n,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ ( suc @ N2 ) @ N2 )
% 5.27/5.56 = ( suc @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_Suc_n
% 5.27/5.56 thf(fact_6022_binomial__n__n,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ N2 @ N2 )
% 5.27/5.56 = one_one_nat ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_n_n
% 5.27/5.56 thf(fact_6023_binomial__0__Suc,axiom,
% 5.27/5.56 ! [K: nat] :
% 5.27/5.56 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.27/5.56 = zero_zero_nat ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_0_Suc
% 5.27/5.56 thf(fact_6024_binomial__1,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = N2 ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_1
% 5.27/5.56 thf(fact_6025_choose__one,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( binomial @ N2 @ one_one_nat )
% 5.27/5.56 = N2 ) ).
% 5.27/5.56
% 5.27/5.56 % choose_one
% 5.27/5.56 thf(fact_6026_binomial__eq__0,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ N2 @ K )
% 5.27/5.56 => ( ( binomial @ N2 @ K )
% 5.27/5.56 = zero_zero_nat ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_eq_0
% 5.27/5.56 thf(fact_6027_Suc__times__binomial,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) )
% 5.27/5.56 = ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % Suc_times_binomial
% 5.27/5.56 thf(fact_6028_Suc__times__binomial__eq,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) )
% 5.27/5.56 = ( times_times_nat @ ( binomial @ ( suc @ N2 ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % Suc_times_binomial_eq
% 5.27/5.56 thf(fact_6029_binomial__symmetric,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ( binomial @ N2 @ K )
% 5.27/5.56 = ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_symmetric
% 5.27/5.56 thf(fact_6030_choose__mult__lemma,axiom,
% 5.27/5.56 ! [M: nat,R3: nat,K: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.27/5.56 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R3 ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R3 ) @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % choose_mult_lemma
% 5.27/5.56 thf(fact_6031_binomial__le__pow,axiom,
% 5.27/5.56 ! [R3: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ R3 @ N2 )
% 5.27/5.56 => ( ord_less_eq_nat @ ( binomial @ N2 @ R3 ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_le_pow
% 5.27/5.56 thf(fact_6032_zero__less__binomial,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N2 @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_binomial
% 5.27/5.56 thf(fact_6033_Suc__times__binomial__add,axiom,
% 5.27/5.56 ! [A: nat,B: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.27/5.56 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % Suc_times_binomial_add
% 5.27/5.56 thf(fact_6034_choose__mult,axiom,
% 5.27/5.56 ! [K: nat,M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.56 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ( times_times_nat @ ( binomial @ N2 @ M ) @ ( binomial @ M @ K ) )
% 5.27/5.56 = ( times_times_nat @ ( binomial @ N2 @ K ) @ ( binomial @ ( minus_minus_nat @ N2 @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % choose_mult
% 5.27/5.56 thf(fact_6035_binomial__Suc__Suc__eq__times,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( binomial @ ( suc @ N2 ) @ ( suc @ K ) )
% 5.27/5.56 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( binomial @ N2 @ K ) ) @ ( suc @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_Suc_Suc_eq_times
% 5.27/5.56 thf(fact_6036_binomial__absorb__comp,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( minus_minus_nat @ N2 @ K ) @ ( binomial @ N2 @ K ) )
% 5.27/5.56 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_absorb_comp
% 5.27/5.56 thf(fact_6037_binomial__absorption,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N2 @ ( suc @ K ) ) )
% 5.27/5.56 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_absorption
% 5.27/5.56 thf(fact_6038_binomial__ge__n__over__k__pow__k,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_ge_n_over_k_pow_k
% 5.27/5.56 thf(fact_6039_binomial__ge__n__over__k__pow__k,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.56 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_ge_n_over_k_pow_k
% 5.27/5.56 thf(fact_6040_binomial__le__pow2,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N2 @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_le_pow2
% 5.27/5.56 thf(fact_6041_choose__reduce__nat,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.56 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.56 => ( ( binomial @ N2 @ K )
% 5.27/5.56 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % choose_reduce_nat
% 5.27/5.56 thf(fact_6042_times__binomial__minus1__eq,axiom,
% 5.27/5.56 ! [K: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.56 => ( ( times_times_nat @ K @ ( binomial @ N2 @ K ) )
% 5.27/5.56 = ( times_times_nat @ N2 @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % times_binomial_minus1_eq
% 5.27/5.56 thf(fact_6043_binomial__addition__formula,axiom,
% 5.27/5.56 ! [N2: nat,K: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.56 => ( ( binomial @ N2 @ ( suc @ K ) )
% 5.27/5.56 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N2 @ one_one_nat ) @ K ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % binomial_addition_formula
% 5.27/5.56 thf(fact_6044_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.56 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.27/5.56 thf(fact_6045_tanh__ln__real,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( tanh_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.56 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_ln_real
% 5.27/5.56 thf(fact_6046_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ln_one_plus_x_minus_x_bound
% 5.27/5.56 thf(fact_6047_signed__take__bit__eq__take__bit__minus,axiom,
% 5.27/5.56 ( bit_ri631733984087533419it_int
% 5.27/5.56 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K3 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % signed_take_bit_eq_take_bit_minus
% 5.27/5.56 thf(fact_6048_fact__double,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri773545260158071498ct_rat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.56 = ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_double
% 5.27/5.56 thf(fact_6049_fact__double,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.56 = ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_double
% 5.27/5.56 thf(fact_6050_fact__double,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.56 = ( times_times_real @ ( times_times_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_double
% 5.27/5.56 thf(fact_6051_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X4 ) ) @ X4 ) ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.27/5.56 thf(fact_6052_abs__abs,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.27/5.56 = ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_abs
% 5.27/5.56 thf(fact_6053_abs__abs,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.27/5.56 = ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_abs
% 5.27/5.56 thf(fact_6054_abs__abs,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_abs
% 5.27/5.56 thf(fact_6055_abs__abs,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.27/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_abs
% 5.27/5.56 thf(fact_6056_abs__idempotent,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.27/5.56 = ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_idempotent
% 5.27/5.56 thf(fact_6057_abs__idempotent,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.27/5.56 = ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_idempotent
% 5.27/5.56 thf(fact_6058_abs__idempotent,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_idempotent
% 5.27/5.56 thf(fact_6059_abs__idempotent,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.27/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_idempotent
% 5.27/5.56 thf(fact_6060_abs__0,axiom,
% 5.27/5.56 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.27/5.56 = zero_z3403309356797280102nteger ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0
% 5.27/5.56 thf(fact_6061_abs__0,axiom,
% 5.27/5.56 ( ( abs_abs_complex @ zero_zero_complex )
% 5.27/5.56 = zero_zero_complex ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0
% 5.27/5.56 thf(fact_6062_abs__0,axiom,
% 5.27/5.56 ( ( abs_abs_real @ zero_zero_real )
% 5.27/5.56 = zero_zero_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0
% 5.27/5.56 thf(fact_6063_abs__0,axiom,
% 5.27/5.56 ( ( abs_abs_rat @ zero_zero_rat )
% 5.27/5.56 = zero_zero_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0
% 5.27/5.56 thf(fact_6064_abs__0,axiom,
% 5.27/5.56 ( ( abs_abs_int @ zero_zero_int )
% 5.27/5.56 = zero_zero_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0
% 5.27/5.56 thf(fact_6065_abs__0__eq,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( zero_z3403309356797280102nteger
% 5.27/5.56 = ( abs_abs_Code_integer @ A ) )
% 5.27/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0_eq
% 5.27/5.56 thf(fact_6066_abs__0__eq,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( zero_zero_real
% 5.27/5.56 = ( abs_abs_real @ A ) )
% 5.27/5.56 = ( A = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0_eq
% 5.27/5.56 thf(fact_6067_abs__0__eq,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( zero_zero_rat
% 5.27/5.56 = ( abs_abs_rat @ A ) )
% 5.27/5.56 = ( A = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0_eq
% 5.27/5.56 thf(fact_6068_abs__0__eq,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( zero_zero_int
% 5.27/5.56 = ( abs_abs_int @ A ) )
% 5.27/5.56 = ( A = zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_0_eq
% 5.27/5.56 thf(fact_6069_abs__eq__0,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ( abs_abs_Code_integer @ A )
% 5.27/5.56 = zero_z3403309356797280102nteger )
% 5.27/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0
% 5.27/5.56 thf(fact_6070_abs__eq__0,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ( abs_abs_real @ A )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 = ( A = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0
% 5.27/5.56 thf(fact_6071_abs__eq__0,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ( abs_abs_rat @ A )
% 5.27/5.56 = zero_zero_rat )
% 5.27/5.56 = ( A = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0
% 5.27/5.56 thf(fact_6072_abs__eq__0,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ( abs_abs_int @ A )
% 5.27/5.56 = zero_zero_int )
% 5.27/5.56 = ( A = zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0
% 5.27/5.56 thf(fact_6073_abs__zero,axiom,
% 5.27/5.56 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.27/5.56 = zero_z3403309356797280102nteger ) ).
% 5.27/5.56
% 5.27/5.56 % abs_zero
% 5.27/5.56 thf(fact_6074_abs__zero,axiom,
% 5.27/5.56 ( ( abs_abs_real @ zero_zero_real )
% 5.27/5.56 = zero_zero_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_zero
% 5.27/5.56 thf(fact_6075_abs__zero,axiom,
% 5.27/5.56 ( ( abs_abs_rat @ zero_zero_rat )
% 5.27/5.56 = zero_zero_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_zero
% 5.27/5.56 thf(fact_6076_abs__zero,axiom,
% 5.27/5.56 ( ( abs_abs_int @ zero_zero_int )
% 5.27/5.56 = zero_zero_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_zero
% 5.27/5.56 thf(fact_6077_abs__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N2 ) )
% 5.27/5.56 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_numeral
% 5.27/5.56 thf(fact_6078_abs__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.56 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_numeral
% 5.27/5.56 thf(fact_6079_abs__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_real @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.56 = ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_numeral
% 5.27/5.56 thf(fact_6080_abs__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_int @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.56 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_numeral
% 5.27/5.56 thf(fact_6081_abs__mult__self__eq,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.56 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_self_eq
% 5.27/5.56 thf(fact_6082_abs__mult__self__eq,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.27/5.56 = ( times_times_rat @ A @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_self_eq
% 5.27/5.56 thf(fact_6083_abs__mult__self__eq,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.27/5.56 = ( times_times_real @ A @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_self_eq
% 5.27/5.56 thf(fact_6084_abs__mult__self__eq,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.27/5.56 = ( times_times_int @ A @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_self_eq
% 5.27/5.56 thf(fact_6085_abs__1,axiom,
% 5.27/5.56 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.27/5.56 = one_one_Code_integer ) ).
% 5.27/5.56
% 5.27/5.56 % abs_1
% 5.27/5.56 thf(fact_6086_abs__1,axiom,
% 5.27/5.56 ( ( abs_abs_complex @ one_one_complex )
% 5.27/5.56 = one_one_complex ) ).
% 5.27/5.56
% 5.27/5.56 % abs_1
% 5.27/5.56 thf(fact_6087_abs__1,axiom,
% 5.27/5.56 ( ( abs_abs_real @ one_one_real )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_1
% 5.27/5.56 thf(fact_6088_abs__1,axiom,
% 5.27/5.56 ( ( abs_abs_rat @ one_one_rat )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_1
% 5.27/5.56 thf(fact_6089_abs__1,axiom,
% 5.27/5.56 ( ( abs_abs_int @ one_one_int )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_1
% 5.27/5.56 thf(fact_6090_abs__add__abs,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.27/5.56 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_add_abs
% 5.27/5.56 thf(fact_6091_abs__add__abs,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.27/5.56 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_add_abs
% 5.27/5.56 thf(fact_6092_abs__add__abs,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.27/5.56 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_add_abs
% 5.27/5.56 thf(fact_6093_abs__add__abs,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.27/5.56 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_add_abs
% 5.27/5.56 thf(fact_6094_abs__divide,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.56 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_divide
% 5.27/5.56 thf(fact_6095_abs__divide,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.56 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_divide
% 5.27/5.56 thf(fact_6096_abs__divide,axiom,
% 5.27/5.56 ! [A: complex,B: complex] :
% 5.27/5.56 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.56 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_divide
% 5.27/5.56 thf(fact_6097_abs__minus,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.56 = ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus
% 5.27/5.56 thf(fact_6098_abs__minus,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.56 = ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus
% 5.27/5.56 thf(fact_6099_abs__minus,axiom,
% 5.27/5.56 ! [A: complex] :
% 5.27/5.56 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.56 = ( abs_abs_complex @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus
% 5.27/5.56 thf(fact_6100_abs__minus,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus
% 5.27/5.56 thf(fact_6101_abs__minus,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus
% 5.27/5.56 thf(fact_6102_abs__minus__cancel,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.56 = ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_cancel
% 5.27/5.56 thf(fact_6103_abs__minus__cancel,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.56 = ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_cancel
% 5.27/5.56 thf(fact_6104_abs__minus__cancel,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_cancel
% 5.27/5.56 thf(fact_6105_abs__minus__cancel,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.56 = ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_cancel
% 5.27/5.56 thf(fact_6106_abs__dvd__iff,axiom,
% 5.27/5.56 ! [M: real,K: real] :
% 5.27/5.56 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.27/5.56 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_dvd_iff
% 5.27/5.56 thf(fact_6107_abs__dvd__iff,axiom,
% 5.27/5.56 ! [M: int,K: int] :
% 5.27/5.56 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.27/5.56 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_dvd_iff
% 5.27/5.56 thf(fact_6108_abs__dvd__iff,axiom,
% 5.27/5.56 ! [M: code_integer,K: code_integer] :
% 5.27/5.56 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.27/5.56 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_dvd_iff
% 5.27/5.56 thf(fact_6109_abs__dvd__iff,axiom,
% 5.27/5.56 ! [M: rat,K: rat] :
% 5.27/5.56 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.27/5.56 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_dvd_iff
% 5.27/5.56 thf(fact_6110_dvd__abs__iff,axiom,
% 5.27/5.56 ! [M: real,K: real] :
% 5.27/5.56 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.27/5.56 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_abs_iff
% 5.27/5.56 thf(fact_6111_dvd__abs__iff,axiom,
% 5.27/5.56 ! [M: int,K: int] :
% 5.27/5.56 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.27/5.56 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_abs_iff
% 5.27/5.56 thf(fact_6112_dvd__abs__iff,axiom,
% 5.27/5.56 ! [M: code_integer,K: code_integer] :
% 5.27/5.56 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.27/5.56 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_abs_iff
% 5.27/5.56 thf(fact_6113_dvd__abs__iff,axiom,
% 5.27/5.56 ! [M: rat,K: rat] :
% 5.27/5.56 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.27/5.56 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_abs_iff
% 5.27/5.56 thf(fact_6114_abs__of__nat,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.27/5.56 = ( semiri4939895301339042750nteger @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nat
% 5.27/5.56 thf(fact_6115_abs__of__nat,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.56 = ( semiri681578069525770553at_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nat
% 5.27/5.56 thf(fact_6116_abs__of__nat,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.56 = ( semiri5074537144036343181t_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nat
% 5.27/5.56 thf(fact_6117_abs__of__nat,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.56 = ( semiri1314217659103216013at_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nat
% 5.27/5.56 thf(fact_6118_abs__bool__eq,axiom,
% 5.27/5.56 ! [P: $o] :
% 5.27/5.56 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.27/5.56 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_bool_eq
% 5.27/5.56 thf(fact_6119_abs__bool__eq,axiom,
% 5.27/5.56 ! [P: $o] :
% 5.27/5.56 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.27/5.56 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_bool_eq
% 5.27/5.56 thf(fact_6120_abs__bool__eq,axiom,
% 5.27/5.56 ! [P: $o] :
% 5.27/5.56 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.27/5.56 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_bool_eq
% 5.27/5.56 thf(fact_6121_abs__bool__eq,axiom,
% 5.27/5.56 ! [P: $o] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.27/5.56 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_bool_eq
% 5.27/5.56 thf(fact_6122_tanh__real__less__iff,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 5.27/5.56 = ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_less_iff
% 5.27/5.56 thf(fact_6123_tanh__real__le__iff,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) )
% 5.27/5.56 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_le_iff
% 5.27/5.56 thf(fact_6124_abs__le__zero__iff,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.27/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_zero_iff
% 5.27/5.56 thf(fact_6125_abs__le__zero__iff,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.27/5.56 = ( A = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_zero_iff
% 5.27/5.56 thf(fact_6126_abs__le__zero__iff,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.27/5.56 = ( A = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_zero_iff
% 5.27/5.56 thf(fact_6127_abs__le__zero__iff,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.27/5.56 = ( A = zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_zero_iff
% 5.27/5.56 thf(fact_6128_abs__le__self__iff,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.27/5.56 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_self_iff
% 5.27/5.56 thf(fact_6129_abs__le__self__iff,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.27/5.56 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_self_iff
% 5.27/5.56 thf(fact_6130_abs__le__self__iff,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.27/5.56 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_self_iff
% 5.27/5.56 thf(fact_6131_abs__le__self__iff,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.27/5.56 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_self_iff
% 5.27/5.56 thf(fact_6132_abs__of__nonneg,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonneg
% 5.27/5.56 thf(fact_6133_abs__of__nonneg,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.56 => ( ( abs_abs_real @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonneg
% 5.27/5.56 thf(fact_6134_abs__of__nonneg,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.56 => ( ( abs_abs_rat @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonneg
% 5.27/5.56 thf(fact_6135_abs__of__nonneg,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.27/5.56 => ( ( abs_abs_int @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonneg
% 5.27/5.56 thf(fact_6136_zero__less__abs__iff,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.56 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_abs_iff
% 5.27/5.56 thf(fact_6137_zero__less__abs__iff,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.27/5.56 = ( A != zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_abs_iff
% 5.27/5.56 thf(fact_6138_zero__less__abs__iff,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.27/5.56 = ( A != zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_abs_iff
% 5.27/5.56 thf(fact_6139_zero__less__abs__iff,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.27/5.56 = ( A != zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_abs_iff
% 5.27/5.56 thf(fact_6140_abs__neg__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.56 = ( numeral_numeral_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_numeral
% 5.27/5.56 thf(fact_6141_abs__neg__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.56 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_numeral
% 5.27/5.56 thf(fact_6142_abs__neg__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.56 = ( numera6620942414471956472nteger @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_numeral
% 5.27/5.56 thf(fact_6143_abs__neg__numeral,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.56 = ( numeral_numeral_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_numeral
% 5.27/5.56 thf(fact_6144_abs__neg__one,axiom,
% 5.27/5.56 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_one
% 5.27/5.56 thf(fact_6145_abs__neg__one,axiom,
% 5.27/5.56 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_one
% 5.27/5.56 thf(fact_6146_abs__neg__one,axiom,
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.56 = one_one_Code_integer ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_one
% 5.27/5.56 thf(fact_6147_abs__neg__one,axiom,
% 5.27/5.56 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_neg_one
% 5.27/5.56 thf(fact_6148_abs__power__minus,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N2 ) )
% 5.27/5.56 = ( abs_abs_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power_minus
% 5.27/5.56 thf(fact_6149_abs__power__minus,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N2 ) )
% 5.27/5.56 = ( abs_abs_int @ ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power_minus
% 5.27/5.56 thf(fact_6150_abs__power__minus,axiom,
% 5.27/5.56 ! [A: code_integer,N2: nat] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N2 ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power_minus
% 5.27/5.56 thf(fact_6151_abs__power__minus,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N2 ) )
% 5.27/5.56 = ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power_minus
% 5.27/5.56 thf(fact_6152_fact__0,axiom,
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ zero_zero_nat )
% 5.27/5.56 = one_one_complex ) ).
% 5.27/5.56
% 5.27/5.56 % fact_0
% 5.27/5.56 thf(fact_6153_fact__0,axiom,
% 5.27/5.56 ( ( semiri773545260158071498ct_rat @ zero_zero_nat )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_0
% 5.27/5.56 thf(fact_6154_fact__0,axiom,
% 5.27/5.56 ( ( semiri1406184849735516958ct_int @ zero_zero_nat )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % fact_0
% 5.27/5.56 thf(fact_6155_fact__0,axiom,
% 5.27/5.56 ( ( semiri1408675320244567234ct_nat @ zero_zero_nat )
% 5.27/5.56 = one_one_nat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_0
% 5.27/5.56 thf(fact_6156_fact__0,axiom,
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ zero_zero_nat )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % fact_0
% 5.27/5.56 thf(fact_6157_fact__1,axiom,
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ one_one_nat )
% 5.27/5.56 = one_one_complex ) ).
% 5.27/5.56
% 5.27/5.56 % fact_1
% 5.27/5.56 thf(fact_6158_fact__1,axiom,
% 5.27/5.56 ( ( semiri773545260158071498ct_rat @ one_one_nat )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_1
% 5.27/5.56 thf(fact_6159_fact__1,axiom,
% 5.27/5.56 ( ( semiri1406184849735516958ct_int @ one_one_nat )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % fact_1
% 5.27/5.56 thf(fact_6160_fact__1,axiom,
% 5.27/5.56 ( ( semiri1408675320244567234ct_nat @ one_one_nat )
% 5.27/5.56 = one_one_nat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_1
% 5.27/5.56 thf(fact_6161_fact__1,axiom,
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ one_one_nat )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % fact_1
% 5.27/5.56 thf(fact_6162_tanh__real__neg__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 5.27/5.56 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_neg_iff
% 5.27/5.56 thf(fact_6163_tanh__real__pos__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 5.27/5.56 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_pos_iff
% 5.27/5.56 thf(fact_6164_tanh__real__nonneg__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X4 ) )
% 5.27/5.56 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_nonneg_iff
% 5.27/5.56 thf(fact_6165_tanh__real__nonpos__iff,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( tanh_real @ X4 ) @ zero_zero_real )
% 5.27/5.56 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_nonpos_iff
% 5.27/5.56 thf(fact_6166_divide__le__0__abs__iff,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.27/5.56 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.56 | ( B = zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % divide_le_0_abs_iff
% 5.27/5.56 thf(fact_6167_divide__le__0__abs__iff,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.27/5.56 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.27/5.56 | ( B = zero_zero_rat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % divide_le_0_abs_iff
% 5.27/5.56 thf(fact_6168_zero__le__divide__abs__iff,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.27/5.56 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.56 | ( B = zero_zero_real ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_le_divide_abs_iff
% 5.27/5.56 thf(fact_6169_zero__le__divide__abs__iff,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.27/5.56 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.56 | ( B = zero_zero_rat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_le_divide_abs_iff
% 5.27/5.56 thf(fact_6170_abs__of__nonpos,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.56 => ( ( abs_abs_real @ A )
% 5.27/5.56 = ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonpos
% 5.27/5.56 thf(fact_6171_abs__of__nonpos,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.27/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.27/5.56 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonpos
% 5.27/5.56 thf(fact_6172_abs__of__nonpos,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.27/5.56 => ( ( abs_abs_rat @ A )
% 5.27/5.56 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonpos
% 5.27/5.56 thf(fact_6173_abs__of__nonpos,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.27/5.56 => ( ( abs_abs_int @ A )
% 5.27/5.56 = ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_nonpos
% 5.27/5.56 thf(fact_6174_bit__numeral__Bit0__Suc__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_Bit0_Suc_iff
% 5.27/5.56 thf(fact_6175_bit__numeral__Bit0__Suc__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_Bit0_Suc_iff
% 5.27/5.56 thf(fact_6176_fact__Suc__0,axiom,
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = one_one_complex ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc_0
% 5.27/5.56 thf(fact_6177_fact__Suc__0,axiom,
% 5.27/5.56 ( ( semiri773545260158071498ct_rat @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc_0
% 5.27/5.56 thf(fact_6178_fact__Suc__0,axiom,
% 5.27/5.56 ( ( semiri1406184849735516958ct_int @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc_0
% 5.27/5.56 thf(fact_6179_fact__Suc__0,axiom,
% 5.27/5.56 ( ( semiri1408675320244567234ct_nat @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = one_one_nat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc_0
% 5.27/5.56 thf(fact_6180_fact__Suc__0,axiom,
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ ( suc @ zero_zero_nat ) )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc_0
% 5.27/5.56 thf(fact_6181_bit__numeral__Bit1__Suc__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_Bit1_Suc_iff
% 5.27/5.56 thf(fact_6182_bit__numeral__Bit1__Suc__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_Bit1_Suc_iff
% 5.27/5.56 thf(fact_6183_fact__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N2 ) ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc
% 5.27/5.56 thf(fact_6184_fact__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri1406184849735516958ct_int @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc
% 5.27/5.56 thf(fact_6185_fact__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri1408675320244567234ct_nat @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( suc @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc
% 5.27/5.56 thf(fact_6186_fact__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ ( suc @ N2 ) )
% 5.27/5.56 = ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_Suc
% 5.27/5.56 thf(fact_6187_artanh__minus__real,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.56 => ( ( artanh_real @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.56 = ( uminus_uminus_real @ ( artanh_real @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % artanh_minus_real
% 5.27/5.56 thf(fact_6188_signed__take__bit__nonnegative__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) )
% 5.27/5.56 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % signed_take_bit_nonnegative_iff
% 5.27/5.56 thf(fact_6189_signed__take__bit__negative__iff,axiom,
% 5.27/5.56 ! [N2: nat,K: int] :
% 5.27/5.56 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ K @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % signed_take_bit_negative_iff
% 5.27/5.56 thf(fact_6190_zero__less__power__abs__iff,axiom,
% 5.27/5.56 ! [A: code_integer,N2: nat] :
% 5.27/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) )
% 5.27/5.56 = ( ( A != zero_z3403309356797280102nteger )
% 5.27/5.56 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_power_abs_iff
% 5.27/5.56 thf(fact_6191_zero__less__power__abs__iff,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.27/5.56 = ( ( A != zero_zero_real )
% 5.27/5.56 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_power_abs_iff
% 5.27/5.56 thf(fact_6192_zero__less__power__abs__iff,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) )
% 5.27/5.56 = ( ( A != zero_zero_rat )
% 5.27/5.56 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_power_abs_iff
% 5.27/5.56 thf(fact_6193_zero__less__power__abs__iff,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) )
% 5.27/5.56 = ( ( A != zero_zero_int )
% 5.27/5.56 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % zero_less_power_abs_iff
% 5.27/5.56 thf(fact_6194_power2__abs,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power2_abs
% 5.27/5.56 thf(fact_6195_power2__abs,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power2_abs
% 5.27/5.56 thf(fact_6196_power2__abs,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power2_abs
% 5.27/5.56 thf(fact_6197_power2__abs,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power2_abs
% 5.27/5.56 thf(fact_6198_abs__power2,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power2
% 5.27/5.56 thf(fact_6199_abs__power2,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.56 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power2
% 5.27/5.56 thf(fact_6200_abs__power2,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power2
% 5.27/5.56 thf(fact_6201_abs__power2,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_power2
% 5.27/5.56 thf(fact_6202_fact__2,axiom,
% 5.27/5.56 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_2
% 5.27/5.56 thf(fact_6203_fact__2,axiom,
% 5.27/5.56 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_2
% 5.27/5.56 thf(fact_6204_fact__2,axiom,
% 5.27/5.56 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_2
% 5.27/5.56 thf(fact_6205_fact__2,axiom,
% 5.27/5.56 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_2
% 5.27/5.56 thf(fact_6206_fact__2,axiom,
% 5.27/5.56 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.56 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_2
% 5.27/5.56 thf(fact_6207_bit__numeral__simps_I2_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(2)
% 5.27/5.56 thf(fact_6208_bit__numeral__simps_I2_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit0 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(2)
% 5.27/5.56 thf(fact_6209_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.27/5.56 ! [W: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_minus_numeral_Bit0_Suc_iff
% 5.27/5.56 thf(fact_6210_bit__numeral__simps_I3_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(3)
% 5.27/5.56 thf(fact_6211_bit__numeral__simps_I3_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ ( bit1 @ W ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ W ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(3)
% 5.27/5.56 thf(fact_6212_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.27/5.56 ! [W: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N2 ) )
% 5.27/5.56 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_minus_numeral_Bit1_Suc_iff
% 5.27/5.56 thf(fact_6213_bit__0,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( bit_se9216721137139052372nteger @ A @ zero_zero_nat )
% 5.27/5.56 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_0
% 5.27/5.56 thf(fact_6214_bit__0,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ A @ zero_zero_nat )
% 5.27/5.56 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_0
% 5.27/5.56 thf(fact_6215_bit__0,axiom,
% 5.27/5.56 ! [A: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ A @ zero_zero_nat )
% 5.27/5.56 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_0
% 5.27/5.56 thf(fact_6216_power__even__abs__numeral,axiom,
% 5.27/5.56 ! [W: num,A: code_integer] :
% 5.27/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_even_abs_numeral
% 5.27/5.56 thf(fact_6217_power__even__abs__numeral,axiom,
% 5.27/5.56 ! [W: num,A: rat] :
% 5.27/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_even_abs_numeral
% 5.27/5.56 thf(fact_6218_power__even__abs__numeral,axiom,
% 5.27/5.56 ! [W: num,A: real] :
% 5.27/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_even_abs_numeral
% 5.27/5.56 thf(fact_6219_power__even__abs__numeral,axiom,
% 5.27/5.56 ! [W: num,A: int] :
% 5.27/5.56 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.27/5.56 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_even_abs_numeral
% 5.27/5.56 thf(fact_6220_bit__minus__numeral__int_I1_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_minus_numeral_int(1)
% 5.27/5.56 thf(fact_6221_bit__minus__numeral__int_I2_J,axiom,
% 5.27/5.56 ! [W: num,N2: num] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.56 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_minus_numeral_int(2)
% 5.27/5.56 thf(fact_6222_bit__mod__2__iff,axiom,
% 5.27/5.56 ! [A: code_integer,N2: nat] :
% 5.27/5.56 ( ( bit_se9216721137139052372nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 )
% 5.27/5.56 = ( ( N2 = zero_zero_nat )
% 5.27/5.56 & ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_mod_2_iff
% 5.27/5.56 thf(fact_6223_bit__mod__2__iff,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 )
% 5.27/5.56 = ( ( N2 = zero_zero_nat )
% 5.27/5.56 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_mod_2_iff
% 5.27/5.56 thf(fact_6224_bit__mod__2__iff,axiom,
% 5.27/5.56 ! [A: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 )
% 5.27/5.56 = ( ( N2 = zero_zero_nat )
% 5.27/5.56 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_mod_2_iff
% 5.27/5.56 thf(fact_6225_bit__numeral__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ M ) @ N2 )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_iff
% 5.27/5.56 thf(fact_6226_bit__numeral__iff,axiom,
% 5.27/5.56 ! [M: num,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ ( numeral_numeral_nat @ M ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_iff
% 5.27/5.56 thf(fact_6227_bit__of__nat__iff__bit,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( semiri1314217659103216013at_int @ M ) @ N2 )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_of_nat_iff_bit
% 5.27/5.56 thf(fact_6228_bit__of__nat__iff__bit,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( semiri1316708129612266289at_nat @ M ) @ N2 )
% 5.27/5.56 = ( bit_se1148574629649215175it_nat @ M @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_of_nat_iff_bit
% 5.27/5.56 thf(fact_6229_bit__disjunctive__add__iff,axiom,
% 5.27/5.56 ! [A: int,B: int,N2: nat] :
% 5.27/5.56 ( ! [N3: nat] :
% 5.27/5.56 ( ~ ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.27/5.56 | ~ ( bit_se1146084159140164899it_int @ B @ N3 ) )
% 5.27/5.56 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.27/5.56 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.56 | ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_disjunctive_add_iff
% 5.27/5.56 thf(fact_6230_bit__disjunctive__add__iff,axiom,
% 5.27/5.56 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.56 ( ! [N3: nat] :
% 5.27/5.56 ( ~ ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.27/5.56 | ~ ( bit_se1148574629649215175it_nat @ B @ N3 ) )
% 5.27/5.56 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.27/5.56 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.56 | ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_disjunctive_add_iff
% 5.27/5.56 thf(fact_6231_abs__ge__self,axiom,
% 5.27/5.56 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_self
% 5.27/5.56 thf(fact_6232_abs__ge__self,axiom,
% 5.27/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_self
% 5.27/5.56 thf(fact_6233_abs__ge__self,axiom,
% 5.27/5.56 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_self
% 5.27/5.56 thf(fact_6234_abs__ge__self,axiom,
% 5.27/5.56 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_self
% 5.27/5.56 thf(fact_6235_abs__le__D1,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D1
% 5.27/5.56 thf(fact_6236_abs__le__D1,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.27/5.56 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D1
% 5.27/5.56 thf(fact_6237_abs__le__D1,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D1
% 5.27/5.56 thf(fact_6238_abs__le__D1,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D1
% 5.27/5.56 thf(fact_6239_abs__eq__0__iff,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ( abs_abs_Code_integer @ A )
% 5.27/5.56 = zero_z3403309356797280102nteger )
% 5.27/5.56 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0_iff
% 5.27/5.56 thf(fact_6240_abs__eq__0__iff,axiom,
% 5.27/5.56 ! [A: complex] :
% 5.27/5.56 ( ( ( abs_abs_complex @ A )
% 5.27/5.56 = zero_zero_complex )
% 5.27/5.56 = ( A = zero_zero_complex ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0_iff
% 5.27/5.56 thf(fact_6241_abs__eq__0__iff,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ( abs_abs_real @ A )
% 5.27/5.56 = zero_zero_real )
% 5.27/5.56 = ( A = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0_iff
% 5.27/5.56 thf(fact_6242_abs__eq__0__iff,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ( abs_abs_rat @ A )
% 5.27/5.56 = zero_zero_rat )
% 5.27/5.56 = ( A = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0_iff
% 5.27/5.56 thf(fact_6243_abs__eq__0__iff,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ( abs_abs_int @ A )
% 5.27/5.56 = zero_zero_int )
% 5.27/5.56 = ( A = zero_zero_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_0_iff
% 5.27/5.56 thf(fact_6244_abs__mult,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.27/5.56 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult
% 5.27/5.56 thf(fact_6245_abs__mult,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.56 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult
% 5.27/5.56 thf(fact_6246_abs__mult,axiom,
% 5.27/5.56 ! [A: complex,B: complex] :
% 5.27/5.56 ( ( abs_abs_complex @ ( times_times_complex @ A @ B ) )
% 5.27/5.56 = ( times_times_complex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult
% 5.27/5.56 thf(fact_6247_abs__mult,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.27/5.56 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult
% 5.27/5.56 thf(fact_6248_abs__mult,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.27/5.56 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult
% 5.27/5.56 thf(fact_6249_abs__one,axiom,
% 5.27/5.56 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.27/5.56 = one_one_Code_integer ) ).
% 5.27/5.56
% 5.27/5.56 % abs_one
% 5.27/5.56 thf(fact_6250_abs__one,axiom,
% 5.27/5.56 ( ( abs_abs_real @ one_one_real )
% 5.27/5.56 = one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_one
% 5.27/5.56 thf(fact_6251_abs__one,axiom,
% 5.27/5.56 ( ( abs_abs_rat @ one_one_rat )
% 5.27/5.56 = one_one_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_one
% 5.27/5.56 thf(fact_6252_abs__one,axiom,
% 5.27/5.56 ( ( abs_abs_int @ one_one_int )
% 5.27/5.56 = one_one_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_one
% 5.27/5.56 thf(fact_6253_abs__minus__commute,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.27/5.56 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_commute
% 5.27/5.56 thf(fact_6254_abs__minus__commute,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.27/5.56 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_commute
% 5.27/5.56 thf(fact_6255_abs__minus__commute,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.27/5.56 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_commute
% 5.27/5.56 thf(fact_6256_abs__minus__commute,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.27/5.56 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_minus_commute
% 5.27/5.56 thf(fact_6257_abs__eq__iff,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ( abs_abs_real @ X4 )
% 5.27/5.56 = ( abs_abs_real @ Y ) )
% 5.27/5.56 = ( ( X4 = Y )
% 5.27/5.56 | ( X4
% 5.27/5.56 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_iff
% 5.27/5.56 thf(fact_6258_abs__eq__iff,axiom,
% 5.27/5.56 ! [X4: int,Y: int] :
% 5.27/5.56 ( ( ( abs_abs_int @ X4 )
% 5.27/5.56 = ( abs_abs_int @ Y ) )
% 5.27/5.56 = ( ( X4 = Y )
% 5.27/5.56 | ( X4
% 5.27/5.56 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_iff
% 5.27/5.56 thf(fact_6259_abs__eq__iff,axiom,
% 5.27/5.56 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.56 ( ( ( abs_abs_Code_integer @ X4 )
% 5.27/5.56 = ( abs_abs_Code_integer @ Y ) )
% 5.27/5.56 = ( ( X4 = Y )
% 5.27/5.56 | ( X4
% 5.27/5.56 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_iff
% 5.27/5.56 thf(fact_6260_abs__eq__iff,axiom,
% 5.27/5.56 ! [X4: rat,Y: rat] :
% 5.27/5.56 ( ( ( abs_abs_rat @ X4 )
% 5.27/5.56 = ( abs_abs_rat @ Y ) )
% 5.27/5.56 = ( ( X4 = Y )
% 5.27/5.56 | ( X4
% 5.27/5.56 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_iff
% 5.27/5.56 thf(fact_6261_fact__ge__self,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_self
% 5.27/5.56 thf(fact_6262_fact__mono__nat,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_mono_nat
% 5.27/5.56 thf(fact_6263_power__abs,axiom,
% 5.27/5.56 ! [A: code_integer,N2: nat] :
% 5.27/5.56 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.27/5.56 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_abs
% 5.27/5.56 thf(fact_6264_power__abs,axiom,
% 5.27/5.56 ! [A: rat,N2: nat] :
% 5.27/5.56 ( ( abs_abs_rat @ ( power_power_rat @ A @ N2 ) )
% 5.27/5.56 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_abs
% 5.27/5.56 thf(fact_6265_power__abs,axiom,
% 5.27/5.56 ! [A: real,N2: nat] :
% 5.27/5.56 ( ( abs_abs_real @ ( power_power_real @ A @ N2 ) )
% 5.27/5.56 = ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_abs
% 5.27/5.56 thf(fact_6266_power__abs,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ( abs_abs_int @ ( power_power_int @ A @ N2 ) )
% 5.27/5.56 = ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % power_abs
% 5.27/5.56 thf(fact_6267_dvd__if__abs__eq,axiom,
% 5.27/5.56 ! [L: real,K: real] :
% 5.27/5.56 ( ( ( abs_abs_real @ L )
% 5.27/5.56 = ( abs_abs_real @ K ) )
% 5.27/5.56 => ( dvd_dvd_real @ L @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_if_abs_eq
% 5.27/5.56 thf(fact_6268_dvd__if__abs__eq,axiom,
% 5.27/5.56 ! [L: int,K: int] :
% 5.27/5.56 ( ( ( abs_abs_int @ L )
% 5.27/5.56 = ( abs_abs_int @ K ) )
% 5.27/5.56 => ( dvd_dvd_int @ L @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_if_abs_eq
% 5.27/5.56 thf(fact_6269_dvd__if__abs__eq,axiom,
% 5.27/5.56 ! [L: code_integer,K: code_integer] :
% 5.27/5.56 ( ( ( abs_abs_Code_integer @ L )
% 5.27/5.56 = ( abs_abs_Code_integer @ K ) )
% 5.27/5.56 => ( dvd_dvd_Code_integer @ L @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_if_abs_eq
% 5.27/5.56 thf(fact_6270_dvd__if__abs__eq,axiom,
% 5.27/5.56 ! [L: rat,K: rat] :
% 5.27/5.56 ( ( ( abs_abs_rat @ L )
% 5.27/5.56 = ( abs_abs_rat @ K ) )
% 5.27/5.56 => ( dvd_dvd_rat @ L @ K ) ) ).
% 5.27/5.56
% 5.27/5.56 % dvd_if_abs_eq
% 5.27/5.56 thf(fact_6271_bit__xor__iff,axiom,
% 5.27/5.56 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( bit_se6528837805403552850or_nat @ A @ B ) @ N2 )
% 5.27/5.56 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.56 != ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_xor_iff
% 5.27/5.56 thf(fact_6272_bit__xor__iff,axiom,
% 5.27/5.56 ! [A: int,B: int,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ A @ B ) @ N2 )
% 5.27/5.56 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.56 != ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_xor_iff
% 5.27/5.56 thf(fact_6273_bit__unset__bit__iff,axiom,
% 5.27/5.56 ! [M: nat,A: int,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( bit_se4203085406695923979it_int @ M @ A ) @ N2 )
% 5.27/5.56 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.56 & ( M != N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_unset_bit_iff
% 5.27/5.56 thf(fact_6274_bit__unset__bit__iff,axiom,
% 5.27/5.56 ! [M: nat,A: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( bit_se4205575877204974255it_nat @ M @ A ) @ N2 )
% 5.27/5.56 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.56 & ( M != N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_unset_bit_iff
% 5.27/5.56 thf(fact_6275_bit__xor__int__iff,axiom,
% 5.27/5.56 ! [K: int,L: int,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L ) @ N2 )
% 5.27/5.56 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.27/5.56 != ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_xor_int_iff
% 5.27/5.56 thf(fact_6276_not__bit__1__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( suc @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % not_bit_1_Suc
% 5.27/5.56 thf(fact_6277_not__bit__1__Suc,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( suc @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % not_bit_1_Suc
% 5.27/5.56 thf(fact_6278_bit__1__iff,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ one_one_int @ N2 )
% 5.27/5.56 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_1_iff
% 5.27/5.56 thf(fact_6279_bit__1__iff,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ one_one_nat @ N2 )
% 5.27/5.56 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_1_iff
% 5.27/5.56 thf(fact_6280_abs__ge__zero,axiom,
% 5.27/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_zero
% 5.27/5.56 thf(fact_6281_abs__ge__zero,axiom,
% 5.27/5.56 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_zero
% 5.27/5.56 thf(fact_6282_abs__ge__zero,axiom,
% 5.27/5.56 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_zero
% 5.27/5.56 thf(fact_6283_abs__ge__zero,axiom,
% 5.27/5.56 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_zero
% 5.27/5.56 thf(fact_6284_bit__numeral__simps_I1_J,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ~ ( bit_se1146084159140164899it_int @ one_one_int @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(1)
% 5.27/5.56 thf(fact_6285_bit__numeral__simps_I1_J,axiom,
% 5.27/5.56 ! [N2: num] :
% 5.27/5.56 ~ ( bit_se1148574629649215175it_nat @ one_one_nat @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_numeral_simps(1)
% 5.27/5.56 thf(fact_6286_abs__of__pos,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.56 => ( ( abs_abs_Code_integer @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_pos
% 5.27/5.56 thf(fact_6287_abs__of__pos,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.56 => ( ( abs_abs_real @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_pos
% 5.27/5.56 thf(fact_6288_abs__of__pos,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.56 => ( ( abs_abs_rat @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_pos
% 5.27/5.56 thf(fact_6289_abs__of__pos,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ( ( ord_less_int @ zero_zero_int @ A )
% 5.27/5.56 => ( ( abs_abs_int @ A )
% 5.27/5.56 = A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_of_pos
% 5.27/5.56 thf(fact_6290_abs__not__less__zero,axiom,
% 5.27/5.56 ! [A: code_integer] :
% 5.27/5.56 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.27/5.56
% 5.27/5.56 % abs_not_less_zero
% 5.27/5.56 thf(fact_6291_abs__not__less__zero,axiom,
% 5.27/5.56 ! [A: real] :
% 5.27/5.56 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.27/5.56
% 5.27/5.56 % abs_not_less_zero
% 5.27/5.56 thf(fact_6292_abs__not__less__zero,axiom,
% 5.27/5.56 ! [A: rat] :
% 5.27/5.56 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.27/5.56
% 5.27/5.56 % abs_not_less_zero
% 5.27/5.56 thf(fact_6293_abs__not__less__zero,axiom,
% 5.27/5.56 ! [A: int] :
% 5.27/5.56 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.27/5.56
% 5.27/5.56 % abs_not_less_zero
% 5.27/5.56 thf(fact_6294_abs__triangle__ineq,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq
% 5.27/5.56 thf(fact_6295_abs__triangle__ineq,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq
% 5.27/5.56 thf(fact_6296_abs__triangle__ineq,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq
% 5.27/5.56 thf(fact_6297_abs__triangle__ineq,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq
% 5.27/5.56 thf(fact_6298_abs__mult__less,axiom,
% 5.27/5.56 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.27/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.27/5.56 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.27/5.56 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_less
% 5.27/5.56 thf(fact_6299_abs__mult__less,axiom,
% 5.27/5.56 ! [A: real,C: real,B: real,D: real] :
% 5.27/5.56 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.27/5.56 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.27/5.56 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_less
% 5.27/5.56 thf(fact_6300_abs__mult__less,axiom,
% 5.27/5.56 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.27/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.27/5.56 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.27/5.56 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_less
% 5.27/5.56 thf(fact_6301_abs__mult__less,axiom,
% 5.27/5.56 ! [A: int,C: int,B: int,D: int] :
% 5.27/5.56 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.27/5.56 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.27/5.56 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_less
% 5.27/5.56 thf(fact_6302_abs__triangle__ineq2__sym,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2_sym
% 5.27/5.56 thf(fact_6303_abs__triangle__ineq2__sym,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2_sym
% 5.27/5.56 thf(fact_6304_abs__triangle__ineq2__sym,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2_sym
% 5.27/5.56 thf(fact_6305_abs__triangle__ineq2__sym,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2_sym
% 5.27/5.56 thf(fact_6306_abs__triangle__ineq3,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq3
% 5.27/5.56 thf(fact_6307_abs__triangle__ineq3,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq3
% 5.27/5.56 thf(fact_6308_abs__triangle__ineq3,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq3
% 5.27/5.56 thf(fact_6309_abs__triangle__ineq3,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq3
% 5.27/5.56 thf(fact_6310_abs__triangle__ineq2,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2
% 5.27/5.56 thf(fact_6311_abs__triangle__ineq2,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2
% 5.27/5.56 thf(fact_6312_abs__triangle__ineq2,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2
% 5.27/5.56 thf(fact_6313_abs__triangle__ineq2,axiom,
% 5.27/5.56 ! [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 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_triangle_ineq2
% 5.27/5.56 thf(fact_6314_abs__ge__minus__self,axiom,
% 5.27/5.56 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_minus_self
% 5.27/5.56 thf(fact_6315_abs__ge__minus__self,axiom,
% 5.27/5.56 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_minus_self
% 5.27/5.56 thf(fact_6316_abs__ge__minus__self,axiom,
% 5.27/5.56 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_minus_self
% 5.27/5.56 thf(fact_6317_abs__ge__minus__self,axiom,
% 5.27/5.56 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_ge_minus_self
% 5.27/5.56 thf(fact_6318_abs__le__iff,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_eq_real @ A @ B )
% 5.27/5.56 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_iff
% 5.27/5.56 thf(fact_6319_abs__le__iff,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.27/5.56 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.27/5.56 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_iff
% 5.27/5.56 thf(fact_6320_abs__le__iff,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.56 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_iff
% 5.27/5.56 thf(fact_6321_abs__le__iff,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_eq_int @ A @ B )
% 5.27/5.56 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_iff
% 5.27/5.56 thf(fact_6322_abs__le__D2,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D2
% 5.27/5.56 thf(fact_6323_abs__le__D2,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.27/5.56 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D2
% 5.27/5.56 thf(fact_6324_abs__le__D2,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D2
% 5.27/5.56 thf(fact_6325_abs__le__D2,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_le_D2
% 5.27/5.56 thf(fact_6326_abs__leI,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.56 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_leI
% 5.27/5.56 thf(fact_6327_abs__leI,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.27/5.56 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.27/5.56 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_leI
% 5.27/5.56 thf(fact_6328_abs__leI,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.56 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_leI
% 5.27/5.56 thf(fact_6329_abs__leI,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ A @ B )
% 5.27/5.56 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.27/5.56 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_leI
% 5.27/5.56 thf(fact_6330_nonzero__abs__divide,axiom,
% 5.27/5.56 ! [B: rat,A: rat] :
% 5.27/5.56 ( ( B != zero_zero_rat )
% 5.27/5.56 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.56 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % nonzero_abs_divide
% 5.27/5.56 thf(fact_6331_nonzero__abs__divide,axiom,
% 5.27/5.56 ! [B: real,A: real] :
% 5.27/5.56 ( ( B != zero_zero_real )
% 5.27/5.56 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.56 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % nonzero_abs_divide
% 5.27/5.56 thf(fact_6332_abs__less__iff,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_real @ A @ B )
% 5.27/5.56 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_less_iff
% 5.27/5.56 thf(fact_6333_abs__less__iff,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_int @ A @ B )
% 5.27/5.56 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_less_iff
% 5.27/5.56 thf(fact_6334_abs__less__iff,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.27/5.56 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.27/5.56 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_less_iff
% 5.27/5.56 thf(fact_6335_abs__less__iff,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.27/5.56 = ( ( ord_less_rat @ A @ B )
% 5.27/5.56 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_less_iff
% 5.27/5.56 thf(fact_6336_fact__less__mono__nat,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.56 => ( ( ord_less_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_less_mono_nat
% 5.27/5.56 thf(fact_6337_bit__take__bit__iff,axiom,
% 5.27/5.56 ! [M: nat,A: int,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ M @ A ) @ N2 )
% 5.27/5.56 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.56 & ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_take_bit_iff
% 5.27/5.56 thf(fact_6338_bit__take__bit__iff,axiom,
% 5.27/5.56 ! [M: nat,A: nat,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( bit_se2925701944663578781it_nat @ M @ A ) @ N2 )
% 5.27/5.56 = ( ( ord_less_nat @ N2 @ M )
% 5.27/5.56 & ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_take_bit_iff
% 5.27/5.56 thf(fact_6339_bit__of__bool__iff,axiom,
% 5.27/5.56 ! [B: $o,N2: nat] :
% 5.27/5.56 ( ( bit_se9216721137139052372nteger @ ( zero_n356916108424825756nteger @ B ) @ N2 )
% 5.27/5.56 = ( B
% 5.27/5.56 & ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_of_bool_iff
% 5.27/5.56 thf(fact_6340_bit__of__bool__iff,axiom,
% 5.27/5.56 ! [B: $o,N2: nat] :
% 5.27/5.56 ( ( bit_se1146084159140164899it_int @ ( zero_n2684676970156552555ol_int @ B ) @ N2 )
% 5.27/5.56 = ( B
% 5.27/5.56 & ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_of_bool_iff
% 5.27/5.56 thf(fact_6341_bit__of__bool__iff,axiom,
% 5.27/5.56 ! [B: $o,N2: nat] :
% 5.27/5.56 ( ( bit_se1148574629649215175it_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ N2 )
% 5.27/5.56 = ( B
% 5.27/5.56 & ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % bit_of_bool_iff
% 5.27/5.56 thf(fact_6342_fact__ge__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_zero
% 5.27/5.56 thf(fact_6343_fact__ge__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_zero
% 5.27/5.56 thf(fact_6344_fact__ge__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_zero
% 5.27/5.56 thf(fact_6345_fact__ge__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_zero
% 5.27/5.56 thf(fact_6346_fact__not__neg,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( ord_less_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ zero_zero_rat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_not_neg
% 5.27/5.56 thf(fact_6347_fact__not__neg,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( ord_less_int @ ( semiri1406184849735516958ct_int @ N2 ) @ zero_zero_int ) ).
% 5.27/5.56
% 5.27/5.56 % fact_not_neg
% 5.27/5.56 thf(fact_6348_fact__not__neg,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ zero_zero_nat ) ).
% 5.27/5.56
% 5.27/5.56 % fact_not_neg
% 5.27/5.56 thf(fact_6349_fact__not__neg,axiom,
% 5.27/5.56 ! [N2: nat] :
% 5.27/5.56 ~ ( ord_less_real @ ( semiri2265585572941072030t_real @ N2 ) @ zero_zero_real ) ).
% 5.27/5.56
% 5.27/5.56 % fact_not_neg
% 5.27/5.56 thf(fact_6350_fact__gt__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_rat @ zero_zero_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_gt_zero
% 5.27/5.56 thf(fact_6351_fact__gt__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_int @ zero_zero_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_gt_zero
% 5.27/5.56 thf(fact_6352_fact__gt__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_nat @ zero_zero_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_gt_zero
% 5.27/5.56 thf(fact_6353_fact__gt__zero,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_real @ zero_zero_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_gt_zero
% 5.27/5.56 thf(fact_6354_fact__ge__1,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_rat @ one_one_rat @ ( semiri773545260158071498ct_rat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_1
% 5.27/5.56 thf(fact_6355_fact__ge__1,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_int @ one_one_int @ ( semiri1406184849735516958ct_int @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_1
% 5.27/5.56 thf(fact_6356_fact__ge__1,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_nat @ one_one_nat @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_1
% 5.27/5.56 thf(fact_6357_fact__ge__1,axiom,
% 5.27/5.56 ! [N2: nat] : ( ord_less_eq_real @ one_one_real @ ( semiri2265585572941072030t_real @ N2 ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_ge_1
% 5.27/5.56 thf(fact_6358_fact__mono,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_mono
% 5.27/5.56 thf(fact_6359_fact__mono,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_mono
% 5.27/5.56 thf(fact_6360_fact__mono,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_mono
% 5.27/5.56 thf(fact_6361_fact__mono,axiom,
% 5.27/5.56 ! [M: nat,N2: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.56 => ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_mono
% 5.27/5.56 thf(fact_6362_signed__take__bit__eq__if__positive,axiom,
% 5.27/5.56 ! [A: int,N2: nat] :
% 5.27/5.56 ( ~ ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.56 => ( ( bit_ri631733984087533419it_int @ N2 @ A )
% 5.27/5.56 = ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % signed_take_bit_eq_if_positive
% 5.27/5.56 thf(fact_6363_fact__dvd,axiom,
% 5.27/5.56 ! [N2: nat,M: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( dvd_dvd_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_dvd
% 5.27/5.56 thf(fact_6364_fact__dvd,axiom,
% 5.27/5.56 ! [N2: nat,M: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( dvd_dvd_Code_integer @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_dvd
% 5.27/5.56 thf(fact_6365_fact__dvd,axiom,
% 5.27/5.56 ! [N2: nat,M: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( dvd_dvd_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_dvd
% 5.27/5.56 thf(fact_6366_fact__dvd,axiom,
% 5.27/5.56 ! [N2: nat,M: nat] :
% 5.27/5.56 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.56 => ( dvd_dvd_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ M ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % fact_dvd
% 5.27/5.56 thf(fact_6367_pochhammer__fact,axiom,
% 5.27/5.56 ( semiri5044797733671781792omplex
% 5.27/5.56 = ( comm_s2602460028002588243omplex @ one_one_complex ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_fact
% 5.27/5.56 thf(fact_6368_pochhammer__fact,axiom,
% 5.27/5.56 ( semiri773545260158071498ct_rat
% 5.27/5.56 = ( comm_s4028243227959126397er_rat @ one_one_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_fact
% 5.27/5.56 thf(fact_6369_pochhammer__fact,axiom,
% 5.27/5.56 ( semiri1406184849735516958ct_int
% 5.27/5.56 = ( comm_s4660882817536571857er_int @ one_one_int ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_fact
% 5.27/5.56 thf(fact_6370_pochhammer__fact,axiom,
% 5.27/5.56 ( semiri1408675320244567234ct_nat
% 5.27/5.56 = ( comm_s4663373288045622133er_nat @ one_one_nat ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_fact
% 5.27/5.56 thf(fact_6371_pochhammer__fact,axiom,
% 5.27/5.56 ( semiri2265585572941072030t_real
% 5.27/5.56 = ( comm_s7457072308508201937r_real @ one_one_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % pochhammer_fact
% 5.27/5.56 thf(fact_6372_tanh__real__lt__1,axiom,
% 5.27/5.56 ! [X4: real] : ( ord_less_real @ ( tanh_real @ X4 ) @ one_one_real ) ).
% 5.27/5.56
% 5.27/5.56 % tanh_real_lt_1
% 5.27/5.56 thf(fact_6373_dense__eq0__I,axiom,
% 5.27/5.56 ! [X4: real] :
% 5.27/5.56 ( ! [E: real] :
% 5.27/5.56 ( ( ord_less_real @ zero_zero_real @ E )
% 5.27/5.56 => ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ E ) )
% 5.27/5.56 => ( X4 = zero_zero_real ) ) ).
% 5.27/5.56
% 5.27/5.56 % dense_eq0_I
% 5.27/5.56 thf(fact_6374_dense__eq0__I,axiom,
% 5.27/5.56 ! [X4: rat] :
% 5.27/5.56 ( ! [E: rat] :
% 5.27/5.56 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.27/5.56 => ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ E ) )
% 5.27/5.56 => ( X4 = zero_zero_rat ) ) ).
% 5.27/5.56
% 5.27/5.56 % dense_eq0_I
% 5.27/5.56 thf(fact_6375_abs__eq__mult,axiom,
% 5.27/5.56 ! [A: code_integer,B: code_integer] :
% 5.27/5.56 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.56 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.27/5.56 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.27/5.56 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.27/5.56 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.27/5.56 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_mult
% 5.27/5.56 thf(fact_6376_abs__eq__mult,axiom,
% 5.27/5.56 ! [A: real,B: real] :
% 5.27/5.56 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.56 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.27/5.56 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.27/5.56 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.27/5.56 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.27/5.56 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_mult
% 5.27/5.56 thf(fact_6377_abs__eq__mult,axiom,
% 5.27/5.56 ! [A: rat,B: rat] :
% 5.27/5.56 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.56 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.27/5.56 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.27/5.56 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.27/5.56 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.56 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_mult
% 5.27/5.56 thf(fact_6378_abs__eq__mult,axiom,
% 5.27/5.56 ! [A: int,B: int] :
% 5.27/5.56 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.27/5.56 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.27/5.56 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.27/5.56 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.27/5.56 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.27/5.56 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_eq_mult
% 5.27/5.56 thf(fact_6379_abs__mult__pos,axiom,
% 5.27/5.56 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.56 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X4 )
% 5.27/5.56 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X4 )
% 5.27/5.56 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_pos
% 5.27/5.56 thf(fact_6380_abs__mult__pos,axiom,
% 5.27/5.56 ! [X4: real,Y: real] :
% 5.27/5.56 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.56 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X4 )
% 5.27/5.56 = ( abs_abs_real @ ( times_times_real @ Y @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_pos
% 5.27/5.56 thf(fact_6381_abs__mult__pos,axiom,
% 5.27/5.56 ! [X4: rat,Y: rat] :
% 5.27/5.56 ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.27/5.56 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X4 )
% 5.27/5.56 = ( abs_abs_rat @ ( times_times_rat @ Y @ X4 ) ) ) ) ).
% 5.27/5.56
% 5.27/5.56 % abs_mult_pos
% 5.27/5.56 thf(fact_6382_abs__mult__pos,axiom,
% 5.27/5.56 ! [X4: int,Y: int] :
% 5.27/5.56 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.57 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X4 )
% 5.27/5.57 = ( abs_abs_int @ ( times_times_int @ Y @ X4 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_pos
% 5.27/5.57 thf(fact_6383_abs__minus__le__zero,axiom,
% 5.27/5.57 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.27/5.57
% 5.27/5.57 % abs_minus_le_zero
% 5.27/5.57 thf(fact_6384_abs__minus__le__zero,axiom,
% 5.27/5.57 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.27/5.57
% 5.27/5.57 % abs_minus_le_zero
% 5.27/5.57 thf(fact_6385_abs__minus__le__zero,axiom,
% 5.27/5.57 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.27/5.57
% 5.27/5.57 % abs_minus_le_zero
% 5.27/5.57 thf(fact_6386_abs__minus__le__zero,axiom,
% 5.27/5.57 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % abs_minus_le_zero
% 5.27/5.57 thf(fact_6387_eq__abs__iff_H,axiom,
% 5.27/5.57 ! [A: real,B: real] :
% 5.27/5.57 ( ( A
% 5.27/5.57 = ( abs_abs_real @ B ) )
% 5.27/5.57 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.57 & ( ( B = A )
% 5.27/5.57 | ( B
% 5.27/5.57 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % eq_abs_iff'
% 5.27/5.57 thf(fact_6388_eq__abs__iff_H,axiom,
% 5.27/5.57 ! [A: code_integer,B: code_integer] :
% 5.27/5.57 ( ( A
% 5.27/5.57 = ( abs_abs_Code_integer @ B ) )
% 5.27/5.57 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.57 & ( ( B = A )
% 5.27/5.57 | ( B
% 5.27/5.57 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % eq_abs_iff'
% 5.27/5.57 thf(fact_6389_eq__abs__iff_H,axiom,
% 5.27/5.57 ! [A: rat,B: rat] :
% 5.27/5.57 ( ( A
% 5.27/5.57 = ( abs_abs_rat @ B ) )
% 5.27/5.57 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.57 & ( ( B = A )
% 5.27/5.57 | ( B
% 5.27/5.57 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % eq_abs_iff'
% 5.27/5.57 thf(fact_6390_eq__abs__iff_H,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( A
% 5.27/5.57 = ( abs_abs_int @ B ) )
% 5.27/5.57 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.27/5.57 & ( ( B = A )
% 5.27/5.57 | ( B
% 5.27/5.57 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % eq_abs_iff'
% 5.27/5.57 thf(fact_6391_abs__eq__iff_H,axiom,
% 5.27/5.57 ! [A: real,B: real] :
% 5.27/5.57 ( ( ( abs_abs_real @ A )
% 5.27/5.57 = B )
% 5.27/5.57 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.27/5.57 & ( ( A = B )
% 5.27/5.57 | ( A
% 5.27/5.57 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_eq_iff'
% 5.27/5.57 thf(fact_6392_abs__eq__iff_H,axiom,
% 5.27/5.57 ! [A: code_integer,B: code_integer] :
% 5.27/5.57 ( ( ( abs_abs_Code_integer @ A )
% 5.27/5.57 = B )
% 5.27/5.57 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.27/5.57 & ( ( A = B )
% 5.27/5.57 | ( A
% 5.27/5.57 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_eq_iff'
% 5.27/5.57 thf(fact_6393_abs__eq__iff_H,axiom,
% 5.27/5.57 ! [A: rat,B: rat] :
% 5.27/5.57 ( ( ( abs_abs_rat @ A )
% 5.27/5.57 = B )
% 5.27/5.57 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.27/5.57 & ( ( A = B )
% 5.27/5.57 | ( A
% 5.27/5.57 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_eq_iff'
% 5.27/5.57 thf(fact_6394_abs__eq__iff_H,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( ( abs_abs_int @ A )
% 5.27/5.57 = B )
% 5.27/5.57 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.27/5.57 & ( ( A = B )
% 5.27/5.57 | ( A
% 5.27/5.57 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_eq_iff'
% 5.27/5.57 thf(fact_6395_zero__le__power__abs,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_le_power_abs
% 5.27/5.57 thf(fact_6396_zero__le__power__abs,axiom,
% 5.27/5.57 ! [A: real,N2: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_le_power_abs
% 5.27/5.57 thf(fact_6397_zero__le__power__abs,axiom,
% 5.27/5.57 ! [A: rat,N2: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_le_power_abs
% 5.27/5.57 thf(fact_6398_zero__le__power__abs,axiom,
% 5.27/5.57 ! [A: int,N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_le_power_abs
% 5.27/5.57 thf(fact_6399_abs__div__pos,axiom,
% 5.27/5.57 ! [Y: rat,X4: rat] :
% 5.27/5.57 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.27/5.57 => ( ( divide_divide_rat @ ( abs_abs_rat @ X4 ) @ Y )
% 5.27/5.57 = ( abs_abs_rat @ ( divide_divide_rat @ X4 @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_div_pos
% 5.27/5.57 thf(fact_6400_abs__div__pos,axiom,
% 5.27/5.57 ! [Y: real,X4: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.57 => ( ( divide_divide_real @ ( abs_abs_real @ X4 ) @ Y )
% 5.27/5.57 = ( abs_abs_real @ ( divide_divide_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_div_pos
% 5.27/5.57 thf(fact_6401_abs__if,axiom,
% 5.27/5.57 ( abs_abs_real
% 5.27/5.57 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if
% 5.27/5.57 thf(fact_6402_abs__if,axiom,
% 5.27/5.57 ( abs_abs_int
% 5.27/5.57 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if
% 5.27/5.57 thf(fact_6403_abs__if,axiom,
% 5.27/5.57 ( abs_abs_Code_integer
% 5.27/5.57 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if
% 5.27/5.57 thf(fact_6404_abs__if,axiom,
% 5.27/5.57 ( abs_abs_rat
% 5.27/5.57 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if
% 5.27/5.57 thf(fact_6405_abs__of__neg,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.57 => ( ( abs_abs_real @ A )
% 5.27/5.57 = ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_of_neg
% 5.27/5.57 thf(fact_6406_abs__of__neg,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ord_less_int @ A @ zero_zero_int )
% 5.27/5.57 => ( ( abs_abs_int @ A )
% 5.27/5.57 = ( uminus_uminus_int @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_of_neg
% 5.27/5.57 thf(fact_6407_abs__of__neg,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.27/5.57 => ( ( abs_abs_Code_integer @ A )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_of_neg
% 5.27/5.57 thf(fact_6408_abs__of__neg,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.57 => ( ( abs_abs_rat @ A )
% 5.27/5.57 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_of_neg
% 5.27/5.57 thf(fact_6409_abs__if__raw,axiom,
% 5.27/5.57 ( abs_abs_real
% 5.27/5.57 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if_raw
% 5.27/5.57 thf(fact_6410_abs__if__raw,axiom,
% 5.27/5.57 ( abs_abs_int
% 5.27/5.57 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if_raw
% 5.27/5.57 thf(fact_6411_abs__if__raw,axiom,
% 5.27/5.57 ( abs_abs_Code_integer
% 5.27/5.57 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if_raw
% 5.27/5.57 thf(fact_6412_abs__if__raw,axiom,
% 5.27/5.57 ( abs_abs_rat
% 5.27/5.57 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_if_raw
% 5.27/5.57 thf(fact_6413_abs__diff__le__iff,axiom,
% 5.27/5.57 ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 5.27/5.57 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_le3102999989581377725nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_le_iff
% 5.27/5.57 thf(fact_6414_abs__diff__le__iff,axiom,
% 5.27/5.57 ! [X4: real,A: real,R3: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_eq_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_le_iff
% 5.27/5.57 thf(fact_6415_abs__diff__le__iff,axiom,
% 5.27/5.57 ! [X4: rat,A: rat,R3: rat] :
% 5.27/5.57 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_le_iff
% 5.27/5.57 thf(fact_6416_abs__diff__le__iff,axiom,
% 5.27/5.57 ! [X4: int,A: int,R3: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_eq_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_le_iff
% 5.27/5.57 thf(fact_6417_abs__triangle__ineq4,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_triangle_ineq4
% 5.27/5.57 thf(fact_6418_abs__triangle__ineq4,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_triangle_ineq4
% 5.27/5.57 thf(fact_6419_abs__triangle__ineq4,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_triangle_ineq4
% 5.27/5.57 thf(fact_6420_abs__triangle__ineq4,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_triangle_ineq4
% 5.27/5.57 thf(fact_6421_abs__diff__triangle__ineq,axiom,
% 5.27/5.57 ! [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 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_triangle_ineq
% 5.27/5.57 thf(fact_6422_abs__diff__triangle__ineq,axiom,
% 5.27/5.57 ! [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 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_triangle_ineq
% 5.27/5.57 thf(fact_6423_abs__diff__triangle__ineq,axiom,
% 5.27/5.57 ! [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 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_triangle_ineq
% 5.27/5.57 thf(fact_6424_abs__diff__triangle__ineq,axiom,
% 5.27/5.57 ! [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 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_triangle_ineq
% 5.27/5.57 thf(fact_6425_abs__diff__less__iff,axiom,
% 5.27/5.57 ! [X4: code_integer,A: code_integer,R3: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_le6747313008572928689nteger @ X4 @ ( plus_p5714425477246183910nteger @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_less_iff
% 5.27/5.57 thf(fact_6426_abs__diff__less__iff,axiom,
% 5.27/5.57 ! [X4: real,A: real,R3: real] :
% 5.27/5.57 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_real @ ( minus_minus_real @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_real @ X4 @ ( plus_plus_real @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_less_iff
% 5.27/5.57 thf(fact_6427_abs__diff__less__iff,axiom,
% 5.27/5.57 ! [X4: rat,A: rat,R3: rat] :
% 5.27/5.57 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_rat @ X4 @ ( plus_plus_rat @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_less_iff
% 5.27/5.57 thf(fact_6428_abs__diff__less__iff,axiom,
% 5.27/5.57 ! [X4: int,A: int,R3: int] :
% 5.27/5.57 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ A ) ) @ R3 )
% 5.27/5.57 = ( ( ord_less_int @ ( minus_minus_int @ A @ R3 ) @ X4 )
% 5.27/5.57 & ( ord_less_int @ X4 @ ( plus_plus_int @ A @ R3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_diff_less_iff
% 5.27/5.57 thf(fact_6429_fact__ge__Suc__0__nat,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_ge_Suc_0_nat
% 5.27/5.57 thf(fact_6430_dvd__fact,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.27/5.57 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % dvd_fact
% 5.27/5.57 thf(fact_6431_bit__not__int__iff_H,axiom,
% 5.27/5.57 ! [K: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N2 )
% 5.27/5.57 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_not_int_iff'
% 5.27/5.57 thf(fact_6432_abs__real__def,axiom,
% 5.27/5.57 ( abs_abs_real
% 5.27/5.57 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_real_def
% 5.27/5.57 thf(fact_6433_fact__less__mono,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.57 => ( ( ord_less_nat @ M @ N2 )
% 5.27/5.57 => ( ord_less_rat @ ( semiri773545260158071498ct_rat @ M ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_less_mono
% 5.27/5.57 thf(fact_6434_fact__less__mono,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.57 => ( ( ord_less_nat @ M @ N2 )
% 5.27/5.57 => ( ord_less_int @ ( semiri1406184849735516958ct_int @ M ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_less_mono
% 5.27/5.57 thf(fact_6435_fact__less__mono,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.57 => ( ( ord_less_nat @ M @ N2 )
% 5.27/5.57 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_less_mono
% 5.27/5.57 thf(fact_6436_fact__less__mono,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.57 => ( ( ord_less_nat @ M @ N2 )
% 5.27/5.57 => ( ord_less_real @ ( semiri2265585572941072030t_real @ M ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_less_mono
% 5.27/5.57 thf(fact_6437_lemma__interval__lt,axiom,
% 5.27/5.57 ! [A: real,X4: real,B: real] :
% 5.27/5.57 ( ( ord_less_real @ A @ X4 )
% 5.27/5.57 => ( ( ord_less_real @ X4 @ B )
% 5.27/5.57 => ? [D3: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.57 & ! [Y4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 5.27/5.57 => ( ( ord_less_real @ A @ Y4 )
% 5.27/5.57 & ( ord_less_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % lemma_interval_lt
% 5.27/5.57 thf(fact_6438_fact__fact__dvd__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] : ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ N2 ) ) @ ( semiri3624122377584611663nteger @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_fact_dvd_fact
% 5.27/5.57 thf(fact_6439_fact__fact__dvd__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] : ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ N2 ) ) @ ( semiri1406184849735516958ct_int @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_fact_dvd_fact
% 5.27/5.57 thf(fact_6440_fact__fact__dvd__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] : ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) @ ( semiri1408675320244567234ct_nat @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_fact_dvd_fact
% 5.27/5.57 thf(fact_6441_fact__fact__dvd__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] : ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_fact_dvd_fact
% 5.27/5.57 thf(fact_6442_fact__mod,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( ( modulo_modulo_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1406184849735516958ct_int @ M ) )
% 5.27/5.57 = zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_mod
% 5.27/5.57 thf(fact_6443_fact__mod,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( ( modulo364778990260209775nteger @ ( semiri3624122377584611663nteger @ N2 ) @ ( semiri3624122377584611663nteger @ M ) )
% 5.27/5.57 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_mod
% 5.27/5.57 thf(fact_6444_fact__mod,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( ( modulo_modulo_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ M ) )
% 5.27/5.57 = zero_zero_nat ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_mod
% 5.27/5.57 thf(fact_6445_fact__le__power,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_rat @ ( semiri773545260158071498ct_rat @ N2 ) @ ( semiri681578069525770553at_rat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_le_power
% 5.27/5.57 thf(fact_6446_fact__le__power,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_int @ ( semiri1406184849735516958ct_int @ N2 ) @ ( semiri1314217659103216013at_int @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_le_power
% 5.27/5.57 thf(fact_6447_fact__le__power,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1316708129612266289at_nat @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_le_power
% 5.27/5.57 thf(fact_6448_fact__le__power,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri5074537144036343181t_real @ ( power_power_nat @ N2 @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_le_power
% 5.27/5.57 thf(fact_6449_sin__bound__lemma,axiom,
% 5.27/5.57 ! [X4: real,Y: real,U: real,V: real] :
% 5.27/5.57 ( ( X4 = Y )
% 5.27/5.57 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.27/5.57 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X4 @ U ) @ Y ) ) @ V ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sin_bound_lemma
% 5.27/5.57 thf(fact_6450_flip__bit__eq__if,axiom,
% 5.27/5.57 ( bit_se2159334234014336723it_int
% 5.27/5.57 = ( ^ [N: nat,A3: int] : ( if_nat_int_int @ ( bit_se1146084159140164899it_int @ A3 @ N ) @ bit_se4203085406695923979it_int @ bit_se7879613467334960850it_int @ N @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % flip_bit_eq_if
% 5.27/5.57 thf(fact_6451_flip__bit__eq__if,axiom,
% 5.27/5.57 ( bit_se2161824704523386999it_nat
% 5.27/5.57 = ( ^ [N: nat,A3: nat] : ( if_nat_nat_nat @ ( bit_se1148574629649215175it_nat @ A3 @ N ) @ bit_se4205575877204974255it_nat @ bit_se7882103937844011126it_nat @ N @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % flip_bit_eq_if
% 5.27/5.57 thf(fact_6452_tanh__real__gt__neg1,axiom,
% 5.27/5.57 ! [X4: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % tanh_real_gt_neg1
% 5.27/5.57 thf(fact_6453_abs__add__one__gt__zero,axiom,
% 5.27/5.57 ! [X4: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_add_one_gt_zero
% 5.27/5.57 thf(fact_6454_abs__add__one__gt__zero,axiom,
% 5.27/5.57 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_add_one_gt_zero
% 5.27/5.57 thf(fact_6455_abs__add__one__gt__zero,axiom,
% 5.27/5.57 ! [X4: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_add_one_gt_zero
% 5.27/5.57 thf(fact_6456_abs__add__one__gt__zero,axiom,
% 5.27/5.57 ! [X4: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_add_one_gt_zero
% 5.27/5.57 thf(fact_6457_fact__diff__Suc,axiom,
% 5.27/5.57 ! [N2: nat,M: nat] :
% 5.27/5.57 ( ( ord_less_nat @ N2 @ ( suc @ M ) )
% 5.27/5.57 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) )
% 5.27/5.57 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_diff_Suc
% 5.27/5.57 thf(fact_6458_fact__div__fact__le__pow,axiom,
% 5.27/5.57 ! [R3: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ R3 @ N2 )
% 5.27/5.57 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ R3 ) ) ) @ ( power_power_nat @ N2 @ R3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_div_fact_le_pow
% 5.27/5.57 thf(fact_6459_binomial__fact__lemma,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( binomial @ N2 @ K ) )
% 5.27/5.57 = ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % binomial_fact_lemma
% 5.27/5.57 thf(fact_6460_bit__imp__take__bit__positive,axiom,
% 5.27/5.57 ! [N2: nat,M: nat,K: int] :
% 5.27/5.57 ( ( ord_less_nat @ N2 @ M )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.27/5.57 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_imp_take_bit_positive
% 5.27/5.57 thf(fact_6461_lemma__interval,axiom,
% 5.27/5.57 ! [A: real,X4: real,B: real] :
% 5.27/5.57 ( ( ord_less_real @ A @ X4 )
% 5.27/5.57 => ( ( ord_less_real @ X4 @ B )
% 5.27/5.57 => ? [D3: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.57 & ! [Y4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y4 ) ) @ D3 )
% 5.27/5.57 => ( ( ord_less_eq_real @ A @ Y4 )
% 5.27/5.57 & ( ord_less_eq_real @ Y4 @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % lemma_interval
% 5.27/5.57 thf(fact_6462_norm__triangle__ineq3,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % norm_triangle_ineq3
% 5.27/5.57 thf(fact_6463_norm__triangle__ineq3,axiom,
% 5.27/5.57 ! [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 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % norm_triangle_ineq3
% 5.27/5.57 thf(fact_6464_bit__concat__bit__iff,axiom,
% 5.27/5.57 ! [M: nat,K: int,L: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L ) @ N2 )
% 5.27/5.57 = ( ( ( ord_less_nat @ N2 @ M )
% 5.27/5.57 & ( bit_se1146084159140164899it_int @ K @ N2 ) )
% 5.27/5.57 | ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 & ( bit_se1146084159140164899it_int @ L @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_concat_bit_iff
% 5.27/5.57 thf(fact_6465_choose__dvd,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ ( semiri3624122377584611663nteger @ K ) @ ( semiri3624122377584611663nteger @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % choose_dvd
% 5.27/5.57 thf(fact_6466_choose__dvd,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( dvd_dvd_int @ ( times_times_int @ ( semiri1406184849735516958ct_int @ K ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % choose_dvd
% 5.27/5.57 thf(fact_6467_choose__dvd,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( dvd_dvd_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri1408675320244567234ct_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % choose_dvd
% 5.27/5.57 thf(fact_6468_choose__dvd,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( dvd_dvd_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % choose_dvd
% 5.27/5.57 thf(fact_6469_fact__numeral,axiom,
% 5.27/5.57 ! [K: num] :
% 5.27/5.57 ( ( semiri4449623510593786356d_enat @ ( numeral_numeral_nat @ K ) )
% 5.27/5.57 = ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ K ) @ ( semiri4449623510593786356d_enat @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_numeral
% 5.27/5.57 thf(fact_6470_fact__numeral,axiom,
% 5.27/5.57 ! [K: num] :
% 5.27/5.57 ( ( semiri5044797733671781792omplex @ ( numeral_numeral_nat @ K ) )
% 5.27/5.57 = ( times_times_complex @ ( numera6690914467698888265omplex @ K ) @ ( semiri5044797733671781792omplex @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_numeral
% 5.27/5.57 thf(fact_6471_fact__numeral,axiom,
% 5.27/5.57 ! [K: num] :
% 5.27/5.57 ( ( semiri1406184849735516958ct_int @ ( numeral_numeral_nat @ K ) )
% 5.27/5.57 = ( times_times_int @ ( numeral_numeral_int @ K ) @ ( semiri1406184849735516958ct_int @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_numeral
% 5.27/5.57 thf(fact_6472_fact__numeral,axiom,
% 5.27/5.57 ! [K: num] :
% 5.27/5.57 ( ( semiri1408675320244567234ct_nat @ ( numeral_numeral_nat @ K ) )
% 5.27/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_numeral
% 5.27/5.57 thf(fact_6473_fact__numeral,axiom,
% 5.27/5.57 ! [K: num] :
% 5.27/5.57 ( ( semiri2265585572941072030t_real @ ( numeral_numeral_nat @ K ) )
% 5.27/5.57 = ( times_times_real @ ( numeral_numeral_real @ K ) @ ( semiri2265585572941072030t_real @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_numeral
% 5.27/5.57 thf(fact_6474_signed__take__bit__eq__concat__bit,axiom,
% 5.27/5.57 ( bit_ri631733984087533419it_int
% 5.27/5.57 = ( ^ [N: nat,K3: int] : ( bit_concat_bit @ N @ K3 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % signed_take_bit_eq_concat_bit
% 5.27/5.57 thf(fact_6475_exp__eq__0__imp__not__bit,axiom,
% 5.27/5.57 ! [N2: nat,A: int] :
% 5.27/5.57 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 => ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_eq_0_imp_not_bit
% 5.27/5.57 thf(fact_6476_exp__eq__0__imp__not__bit,axiom,
% 5.27/5.57 ! [N2: nat,A: nat] :
% 5.27/5.57 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 = zero_zero_nat )
% 5.27/5.57 => ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_eq_0_imp_not_bit
% 5.27/5.57 thf(fact_6477_bit__Suc,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] :
% 5.27/5.57 ( ( bit_se9216721137139052372nteger @ A @ ( suc @ N2 ) )
% 5.27/5.57 = ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_Suc
% 5.27/5.57 thf(fact_6478_bit__Suc,axiom,
% 5.27/5.57 ! [A: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ A @ ( suc @ N2 ) )
% 5.27/5.57 = ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_Suc
% 5.27/5.57 thf(fact_6479_bit__Suc,axiom,
% 5.27/5.57 ! [A: nat,N2: nat] :
% 5.27/5.57 ( ( bit_se1148574629649215175it_nat @ A @ ( suc @ N2 ) )
% 5.27/5.57 = ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_Suc
% 5.27/5.57 thf(fact_6480_stable__imp__bit__iff__odd,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] :
% 5.27/5.57 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.57 = A )
% 5.27/5.57 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.27/5.57 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % stable_imp_bit_iff_odd
% 5.27/5.57 thf(fact_6481_stable__imp__bit__iff__odd,axiom,
% 5.27/5.57 ! [A: int,N2: nat] :
% 5.27/5.57 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.57 = A )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.57 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % stable_imp_bit_iff_odd
% 5.27/5.57 thf(fact_6482_stable__imp__bit__iff__odd,axiom,
% 5.27/5.57 ! [A: nat,N2: nat] :
% 5.27/5.57 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = A )
% 5.27/5.57 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.57 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % stable_imp_bit_iff_odd
% 5.27/5.57 thf(fact_6483_bit__iff__idd__imp__stable,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ! [N3: nat] :
% 5.27/5.57 ( ( bit_se9216721137139052372nteger @ A @ N3 )
% 5.27/5.57 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.57 => ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.57 = A ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_idd_imp_stable
% 5.27/5.57 thf(fact_6484_bit__iff__idd__imp__stable,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ! [N3: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ A @ N3 )
% 5.27/5.57 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.57 => ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.57 = A ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_idd_imp_stable
% 5.27/5.57 thf(fact_6485_bit__iff__idd__imp__stable,axiom,
% 5.27/5.57 ! [A: nat] :
% 5.27/5.57 ( ! [N3: nat] :
% 5.27/5.57 ( ( bit_se1148574629649215175it_nat @ A @ N3 )
% 5.27/5.57 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) )
% 5.27/5.57 => ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = A ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_idd_imp_stable
% 5.27/5.57 thf(fact_6486_abs__le__square__iff,axiom,
% 5.27/5.57 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.57 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ Y ) )
% 5.27/5.57 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_le_square_iff
% 5.27/5.57 thf(fact_6487_abs__le__square__iff,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) )
% 5.27/5.57 = ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_le_square_iff
% 5.27/5.57 thf(fact_6488_abs__le__square__iff,axiom,
% 5.27/5.57 ! [X4: rat,Y: rat] :
% 5.27/5.57 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ ( abs_abs_rat @ Y ) )
% 5.27/5.57 = ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_le_square_iff
% 5.27/5.57 thf(fact_6489_abs__le__square__iff,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) )
% 5.27/5.57 = ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_le_square_iff
% 5.27/5.57 thf(fact_6490_abs__square__eq__1,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = one_one_Code_integer )
% 5.27/5.57 = ( ( abs_abs_Code_integer @ X4 )
% 5.27/5.57 = one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_eq_1
% 5.27/5.57 thf(fact_6491_abs__square__eq__1,axiom,
% 5.27/5.57 ! [X4: rat] :
% 5.27/5.57 ( ( ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = one_one_rat )
% 5.27/5.57 = ( ( abs_abs_rat @ X4 )
% 5.27/5.57 = one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_eq_1
% 5.27/5.57 thf(fact_6492_abs__square__eq__1,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = one_one_real )
% 5.27/5.57 = ( ( abs_abs_real @ X4 )
% 5.27/5.57 = one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_eq_1
% 5.27/5.57 thf(fact_6493_abs__square__eq__1,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.57 = one_one_int )
% 5.27/5.57 = ( ( abs_abs_int @ X4 )
% 5.27/5.57 = one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_eq_1
% 5.27/5.57 thf(fact_6494_power__even__abs,axiom,
% 5.27/5.57 ! [N2: nat,A: code_integer] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N2 )
% 5.27/5.57 = ( power_8256067586552552935nteger @ A @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_even_abs
% 5.27/5.57 thf(fact_6495_power__even__abs,axiom,
% 5.27/5.57 ! [N2: nat,A: rat] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N2 )
% 5.27/5.57 = ( power_power_rat @ A @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_even_abs
% 5.27/5.57 thf(fact_6496_power__even__abs,axiom,
% 5.27/5.57 ! [N2: nat,A: real] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N2 )
% 5.27/5.57 = ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_even_abs
% 5.27/5.57 thf(fact_6497_power__even__abs,axiom,
% 5.27/5.57 ! [N2: nat,A: int] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N2 )
% 5.27/5.57 = ( power_power_int @ A @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_even_abs
% 5.27/5.57 thf(fact_6498_int__bit__bound,axiom,
% 5.27/5.57 ! [K: int] :
% 5.27/5.57 ~ ! [N3: nat] :
% 5.27/5.57 ( ! [M2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.27/5.57 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.27/5.57 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.27/5.57 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % int_bit_bound
% 5.27/5.57 thf(fact_6499_binomial__altdef__nat,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( binomial @ N2 @ K )
% 5.27/5.57 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N2 ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % binomial_altdef_nat
% 5.27/5.57 thf(fact_6500_bit__iff__odd,axiom,
% 5.27/5.57 ( bit_se9216721137139052372nteger
% 5.27/5.57 = ( ^ [A3: code_integer,N: nat] :
% 5.27/5.57 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_odd
% 5.27/5.57 thf(fact_6501_bit__iff__odd,axiom,
% 5.27/5.57 ( bit_se1146084159140164899it_int
% 5.27/5.57 = ( ^ [A3: int,N: nat] :
% 5.27/5.57 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_odd
% 5.27/5.57 thf(fact_6502_bit__iff__odd,axiom,
% 5.27/5.57 ( bit_se1148574629649215175it_nat
% 5.27/5.57 = ( ^ [A3: nat,N: nat] :
% 5.27/5.57 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_iff_odd
% 5.27/5.57 thf(fact_6503_power2__le__iff__abs__le,axiom,
% 5.27/5.57 ! [Y: code_integer,X4: code_integer] :
% 5.27/5.57 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.27/5.57 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.57 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power2_le_iff_abs_le
% 5.27/5.57 thf(fact_6504_power2__le__iff__abs__le,axiom,
% 5.27/5.57 ! [Y: real,X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.57 => ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.57 = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power2_le_iff_abs_le
% 5.27/5.57 thf(fact_6505_power2__le__iff__abs__le,axiom,
% 5.27/5.57 ! [Y: rat,X4: rat] :
% 5.27/5.57 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.27/5.57 => ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.57 = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power2_le_iff_abs_le
% 5.27/5.57 thf(fact_6506_power2__le__iff__abs__le,axiom,
% 5.27/5.57 ! [Y: int,X4: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.57 => ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.57 = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power2_le_iff_abs_le
% 5.27/5.57 thf(fact_6507_abs__square__le__1,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.27/5.57 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_le_1
% 5.27/5.57 thf(fact_6508_abs__square__le__1,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.27/5.57 = ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_le_1
% 5.27/5.57 thf(fact_6509_abs__square__le__1,axiom,
% 5.27/5.57 ! [X4: rat] :
% 5.27/5.57 ( ( ord_less_eq_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.27/5.57 = ( ord_less_eq_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_le_1
% 5.27/5.57 thf(fact_6510_abs__square__le__1,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.27/5.57 = ( ord_less_eq_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_le_1
% 5.27/5.57 thf(fact_6511_abs__square__less__1,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.27/5.57 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_less_1
% 5.27/5.57 thf(fact_6512_abs__square__less__1,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.27/5.57 = ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_less_1
% 5.27/5.57 thf(fact_6513_abs__square__less__1,axiom,
% 5.27/5.57 ! [X4: rat] :
% 5.27/5.57 ( ( ord_less_rat @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.27/5.57 = ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_less_1
% 5.27/5.57 thf(fact_6514_abs__square__less__1,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( ord_less_int @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.27/5.57 = ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_square_less_1
% 5.27/5.57 thf(fact_6515_square__fact__le__2__fact,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % square_fact_le_2_fact
% 5.27/5.57 thf(fact_6516_power__mono__even,axiom,
% 5.27/5.57 ! [N2: nat,A: code_integer,B: code_integer] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.27/5.57 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N2 ) @ ( power_8256067586552552935nteger @ B @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_mono_even
% 5.27/5.57 thf(fact_6517_power__mono__even,axiom,
% 5.27/5.57 ! [N2: nat,A: real,B: real] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.27/5.57 => ( ord_less_eq_real @ ( power_power_real @ A @ N2 ) @ ( power_power_real @ B @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_mono_even
% 5.27/5.57 thf(fact_6518_power__mono__even,axiom,
% 5.27/5.57 ! [N2: nat,A: rat,B: rat] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.27/5.57 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N2 ) @ ( power_power_rat @ B @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_mono_even
% 5.27/5.57 thf(fact_6519_power__mono__even,axiom,
% 5.27/5.57 ! [N2: nat,A: int,B: int] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.57 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.27/5.57 => ( ord_less_eq_int @ ( power_power_int @ A @ N2 ) @ ( power_power_int @ B @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_mono_even
% 5.27/5.57 thf(fact_6520_bit__int__def,axiom,
% 5.27/5.57 ( bit_se1146084159140164899it_int
% 5.27/5.57 = ( ^ [K3: int,N: nat] :
% 5.27/5.57 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_int_def
% 5.27/5.57 thf(fact_6521_fact__num__eq__if,axiom,
% 5.27/5.57 ( semiri773545260158071498ct_rat
% 5.27/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_num_eq_if
% 5.27/5.57 thf(fact_6522_fact__num__eq__if,axiom,
% 5.27/5.57 ( semiri5044797733671781792omplex
% 5.27/5.57 = ( ^ [M6: nat] : ( if_complex @ ( M6 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ M6 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ M6 @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_num_eq_if
% 5.27/5.57 thf(fact_6523_fact__num__eq__if,axiom,
% 5.27/5.57 ( semiri1406184849735516958ct_int
% 5.27/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_num_eq_if
% 5.27/5.57 thf(fact_6524_fact__num__eq__if,axiom,
% 5.27/5.57 ( semiri1408675320244567234ct_nat
% 5.27/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_num_eq_if
% 5.27/5.57 thf(fact_6525_fact__num__eq__if,axiom,
% 5.27/5.57 ( semiri2265585572941072030t_real
% 5.27/5.57 = ( ^ [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 ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_num_eq_if
% 5.27/5.57 thf(fact_6526_fact__reduce,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.57 => ( ( semiri5044797733671781792omplex @ N2 )
% 5.27/5.57 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_reduce
% 5.27/5.57 thf(fact_6527_fact__reduce,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.57 => ( ( semiri1406184849735516958ct_int @ N2 )
% 5.27/5.57 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( semiri1406184849735516958ct_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_reduce
% 5.27/5.57 thf(fact_6528_fact__reduce,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.57 => ( ( semiri1408675320244567234ct_nat @ N2 )
% 5.27/5.57 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_reduce
% 5.27/5.57 thf(fact_6529_fact__reduce,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.57 => ( ( semiri2265585572941072030t_real @ N2 )
% 5.27/5.57 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_reduce
% 5.27/5.57 thf(fact_6530_pochhammer__same,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ N2 )
% 5.27/5.57 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( semiri5044797733671781792omplex @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % pochhammer_same
% 5.27/5.57 thf(fact_6531_pochhammer__same,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( comm_s8582702949713902594nteger @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ N2 ) ) @ N2 )
% 5.27/5.57 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N2 ) @ ( semiri3624122377584611663nteger @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % pochhammer_same
% 5.27/5.57 thf(fact_6532_pochhammer__same,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( comm_s4028243227959126397er_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ N2 )
% 5.27/5.57 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( semiri773545260158071498ct_rat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % pochhammer_same
% 5.27/5.57 thf(fact_6533_pochhammer__same,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( comm_s4660882817536571857er_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N2 ) ) @ N2 )
% 5.27/5.57 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N2 ) @ ( semiri1406184849735516958ct_int @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % pochhammer_same
% 5.27/5.57 thf(fact_6534_pochhammer__same,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( comm_s7457072308508201937r_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ N2 )
% 5.27/5.57 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % pochhammer_same
% 5.27/5.57 thf(fact_6535_binomial__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) )
% 5.27/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % binomial_fact
% 5.27/5.57 thf(fact_6536_binomial__fact,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) )
% 5.27/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % binomial_fact
% 5.27/5.57 thf(fact_6537_fact__binomial,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( times_times_complex @ ( semiri5044797733671781792omplex @ K ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K ) ) )
% 5.27/5.57 = ( divide1717551699836669952omplex @ ( semiri5044797733671781792omplex @ N2 ) @ ( semiri5044797733671781792omplex @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_binomial
% 5.27/5.57 thf(fact_6538_fact__binomial,axiom,
% 5.27/5.57 ! [K: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.57 => ( ( times_times_real @ ( semiri2265585572941072030t_real @ K ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K ) ) )
% 5.27/5.57 = ( divide_divide_real @ ( semiri2265585572941072030t_real @ N2 ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ K ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_binomial
% 5.27/5.57 thf(fact_6539_even__bit__succ__iff,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] :
% 5.27/5.57 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ N2 )
% 5.27/5.57 = ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_bit_succ_iff
% 5.27/5.57 thf(fact_6540_even__bit__succ__iff,axiom,
% 5.27/5.57 ! [A: int,N2: nat] :
% 5.27/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ one_one_int @ A ) @ N2 )
% 5.27/5.57 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_bit_succ_iff
% 5.27/5.57 thf(fact_6541_even__bit__succ__iff,axiom,
% 5.27/5.57 ! [A: nat,N2: nat] :
% 5.27/5.57 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ N2 )
% 5.27/5.57 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_bit_succ_iff
% 5.27/5.57 thf(fact_6542_odd__bit__iff__bit__pred,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] :
% 5.27/5.57 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se9216721137139052372nteger @ A @ N2 )
% 5.27/5.57 = ( ( bit_se9216721137139052372nteger @ ( minus_8373710615458151222nteger @ A @ one_one_Code_integer ) @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % odd_bit_iff_bit_pred
% 5.27/5.57 thf(fact_6543_odd__bit__iff__bit__pred,axiom,
% 5.27/5.57 ! [A: int,N2: nat] :
% 5.27/5.57 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.57 = ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ A @ one_one_int ) @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % odd_bit_iff_bit_pred
% 5.27/5.57 thf(fact_6544_odd__bit__iff__bit__pred,axiom,
% 5.27/5.57 ! [A: nat,N2: nat] :
% 5.27/5.57 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.57 => ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.57 = ( ( bit_se1148574629649215175it_nat @ ( minus_minus_nat @ A @ one_one_nat ) @ N2 )
% 5.27/5.57 | ( N2 = zero_zero_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % odd_bit_iff_bit_pred
% 5.27/5.57 thf(fact_6545_bit__sum__mult__2__cases,axiom,
% 5.27/5.57 ! [A: code_integer,B: code_integer,N2: nat] :
% 5.27/5.57 ( ! [J2: nat] :
% 5.27/5.57 ~ ( bit_se9216721137139052372nteger @ A @ ( suc @ J2 ) )
% 5.27/5.57 => ( ( bit_se9216721137139052372nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.27/5.57 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.57 & ( ( N2 != zero_zero_nat )
% 5.27/5.57 => ( bit_se9216721137139052372nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_sum_mult_2_cases
% 5.27/5.57 thf(fact_6546_bit__sum__mult__2__cases,axiom,
% 5.27/5.57 ! [A: int,B: int,N2: nat] :
% 5.27/5.57 ( ! [J2: nat] :
% 5.27/5.57 ~ ( bit_se1146084159140164899it_int @ A @ ( suc @ J2 ) )
% 5.27/5.57 => ( ( bit_se1146084159140164899it_int @ ( plus_plus_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.27/5.57 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.57 & ( ( N2 != zero_zero_nat )
% 5.27/5.57 => ( bit_se1146084159140164899it_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_sum_mult_2_cases
% 5.27/5.57 thf(fact_6547_bit__sum__mult__2__cases,axiom,
% 5.27/5.57 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.57 ( ! [J2: nat] :
% 5.27/5.57 ~ ( bit_se1148574629649215175it_nat @ A @ ( suc @ J2 ) )
% 5.27/5.57 => ( ( bit_se1148574629649215175it_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ N2 )
% 5.27/5.57 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.27/5.57 & ( ( N2 != zero_zero_nat )
% 5.27/5.57 => ( bit_se1148574629649215175it_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_sum_mult_2_cases
% 5.27/5.57 thf(fact_6548_bit__rec,axiom,
% 5.27/5.57 ( bit_se9216721137139052372nteger
% 5.27/5.57 = ( ^ [A3: code_integer,N: nat] :
% 5.27/5.57 ( ( ( N = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 ) )
% 5.27/5.57 & ( ( N != zero_zero_nat )
% 5.27/5.57 => ( bit_se9216721137139052372nteger @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_rec
% 5.27/5.57 thf(fact_6549_bit__rec,axiom,
% 5.27/5.57 ( bit_se1146084159140164899it_int
% 5.27/5.57 = ( ^ [A3: int,N: nat] :
% 5.27/5.57 ( ( ( N = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 ) )
% 5.27/5.57 & ( ( N != zero_zero_nat )
% 5.27/5.57 => ( bit_se1146084159140164899it_int @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_rec
% 5.27/5.57 thf(fact_6550_bit__rec,axiom,
% 5.27/5.57 ( bit_se1148574629649215175it_nat
% 5.27/5.57 = ( ^ [A3: nat,N: nat] :
% 5.27/5.57 ( ( ( N = zero_zero_nat )
% 5.27/5.57 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 ) )
% 5.27/5.57 & ( ( N != zero_zero_nat )
% 5.27/5.57 => ( bit_se1148574629649215175it_nat @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_rec
% 5.27/5.57 thf(fact_6551_set__bit__eq,axiom,
% 5.27/5.57 ( bit_se7879613467334960850it_int
% 5.27/5.57 = ( ^ [N: nat,K3: int] :
% 5.27/5.57 ( plus_plus_int @ K3
% 5.27/5.57 @ ( times_times_int
% 5.27/5.57 @ ( zero_n2684676970156552555ol_int
% 5.27/5.57 @ ~ ( bit_se1146084159140164899it_int @ K3 @ N ) )
% 5.27/5.57 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % set_bit_eq
% 5.27/5.57 thf(fact_6552_unset__bit__eq,axiom,
% 5.27/5.57 ( bit_se4203085406695923979it_int
% 5.27/5.57 = ( ^ [N: nat,K3: int] : ( minus_minus_int @ K3 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K3 @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % unset_bit_eq
% 5.27/5.57 thf(fact_6553_take__bit__Suc__from__most,axiom,
% 5.27/5.57 ! [N2: nat,K: int] :
% 5.27/5.57 ( ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K )
% 5.27/5.57 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_Suc_from_most
% 5.27/5.57 thf(fact_6554_abs__sqrt__wlog,axiom,
% 5.27/5.57 ! [P: code_integer > code_integer > $o,X4: code_integer] :
% 5.27/5.57 ( ! [X5: code_integer] :
% 5.27/5.57 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X5 )
% 5.27/5.57 => ( P @ X5 @ ( power_8256067586552552935nteger @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.57 => ( P @ ( abs_abs_Code_integer @ X4 ) @ ( power_8256067586552552935nteger @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sqrt_wlog
% 5.27/5.57 thf(fact_6555_abs__sqrt__wlog,axiom,
% 5.27/5.57 ! [P: real > real > $o,X4: real] :
% 5.27/5.57 ( ! [X5: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.27/5.57 => ( P @ X5 @ ( power_power_real @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.57 => ( P @ ( abs_abs_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sqrt_wlog
% 5.27/5.57 thf(fact_6556_abs__sqrt__wlog,axiom,
% 5.27/5.57 ! [P: rat > rat > $o,X4: rat] :
% 5.27/5.57 ( ! [X5: rat] :
% 5.27/5.57 ( ( ord_less_eq_rat @ zero_zero_rat @ X5 )
% 5.27/5.57 => ( P @ X5 @ ( power_power_rat @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.57 => ( P @ ( abs_abs_rat @ X4 ) @ ( power_power_rat @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sqrt_wlog
% 5.27/5.57 thf(fact_6557_abs__sqrt__wlog,axiom,
% 5.27/5.57 ! [P: int > int > $o,X4: int] :
% 5.27/5.57 ( ! [X5: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.27/5.57 => ( P @ X5 @ ( power_power_int @ X5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.57 => ( P @ ( abs_abs_int @ X4 ) @ ( power_power_int @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sqrt_wlog
% 5.27/5.57 thf(fact_6558_sin__coeff__def,axiom,
% 5.27/5.57 ( sin_coeff
% 5.27/5.57 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sin_coeff_def
% 5.27/5.57 thf(fact_6559_binomial__code,axiom,
% 5.27/5.57 ( binomial
% 5.27/5.57 = ( ^ [N: nat,K3: nat] : ( if_nat @ ( ord_less_nat @ N @ K3 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K3 ) ) @ ( binomial @ N @ ( minus_minus_nat @ N @ K3 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N @ K3 ) @ one_one_nat ) @ N @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K3 ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % binomial_code
% 5.27/5.57 thf(fact_6560_cos__coeff__def,axiom,
% 5.27/5.57 ( cos_coeff
% 5.27/5.57 = ( ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ zero_zero_real ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % cos_coeff_def
% 5.27/5.57 thf(fact_6561_arctan__double,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.57 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X4 ) )
% 5.27/5.57 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_double
% 5.27/5.57 thf(fact_6562_fact__code,axiom,
% 5.27/5.57 ( semiri1406184849735516958ct_int
% 5.27/5.57 = ( ^ [N: nat] : ( semiri1314217659103216013at_int @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_code
% 5.27/5.57 thf(fact_6563_fact__code,axiom,
% 5.27/5.57 ( semiri1408675320244567234ct_nat
% 5.27/5.57 = ( ^ [N: nat] : ( semiri1316708129612266289at_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_code
% 5.27/5.57 thf(fact_6564_fact__code,axiom,
% 5.27/5.57 ( semiri2265585572941072030t_real
% 5.27/5.57 = ( ^ [N: nat] : ( semiri5074537144036343181t_real @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N @ one_one_nat ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fact_code
% 5.27/5.57 thf(fact_6565_zabs__less__one__iff,axiom,
% 5.27/5.57 ! [Z: int] :
% 5.27/5.57 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.27/5.57 = ( Z = zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % zabs_less_one_iff
% 5.27/5.57 thf(fact_6566_zero__less__arctan__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X4 ) )
% 5.27/5.57 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_less_arctan_iff
% 5.27/5.57 thf(fact_6567_arctan__less__zero__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( arctan @ X4 ) @ zero_zero_real )
% 5.27/5.57 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_less_zero_iff
% 5.27/5.57 thf(fact_6568_zero__le__arctan__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X4 ) )
% 5.27/5.57 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % zero_le_arctan_iff
% 5.27/5.57 thf(fact_6569_arctan__le__zero__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( arctan @ X4 ) @ zero_zero_real )
% 5.27/5.57 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_le_zero_iff
% 5.27/5.57 thf(fact_6570_cos__coeff__0,axiom,
% 5.27/5.57 ( ( cos_coeff @ zero_zero_nat )
% 5.27/5.57 = one_one_real ) ).
% 5.27/5.57
% 5.27/5.57 % cos_coeff_0
% 5.27/5.57 thf(fact_6571_arctan__less__iff,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 5.27/5.57 = ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_less_iff
% 5.27/5.57 thf(fact_6572_arctan__monotone,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_real @ X4 @ Y )
% 5.27/5.57 => ( ord_less_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_monotone
% 5.27/5.57 thf(fact_6573_arctan__le__iff,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 5.27/5.57 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_le_iff
% 5.27/5.57 thf(fact_6574_arctan__monotone_H,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.57 => ( ord_less_eq_real @ ( arctan @ X4 ) @ ( arctan @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_monotone'
% 5.27/5.57 thf(fact_6575_bit__Suc__0__iff,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.57 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_Suc_0_iff
% 5.27/5.57 thf(fact_6576_not__bit__Suc__0__Suc,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_bit_Suc_0_Suc
% 5.27/5.57 thf(fact_6577_abs__div,axiom,
% 5.27/5.57 ! [Y: int,X4: int] :
% 5.27/5.57 ( ( dvd_dvd_int @ Y @ X4 )
% 5.27/5.57 => ( ( abs_abs_int @ ( divide_divide_int @ X4 @ Y ) )
% 5.27/5.57 = ( divide_divide_int @ ( abs_abs_int @ X4 ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_div
% 5.27/5.57 thf(fact_6578_sin__coeff__Suc,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( sin_coeff @ ( suc @ N2 ) )
% 5.27/5.57 = ( divide_divide_real @ ( cos_coeff @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sin_coeff_Suc
% 5.27/5.57 thf(fact_6579_not__bit__Suc__0__numeral,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_bit_Suc_0_numeral
% 5.27/5.57 thf(fact_6580_zabs__def,axiom,
% 5.27/5.57 ( abs_abs_int
% 5.27/5.57 = ( ^ [I3: int] : ( if_int @ ( ord_less_int @ I3 @ zero_zero_int ) @ ( uminus_uminus_int @ I3 ) @ I3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % zabs_def
% 5.27/5.57 thf(fact_6581_dvd__imp__le__int,axiom,
% 5.27/5.57 ! [I2: int,D: int] :
% 5.27/5.57 ( ( I2 != zero_zero_int )
% 5.27/5.57 => ( ( dvd_dvd_int @ D @ I2 )
% 5.27/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % dvd_imp_le_int
% 5.27/5.57 thf(fact_6582_abs__mod__less,axiom,
% 5.27/5.57 ! [L: int,K: int] :
% 5.27/5.57 ( ( L != zero_zero_int )
% 5.27/5.57 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L ) ) @ ( abs_abs_int @ L ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mod_less
% 5.27/5.57 thf(fact_6583_cos__coeff__Suc,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( cos_coeff @ ( suc @ N2 ) )
% 5.27/5.57 = ( divide_divide_real @ ( uminus_uminus_real @ ( sin_coeff @ N2 ) ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % cos_coeff_Suc
% 5.27/5.57 thf(fact_6584_fold__atLeastAtMost__nat_Oelims,axiom,
% 5.27/5.57 ! [X4: nat > nat > nat,Xa: nat,Xb: nat,Xc: nat,Y: nat] :
% 5.27/5.57 ( ( ( set_fo2584398358068434914at_nat @ X4 @ Xa @ Xb @ Xc )
% 5.27/5.57 = Y )
% 5.27/5.57 => ( ( ( ord_less_nat @ Xb @ Xa )
% 5.27/5.57 => ( Y = Xc ) )
% 5.27/5.57 & ( ~ ( ord_less_nat @ Xb @ Xa )
% 5.27/5.57 => ( Y
% 5.27/5.57 = ( set_fo2584398358068434914at_nat @ X4 @ ( plus_plus_nat @ Xa @ one_one_nat ) @ Xb @ ( X4 @ Xa @ Xc ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fold_atLeastAtMost_nat.elims
% 5.27/5.57 thf(fact_6585_fold__atLeastAtMost__nat_Osimps,axiom,
% 5.27/5.57 ( set_fo2584398358068434914at_nat
% 5.27/5.57 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % fold_atLeastAtMost_nat.simps
% 5.27/5.57 thf(fact_6586_even__add__abs__iff,axiom,
% 5.27/5.57 ! [K: int,L: int] :
% 5.27/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L ) ) )
% 5.27/5.57 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_add_abs_iff
% 5.27/5.57 thf(fact_6587_even__abs__add__iff,axiom,
% 5.27/5.57 ! [K: int,L: int] :
% 5.27/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L ) )
% 5.27/5.57 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_abs_add_iff
% 5.27/5.57 thf(fact_6588_bit__nat__def,axiom,
% 5.27/5.57 ( bit_se1148574629649215175it_nat
% 5.27/5.57 = ( ^ [M6: nat,N: nat] :
% 5.27/5.57 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_nat_def
% 5.27/5.57 thf(fact_6589_nat__intermed__int__val,axiom,
% 5.27/5.57 ! [M: nat,N2: nat,F: nat > int,K: int] :
% 5.27/5.57 ( ! [I4: nat] :
% 5.27/5.57 ( ( ( ord_less_eq_nat @ M @ I4 )
% 5.27/5.57 & ( ord_less_nat @ I4 @ N2 ) )
% 5.27/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.27/5.57 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.27/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.27/5.57 => ? [I4: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ M @ I4 )
% 5.27/5.57 & ( ord_less_eq_nat @ I4 @ N2 )
% 5.27/5.57 & ( ( F @ I4 )
% 5.27/5.57 = K ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % nat_intermed_int_val
% 5.27/5.57 thf(fact_6590_incr__lemma,axiom,
% 5.27/5.57 ! [D: int,Z: int,X4: int] :
% 5.27/5.57 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.57 => ( ord_less_int @ Z @ ( plus_plus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % incr_lemma
% 5.27/5.57 thf(fact_6591_decr__lemma,axiom,
% 5.27/5.57 ! [D: int,X4: int,Z: int] :
% 5.27/5.57 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.57 => ( ord_less_int @ ( minus_minus_int @ X4 @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.27/5.57
% 5.27/5.57 % decr_lemma
% 5.27/5.57 thf(fact_6592_nat__ivt__aux,axiom,
% 5.27/5.57 ! [N2: nat,F: nat > int,K: int] :
% 5.27/5.57 ( ! [I4: nat] :
% 5.27/5.57 ( ( ord_less_nat @ I4 @ N2 )
% 5.27/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.27/5.57 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.27/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.27/5.57 => ? [I4: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ I4 @ N2 )
% 5.27/5.57 & ( ( F @ I4 )
% 5.27/5.57 = K ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % nat_ivt_aux
% 5.27/5.57 thf(fact_6593_complex__mod__minus__le__complex__mod,axiom,
% 5.27/5.57 ! [X4: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % complex_mod_minus_le_complex_mod
% 5.27/5.57 thf(fact_6594_complex__mod__triangle__ineq2,axiom,
% 5.27/5.57 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % complex_mod_triangle_ineq2
% 5.27/5.57 thf(fact_6595_nat0__intermed__int__val,axiom,
% 5.27/5.57 ! [N2: nat,F: nat > int,K: int] :
% 5.27/5.57 ( ! [I4: nat] :
% 5.27/5.57 ( ( ord_less_nat @ I4 @ N2 )
% 5.27/5.57 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.27/5.57 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.27/5.57 => ( ( ord_less_eq_int @ K @ ( F @ N2 ) )
% 5.27/5.57 => ? [I4: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ I4 @ N2 )
% 5.27/5.57 & ( ( F @ I4 )
% 5.27/5.57 = K ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % nat0_intermed_int_val
% 5.27/5.57 thf(fact_6596_arctan__add,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.57 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.57 => ( ( plus_plus_real @ ( arctan @ X4 ) @ ( arctan @ Y ) )
% 5.27/5.57 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % arctan_add
% 5.27/5.57 thf(fact_6597_xor__int__unfold,axiom,
% 5.27/5.57 ( bit_se6526347334894502574or_int
% 5.27/5.57 = ( ^ [K3: int,L2: int] :
% 5.27/5.57 ( if_int
% 5.27/5.57 @ ( K3
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 @ ( bit_ri7919022796975470100ot_int @ L2 )
% 5.27/5.57 @ ( if_int
% 5.27/5.57 @ ( L2
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 @ ( bit_ri7919022796975470100ot_int @ K3 )
% 5.27/5.57 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = 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 @ L2 @ ( 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 @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % xor_int_unfold
% 5.27/5.57 thf(fact_6598_mask__numeral,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.57 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % mask_numeral
% 5.27/5.57 thf(fact_6599_mask__numeral,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.57 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % mask_numeral
% 5.27/5.57 thf(fact_6600_modulo__int__unfold,axiom,
% 5.27/5.57 ! [L: int,K: int,N2: nat,M: nat] :
% 5.27/5.57 ( ( ( ( ( sgn_sgn_int @ L )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( ( sgn_sgn_int @ K )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( N2 = zero_zero_nat ) )
% 5.27/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.27/5.57 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( ( sgn_sgn_int @ K )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( N2 = zero_zero_nat ) )
% 5.27/5.57 => ( ( ( ( sgn_sgn_int @ K )
% 5.27/5.57 = ( sgn_sgn_int @ L ) )
% 5.27/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) )
% 5.27/5.57 & ( ( ( sgn_sgn_int @ K )
% 5.27/5.57 != ( sgn_sgn_int @ L ) )
% 5.27/5.57 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = ( times_times_int @ ( sgn_sgn_int @ L )
% 5.27/5.57 @ ( minus_minus_int
% 5.27/5.57 @ ( semiri1314217659103216013at_int
% 5.27/5.57 @ ( times_times_nat @ N2
% 5.27/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.57 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) )
% 5.27/5.57 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % modulo_int_unfold
% 5.27/5.57 thf(fact_6601_divide__int__unfold,axiom,
% 5.27/5.57 ! [L: int,K: int,N2: nat,M: nat] :
% 5.27/5.57 ( ( ( ( ( sgn_sgn_int @ L )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( ( sgn_sgn_int @ K )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( N2 = zero_zero_nat ) )
% 5.27/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = zero_zero_int ) )
% 5.27/5.57 & ( ~ ( ( ( sgn_sgn_int @ L )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( ( sgn_sgn_int @ K )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 | ( N2 = zero_zero_nat ) )
% 5.27/5.57 => ( ( ( ( sgn_sgn_int @ K )
% 5.27/5.57 = ( sgn_sgn_int @ L ) )
% 5.27/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) )
% 5.27/5.57 & ( ( ( sgn_sgn_int @ K )
% 5.27/5.57 != ( sgn_sgn_int @ L ) )
% 5.27/5.57 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ N2 ) ) )
% 5.27/5.57 = ( uminus_uminus_int
% 5.27/5.57 @ ( semiri1314217659103216013at_int
% 5.27/5.57 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N2 )
% 5.27/5.57 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.57 @ ~ ( dvd_dvd_nat @ N2 @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % divide_int_unfold
% 5.27/5.57 thf(fact_6602_tanh__real__altdef,axiom,
% 5.27/5.57 ( tanh_real
% 5.27/5.57 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % tanh_real_altdef
% 5.27/5.57 thf(fact_6603_and__int__unfold,axiom,
% 5.27/5.57 ( bit_se725231765392027082nd_int
% 5.27/5.57 = ( ^ [K3: int,L2: int] :
% 5.27/5.57 ( if_int
% 5.27/5.57 @ ( ( K3 = zero_zero_int )
% 5.27/5.57 | ( L2 = zero_zero_int ) )
% 5.27/5.57 @ zero_zero_int
% 5.27/5.57 @ ( if_int
% 5.27/5.57 @ ( K3
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 @ L2
% 5.27/5.57 @ ( if_int
% 5.27/5.57 @ ( L2
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 @ K3
% 5.27/5.57 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_int_unfold
% 5.27/5.57 thf(fact_6604_and_Oidem,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.idem
% 5.27/5.57 thf(fact_6605_and_Oidem,axiom,
% 5.27/5.57 ! [A: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.idem
% 5.27/5.57 thf(fact_6606_and_Oleft__idem,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_idem
% 5.27/5.57 thf(fact_6607_and_Oleft__idem,axiom,
% 5.27/5.57 ! [A: nat,B: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_idem
% 5.27/5.57 thf(fact_6608_and_Oright__idem,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.right_idem
% 5.27/5.57 thf(fact_6609_and_Oright__idem,axiom,
% 5.27/5.57 ! [A: nat,B: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.right_idem
% 5.27/5.57 thf(fact_6610_sgn__sgn,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = ( sgn_sgn_int @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_sgn
% 5.27/5.57 thf(fact_6611_sgn__sgn,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = ( sgn_sgn_real @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_sgn
% 5.27/5.57 thf(fact_6612_sgn__sgn,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( sgn_sgn_complex @ ( sgn_sgn_complex @ A ) )
% 5.27/5.57 = ( sgn_sgn_complex @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_sgn
% 5.27/5.57 thf(fact_6613_sgn__sgn,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = ( sgn_sgn_Code_integer @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_sgn
% 5.27/5.57 thf(fact_6614_sgn__sgn,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = ( sgn_sgn_rat @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_sgn
% 5.27/5.57 thf(fact_6615_bit_Odouble__compl,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % bit.double_compl
% 5.27/5.57 thf(fact_6616_bit_Ocompl__eq__compl__iff,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( ( bit_ri7919022796975470100ot_int @ X4 )
% 5.27/5.57 = ( bit_ri7919022796975470100ot_int @ Y ) )
% 5.27/5.57 = ( X4 = Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.compl_eq_compl_iff
% 5.27/5.57 thf(fact_6617_mask__nat__positive__iff,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.27/5.57 = ( ord_less_nat @ zero_zero_nat @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % mask_nat_positive_iff
% 5.27/5.57 thf(fact_6618_and__zero__eq,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_zero_eq
% 5.27/5.57 thf(fact_6619_and__zero__eq,axiom,
% 5.27/5.57 ! [A: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.27/5.57 = zero_zero_nat ) ).
% 5.27/5.57
% 5.27/5.57 % and_zero_eq
% 5.27/5.57 thf(fact_6620_zero__and__eq,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % zero_and_eq
% 5.27/5.57 thf(fact_6621_zero__and__eq,axiom,
% 5.27/5.57 ! [A: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.27/5.57 = zero_zero_nat ) ).
% 5.27/5.57
% 5.27/5.57 % zero_and_eq
% 5.27/5.57 thf(fact_6622_bit_Oconj__zero__left,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X4 )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_zero_left
% 5.27/5.57 thf(fact_6623_bit_Oconj__zero__right,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ X4 @ zero_zero_int )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_zero_right
% 5.27/5.57 thf(fact_6624_sgn__0,axiom,
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ zero_z3403309356797280102nteger )
% 5.27/5.57 = zero_z3403309356797280102nteger ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0
% 5.27/5.57 thf(fact_6625_sgn__0,axiom,
% 5.27/5.57 ( ( sgn_sgn_complex @ zero_zero_complex )
% 5.27/5.57 = zero_zero_complex ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0
% 5.27/5.57 thf(fact_6626_sgn__0,axiom,
% 5.27/5.57 ( ( sgn_sgn_real @ zero_zero_real )
% 5.27/5.57 = zero_zero_real ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0
% 5.27/5.57 thf(fact_6627_sgn__0,axiom,
% 5.27/5.57 ( ( sgn_sgn_rat @ zero_zero_rat )
% 5.27/5.57 = zero_zero_rat ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0
% 5.27/5.57 thf(fact_6628_sgn__0,axiom,
% 5.27/5.57 ( ( sgn_sgn_int @ zero_zero_int )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0
% 5.27/5.57 thf(fact_6629_sgn__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_int @ one_one_int )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_1
% 5.27/5.57 thf(fact_6630_sgn__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_real @ one_one_real )
% 5.27/5.57 = one_one_real ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_1
% 5.27/5.57 thf(fact_6631_sgn__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_complex @ one_one_complex )
% 5.27/5.57 = one_one_complex ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_1
% 5.27/5.57 thf(fact_6632_sgn__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ one_one_Code_integer )
% 5.27/5.57 = one_one_Code_integer ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_1
% 5.27/5.57 thf(fact_6633_sgn__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_rat @ one_one_rat )
% 5.27/5.57 = one_one_rat ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_1
% 5.27/5.57 thf(fact_6634_sgn__one,axiom,
% 5.27/5.57 ( ( sgn_sgn_real @ one_one_real )
% 5.27/5.57 = one_one_real ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_one
% 5.27/5.57 thf(fact_6635_sgn__one,axiom,
% 5.27/5.57 ( ( sgn_sgn_complex @ one_one_complex )
% 5.27/5.57 = one_one_complex ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_one
% 5.27/5.57 thf(fact_6636_sgn__divide,axiom,
% 5.27/5.57 ! [A: rat,B: rat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( divide_divide_rat @ A @ B ) )
% 5.27/5.57 = ( divide_divide_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_divide
% 5.27/5.57 thf(fact_6637_sgn__divide,axiom,
% 5.27/5.57 ! [A: real,B: real] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.57 = ( divide_divide_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_divide
% 5.27/5.57 thf(fact_6638_sgn__divide,axiom,
% 5.27/5.57 ! [A: complex,B: complex] :
% 5.27/5.57 ( ( sgn_sgn_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.57 = ( divide1717551699836669952omplex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_divide
% 5.27/5.57 thf(fact_6639_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.57 = ( uminus_uminus_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.sgn_minus
% 5.27/5.57 thf(fact_6640_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( uminus_uminus_int @ A ) )
% 5.27/5.57 = ( uminus_uminus_int @ ( sgn_sgn_int @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.sgn_minus
% 5.27/5.57 thf(fact_6641_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.57 = ( uminus1482373934393186551omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.sgn_minus
% 5.27/5.57 thf(fact_6642_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.sgn_minus
% 5.27/5.57 thf(fact_6643_idom__abs__sgn__class_Osgn__minus,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.57 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.sgn_minus
% 5.27/5.57 thf(fact_6644_power__sgn,axiom,
% 5.27/5.57 ! [A: code_integer,N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( power_8256067586552552935nteger @ A @ N2 ) )
% 5.27/5.57 = ( power_8256067586552552935nteger @ ( sgn_sgn_Code_integer @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_sgn
% 5.27/5.57 thf(fact_6645_power__sgn,axiom,
% 5.27/5.57 ! [A: rat,N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( power_power_rat @ A @ N2 ) )
% 5.27/5.57 = ( power_power_rat @ ( sgn_sgn_rat @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_sgn
% 5.27/5.57 thf(fact_6646_power__sgn,axiom,
% 5.27/5.57 ! [A: real,N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( power_power_real @ A @ N2 ) )
% 5.27/5.57 = ( power_power_real @ ( sgn_sgn_real @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_sgn
% 5.27/5.57 thf(fact_6647_power__sgn,axiom,
% 5.27/5.57 ! [A: int,N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( power_power_int @ A @ N2 ) )
% 5.27/5.57 = ( power_power_int @ ( sgn_sgn_int @ A ) @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % power_sgn
% 5.27/5.57 thf(fact_6648_exp__less__cancel__iff,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 5.27/5.57 = ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_less_cancel_iff
% 5.27/5.57 thf(fact_6649_exp__less__mono,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_real @ X4 @ Y )
% 5.27/5.57 => ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_less_mono
% 5.27/5.57 thf(fact_6650_take__bit__and,axiom,
% 5.27/5.57 ! [N2: nat,A: int,B: int] :
% 5.27/5.57 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) @ ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_and
% 5.27/5.57 thf(fact_6651_take__bit__and,axiom,
% 5.27/5.57 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.57 ( ( bit_se2925701944663578781it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N2 @ A ) @ ( bit_se2925701944663578781it_nat @ N2 @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_and
% 5.27/5.57 thf(fact_6652_exp__le__cancel__iff,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 5.27/5.57 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_le_cancel_iff
% 5.27/5.57 thf(fact_6653_bit_Oxor__compl__left,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ Y )
% 5.27/5.57 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_compl_left
% 5.27/5.57 thf(fact_6654_bit_Oxor__compl__right,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ Y ) )
% 5.27/5.57 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ X4 @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_compl_right
% 5.27/5.57 thf(fact_6655_sgn__less,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ ( sgn_sgn_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.27/5.57 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_less
% 5.27/5.57 thf(fact_6656_sgn__less,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ord_less_real @ ( sgn_sgn_real @ A ) @ zero_zero_real )
% 5.27/5.57 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_less
% 5.27/5.57 thf(fact_6657_sgn__less,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ord_less_rat @ ( sgn_sgn_rat @ A ) @ zero_zero_rat )
% 5.27/5.57 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_less
% 5.27/5.57 thf(fact_6658_sgn__less,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ord_less_int @ ( sgn_sgn_int @ A ) @ zero_zero_int )
% 5.27/5.57 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_less
% 5.27/5.57 thf(fact_6659_sgn__greater,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_greater
% 5.27/5.57 thf(fact_6660_sgn__greater,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_greater
% 5.27/5.57 thf(fact_6661_sgn__greater,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ord_less_rat @ zero_zero_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_greater
% 5.27/5.57 thf(fact_6662_sgn__greater,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ord_less_int @ zero_zero_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_greater
% 5.27/5.57 thf(fact_6663_exp__zero,axiom,
% 5.27/5.57 ( ( exp_complex @ zero_zero_complex )
% 5.27/5.57 = one_one_complex ) ).
% 5.27/5.57
% 5.27/5.57 % exp_zero
% 5.27/5.57 thf(fact_6664_exp__zero,axiom,
% 5.27/5.57 ( ( exp_real @ zero_zero_real )
% 5.27/5.57 = one_one_real ) ).
% 5.27/5.57
% 5.27/5.57 % exp_zero
% 5.27/5.57 thf(fact_6665_bit_Oconj__one__right,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( bit_se3949692690581998587nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_one_right
% 5.27/5.57 thf(fact_6666_bit_Oconj__one__right,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_one_right
% 5.27/5.57 thf(fact_6667_and_Oright__neutral,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.right_neutral
% 5.27/5.57 thf(fact_6668_and_Oright__neutral,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.right_neutral
% 5.27/5.57 thf(fact_6669_and_Oleft__neutral,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_neutral
% 5.27/5.57 thf(fact_6670_and_Oleft__neutral,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_neutral
% 5.27/5.57 thf(fact_6671_divide__sgn,axiom,
% 5.27/5.57 ! [A: rat,B: rat] :
% 5.27/5.57 ( ( divide_divide_rat @ A @ ( sgn_sgn_rat @ B ) )
% 5.27/5.57 = ( times_times_rat @ A @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % divide_sgn
% 5.27/5.57 thf(fact_6672_divide__sgn,axiom,
% 5.27/5.57 ! [A: real,B: real] :
% 5.27/5.57 ( ( divide_divide_real @ A @ ( sgn_sgn_real @ B ) )
% 5.27/5.57 = ( times_times_real @ A @ ( sgn_sgn_real @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % divide_sgn
% 5.27/5.57 thf(fact_6673_mask__0,axiom,
% 5.27/5.57 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.27/5.57 = zero_zero_nat ) ).
% 5.27/5.57
% 5.27/5.57 % mask_0
% 5.27/5.57 thf(fact_6674_mask__0,axiom,
% 5.27/5.57 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % mask_0
% 5.27/5.57 thf(fact_6675_mask__eq__0__iff,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ( bit_se2002935070580805687sk_nat @ N2 )
% 5.27/5.57 = zero_zero_nat )
% 5.27/5.57 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.57
% 5.27/5.57 % mask_eq_0_iff
% 5.27/5.57 thf(fact_6676_mask__eq__0__iff,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( ( bit_se2000444600071755411sk_int @ N2 )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.57
% 5.27/5.57 % mask_eq_0_iff
% 5.27/5.57 thf(fact_6677_bit_Oconj__cancel__left,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_cancel_left
% 5.27/5.57 thf(fact_6678_bit_Oconj__cancel__right,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_cancel_right
% 5.27/5.57 thf(fact_6679_exp__eq__one__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ( exp_real @ X4 )
% 5.27/5.57 = one_one_real )
% 5.27/5.57 = ( X4 = zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_eq_one_iff
% 5.27/5.57 thf(fact_6680_and__nonnegative__int__iff,axiom,
% 5.27/5.57 ! [K: int,L: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.27/5.57 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.57 | ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_nonnegative_int_iff
% 5.27/5.57 thf(fact_6681_and__negative__int__iff,axiom,
% 5.27/5.57 ! [K: int,L: int] :
% 5.27/5.57 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ zero_zero_int )
% 5.27/5.57 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.27/5.57 & ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_negative_int_iff
% 5.27/5.57 thf(fact_6682_sgn__pos,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.27/5.57 => ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 = one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_pos
% 5.27/5.57 thf(fact_6683_sgn__pos,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.57 => ( ( sgn_sgn_real @ A )
% 5.27/5.57 = one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_pos
% 5.27/5.57 thf(fact_6684_sgn__pos,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.57 => ( ( sgn_sgn_rat @ A )
% 5.27/5.57 = one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_pos
% 5.27/5.57 thf(fact_6685_sgn__pos,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ord_less_int @ zero_zero_int @ A )
% 5.27/5.57 => ( ( sgn_sgn_int @ A )
% 5.27/5.57 = one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_pos
% 5.27/5.57 thf(fact_6686_bit_Ocompl__one,axiom,
% 5.27/5.57 ( ( bit_ri7632146776885996613nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = zero_z3403309356797280102nteger ) ).
% 5.27/5.57
% 5.27/5.57 % bit.compl_one
% 5.27/5.57 thf(fact_6687_bit_Ocompl__one,axiom,
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % bit.compl_one
% 5.27/5.57 thf(fact_6688_bit_Ocompl__zero,axiom,
% 5.27/5.57 ( ( bit_ri7632146776885996613nteger @ zero_z3403309356797280102nteger )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.compl_zero
% 5.27/5.57 thf(fact_6689_bit_Ocompl__zero,axiom,
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ zero_zero_int )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.compl_zero
% 5.27/5.57 thf(fact_6690_and__numerals_I2_J,axiom,
% 5.27/5.57 ! [Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(2)
% 5.27/5.57 thf(fact_6691_and__numerals_I2_J,axiom,
% 5.27/5.57 ! [Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.57 = one_one_nat ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(2)
% 5.27/5.57 thf(fact_6692_and__numerals_I8_J,axiom,
% 5.27/5.57 ! [X4: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ one_one_int )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(8)
% 5.27/5.57 thf(fact_6693_and__numerals_I8_J,axiom,
% 5.27/5.57 ! [X4: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ one_one_nat )
% 5.27/5.57 = one_one_nat ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(8)
% 5.27/5.57 thf(fact_6694_abs__sgn__eq__1,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( A != zero_z3403309356797280102nteger )
% 5.27/5.57 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sgn_eq_1
% 5.27/5.57 thf(fact_6695_abs__sgn__eq__1,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( A != zero_zero_real )
% 5.27/5.57 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sgn_eq_1
% 5.27/5.57 thf(fact_6696_abs__sgn__eq__1,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( A != zero_zero_rat )
% 5.27/5.57 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sgn_eq_1
% 5.27/5.57 thf(fact_6697_abs__sgn__eq__1,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( A != zero_zero_int )
% 5.27/5.57 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % abs_sgn_eq_1
% 5.27/5.57 thf(fact_6698_sgn__mult__self__eq,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_self_eq
% 5.27/5.57 thf(fact_6699_sgn__mult__self__eq,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_self_eq
% 5.27/5.57 thf(fact_6700_sgn__mult__self__eq,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_self_eq
% 5.27/5.57 thf(fact_6701_sgn__mult__self__eq,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_self_eq
% 5.27/5.57 thf(fact_6702_mask__Suc__0,axiom,
% 5.27/5.57 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.27/5.57 = one_one_nat ) ).
% 5.27/5.57
% 5.27/5.57 % mask_Suc_0
% 5.27/5.57 thf(fact_6703_mask__Suc__0,axiom,
% 5.27/5.57 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % mask_Suc_0
% 5.27/5.57 thf(fact_6704_bit_Oxor__one__left,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( bit_se3222712562003087583nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X4 )
% 5.27/5.57 = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_one_left
% 5.27/5.57 thf(fact_6705_bit_Oxor__one__left,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ one_one_int ) @ X4 )
% 5.27/5.57 = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_one_left
% 5.27/5.57 thf(fact_6706_bit_Oxor__one__right,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( bit_se3222712562003087583nteger @ X4 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = ( bit_ri7632146776885996613nteger @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_one_right
% 5.27/5.57 thf(fact_6707_bit_Oxor__one__right,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ X4 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = ( bit_ri7919022796975470100ot_int @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_one_right
% 5.27/5.57 thf(fact_6708_bit_Oxor__cancel__left,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( bit_se3222712562003087583nteger @ ( bit_ri7632146776885996613nteger @ X4 ) @ X4 )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_cancel_left
% 5.27/5.57 thf(fact_6709_bit_Oxor__cancel__left,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ ( bit_ri7919022796975470100ot_int @ X4 ) @ X4 )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_cancel_left
% 5.27/5.57 thf(fact_6710_bit_Oxor__cancel__right,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( bit_se3222712562003087583nteger @ X4 @ ( bit_ri7632146776885996613nteger @ X4 ) )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_cancel_right
% 5.27/5.57 thf(fact_6711_bit_Oxor__cancel__right,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( bit_se6526347334894502574or_int @ X4 @ ( bit_ri7919022796975470100ot_int @ X4 ) )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.xor_cancel_right
% 5.27/5.57 thf(fact_6712_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( sgn_sgn_complex @ ( abs_abs_complex @ A ) )
% 5.27/5.57 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.abs_sgn
% 5.27/5.57 thf(fact_6713_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( abs_abs_real @ A ) )
% 5.27/5.57 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.abs_sgn
% 5.27/5.57 thf(fact_6714_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( abs_abs_rat @ A ) )
% 5.27/5.57 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.abs_sgn
% 5.27/5.57 thf(fact_6715_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( abs_abs_int @ A ) )
% 5.27/5.57 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.abs_sgn
% 5.27/5.57 thf(fact_6716_idom__abs__sgn__class_Oabs__sgn,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.57 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % idom_abs_sgn_class.abs_sgn
% 5.27/5.57 thf(fact_6717_sgn__abs,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( abs_abs_complex @ ( sgn_sgn_complex @ A ) )
% 5.27/5.57 = ( zero_n1201886186963655149omplex @ ( A != zero_zero_complex ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_abs
% 5.27/5.57 thf(fact_6718_sgn__abs,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = ( zero_n3304061248610475627l_real @ ( A != zero_zero_real ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_abs
% 5.27/5.57 thf(fact_6719_sgn__abs,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = ( zero_n2052037380579107095ol_rat @ ( A != zero_zero_rat ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_abs
% 5.27/5.57 thf(fact_6720_sgn__abs,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = ( zero_n2684676970156552555ol_int @ ( A != zero_zero_int ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_abs
% 5.27/5.57 thf(fact_6721_sgn__abs,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = ( zero_n356916108424825756nteger @ ( A != zero_z3403309356797280102nteger ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_abs
% 5.27/5.57 thf(fact_6722_one__less__exp__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) )
% 5.27/5.57 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % one_less_exp_iff
% 5.27/5.57 thf(fact_6723_exp__less__one__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ ( exp_real @ X4 ) @ one_one_real )
% 5.27/5.57 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_less_one_iff
% 5.27/5.57 thf(fact_6724_exp__le__one__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ ( exp_real @ X4 ) @ one_one_real )
% 5.27/5.57 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_le_one_iff
% 5.27/5.57 thf(fact_6725_one__le__exp__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X4 ) )
% 5.27/5.57 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % one_le_exp_iff
% 5.27/5.57 thf(fact_6726_take__bit__minus__one__eq__mask,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( bit_se1745604003318907178nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = ( bit_se2119862282449309892nteger @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_minus_one_eq_mask
% 5.27/5.57 thf(fact_6727_take__bit__minus__one__eq__mask,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( bit_se2923211474154528505it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_minus_one_eq_mask
% 5.27/5.57 thf(fact_6728_not__negative__int__iff,axiom,
% 5.27/5.57 ! [K: int] :
% 5.27/5.57 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.27/5.57 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_negative_int_iff
% 5.27/5.57 thf(fact_6729_not__nonnegative__int__iff,axiom,
% 5.27/5.57 ! [K: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.27/5.57 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_nonnegative_int_iff
% 5.27/5.57 thf(fact_6730_exp__ln,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.57 => ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.57 = X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_ln
% 5.27/5.57 thf(fact_6731_exp__ln__iff,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( ( exp_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.57 = X4 )
% 5.27/5.57 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_ln_iff
% 5.27/5.57 thf(fact_6732_minus__not__numeral__eq,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( uminus1351360451143612070nteger @ ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) )
% 5.27/5.57 = ( numera6620942414471956472nteger @ ( inc @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % minus_not_numeral_eq
% 5.27/5.57 thf(fact_6733_minus__not__numeral__eq,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( uminus_uminus_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.57 = ( numeral_numeral_int @ ( inc @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % minus_not_numeral_eq
% 5.27/5.57 thf(fact_6734_and__numerals_I1_J,axiom,
% 5.27/5.57 ! [Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(1)
% 5.27/5.57 thf(fact_6735_and__numerals_I1_J,axiom,
% 5.27/5.57 ! [Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.57 = zero_zero_nat ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(1)
% 5.27/5.57 thf(fact_6736_and__numerals_I5_J,axiom,
% 5.27/5.57 ! [X4: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ one_one_int )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(5)
% 5.27/5.57 thf(fact_6737_and__numerals_I5_J,axiom,
% 5.27/5.57 ! [X4: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ one_one_nat )
% 5.27/5.57 = zero_zero_nat ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(5)
% 5.27/5.57 thf(fact_6738_sgn__neg,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.57 => ( ( sgn_sgn_real @ A )
% 5.27/5.57 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_neg
% 5.27/5.57 thf(fact_6739_sgn__neg,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ord_less_int @ A @ zero_zero_int )
% 5.27/5.57 => ( ( sgn_sgn_int @ A )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_neg
% 5.27/5.57 thf(fact_6740_sgn__neg,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.27/5.57 => ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_neg
% 5.27/5.57 thf(fact_6741_sgn__neg,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.57 => ( ( sgn_sgn_rat @ A )
% 5.27/5.57 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_neg
% 5.27/5.57 thf(fact_6742_and__numerals_I3_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.57 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(3)
% 5.27/5.57 thf(fact_6743_and__numerals_I3_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(3)
% 5.27/5.57 thf(fact_6744_even__not__iff,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri7632146776885996613nteger @ A ) )
% 5.27/5.57 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_not_iff
% 5.27/5.57 thf(fact_6745_even__not__iff,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.27/5.57 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % even_not_iff
% 5.27/5.57 thf(fact_6746_sgn__of__nat,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( semiri681578069525770553at_rat @ N2 ) )
% 5.27/5.57 = ( zero_n2052037380579107095ol_rat @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_of_nat
% 5.27/5.57 thf(fact_6747_sgn__of__nat,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.57 = ( zero_n3304061248610475627l_real @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_of_nat
% 5.27/5.57 thf(fact_6748_sgn__of__nat,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.57 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_of_nat
% 5.27/5.57 thf(fact_6749_sgn__of__nat,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( semiri4939895301339042750nteger @ N2 ) )
% 5.27/5.57 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_of_nat
% 5.27/5.57 thf(fact_6750_and__minus__numerals_I2_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_minus_numerals(2)
% 5.27/5.57 thf(fact_6751_and__minus__numerals_I6_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_minus_numerals(6)
% 5.27/5.57 thf(fact_6752_not__one__eq,axiom,
% 5.27/5.57 ( ( bit_ri7632146776885996613nteger @ one_one_Code_integer )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_one_eq
% 5.27/5.57 thf(fact_6753_not__one__eq,axiom,
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ one_one_int )
% 5.27/5.57 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_one_eq
% 5.27/5.57 thf(fact_6754_and__numerals_I4_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.57 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(4)
% 5.27/5.57 thf(fact_6755_and__numerals_I4_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(4)
% 5.27/5.57 thf(fact_6756_and__numerals_I6_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.27/5.57 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(6)
% 5.27/5.57 thf(fact_6757_and__numerals_I6_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.57 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(6)
% 5.27/5.57 thf(fact_6758_and__minus__numerals_I1_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_minus_numerals(1)
% 5.27/5.57 thf(fact_6759_and__minus__numerals_I5_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_minus_numerals(5)
% 5.27/5.57 thf(fact_6760_and__numerals_I7_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X4 ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.27/5.57 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X4 ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(7)
% 5.27/5.57 thf(fact_6761_and__numerals_I7_J,axiom,
% 5.27/5.57 ! [X4: num,Y: num] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.57 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X4 ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_numerals(7)
% 5.27/5.57 thf(fact_6762_disjunctive__diff,axiom,
% 5.27/5.57 ! [B: int,A: int] :
% 5.27/5.57 ( ! [N3: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ B @ N3 )
% 5.27/5.57 => ( bit_se1146084159140164899it_int @ A @ N3 ) )
% 5.27/5.57 => ( ( minus_minus_int @ A @ B )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ A @ ( bit_ri7919022796975470100ot_int @ B ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % disjunctive_diff
% 5.27/5.57 thf(fact_6763_norm__exp,axiom,
% 5.27/5.57 ! [X4: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X4 ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % norm_exp
% 5.27/5.57 thf(fact_6764_norm__exp,axiom,
% 5.27/5.57 ! [X4: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X4 ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % norm_exp
% 5.27/5.57 thf(fact_6765_and__not__numerals_I1_J,axiom,
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(1)
% 5.27/5.57 thf(fact_6766_take__bit__eq__mask,axiom,
% 5.27/5.57 ( bit_se2923211474154528505it_int
% 5.27/5.57 = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_eq_mask
% 5.27/5.57 thf(fact_6767_take__bit__eq__mask,axiom,
% 5.27/5.57 ( bit_se2925701944663578781it_nat
% 5.27/5.57 = ( ^ [N: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_eq_mask
% 5.27/5.57 thf(fact_6768_and_Oassoc,axiom,
% 5.27/5.57 ! [A: int,B: int,C: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.assoc
% 5.27/5.57 thf(fact_6769_and_Oassoc,axiom,
% 5.27/5.57 ! [A: nat,B: nat,C: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.assoc
% 5.27/5.57 thf(fact_6770_and_Ocommute,axiom,
% 5.27/5.57 ( bit_se725231765392027082nd_int
% 5.27/5.57 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.commute
% 5.27/5.57 thf(fact_6771_and_Ocommute,axiom,
% 5.27/5.57 ( bit_se727722235901077358nd_nat
% 5.27/5.57 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.commute
% 5.27/5.57 thf(fact_6772_and_Oleft__commute,axiom,
% 5.27/5.57 ! [B: int,A: int,C: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_commute
% 5.27/5.57 thf(fact_6773_and_Oleft__commute,axiom,
% 5.27/5.57 ! [B: nat,A: nat,C: nat] :
% 5.27/5.57 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and.left_commute
% 5.27/5.57 thf(fact_6774_of__nat__mask__eq,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.27/5.57 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % of_nat_mask_eq
% 5.27/5.57 thf(fact_6775_of__nat__mask__eq,axiom,
% 5.27/5.57 ! [N2: nat] :
% 5.27/5.57 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.27/5.57 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % of_nat_mask_eq
% 5.27/5.57 thf(fact_6776_of__nat__and__eq,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.27/5.57 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % of_nat_and_eq
% 5.27/5.57 thf(fact_6777_of__nat__and__eq,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N2 ) )
% 5.27/5.57 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % of_nat_and_eq
% 5.27/5.57 thf(fact_6778_exp__less__cancel,axiom,
% 5.27/5.57 ! [X4: real,Y: real] :
% 5.27/5.57 ( ( ord_less_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 5.27/5.57 => ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_less_cancel
% 5.27/5.57 thf(fact_6779_sgn__0__0,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 = zero_z3403309356797280102nteger )
% 5.27/5.57 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0_0
% 5.27/5.57 thf(fact_6780_sgn__0__0,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ( sgn_sgn_real @ A )
% 5.27/5.57 = zero_zero_real )
% 5.27/5.57 = ( A = zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0_0
% 5.27/5.57 thf(fact_6781_sgn__0__0,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ( sgn_sgn_rat @ A )
% 5.27/5.57 = zero_zero_rat )
% 5.27/5.57 = ( A = zero_zero_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0_0
% 5.27/5.57 thf(fact_6782_sgn__0__0,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ( sgn_sgn_int @ A )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 = ( A = zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_0_0
% 5.27/5.57 thf(fact_6783_sgn__eq__0__iff,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 = zero_z3403309356797280102nteger )
% 5.27/5.57 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_eq_0_iff
% 5.27/5.57 thf(fact_6784_sgn__eq__0__iff,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( ( sgn_sgn_complex @ A )
% 5.27/5.57 = zero_zero_complex )
% 5.27/5.57 = ( A = zero_zero_complex ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_eq_0_iff
% 5.27/5.57 thf(fact_6785_sgn__eq__0__iff,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( ( sgn_sgn_real @ A )
% 5.27/5.57 = zero_zero_real )
% 5.27/5.57 = ( A = zero_zero_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_eq_0_iff
% 5.27/5.57 thf(fact_6786_sgn__eq__0__iff,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( ( sgn_sgn_rat @ A )
% 5.27/5.57 = zero_zero_rat )
% 5.27/5.57 = ( A = zero_zero_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_eq_0_iff
% 5.27/5.57 thf(fact_6787_sgn__eq__0__iff,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( ( sgn_sgn_int @ A )
% 5.27/5.57 = zero_zero_int )
% 5.27/5.57 = ( A = zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_eq_0_iff
% 5.27/5.57 thf(fact_6788_sgn__mult,axiom,
% 5.27/5.57 ! [A: code_integer,B: code_integer] :
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.27/5.57 = ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult
% 5.27/5.57 thf(fact_6789_sgn__mult,axiom,
% 5.27/5.57 ! [A: rat,B: rat] :
% 5.27/5.57 ( ( sgn_sgn_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.57 = ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( sgn_sgn_rat @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult
% 5.27/5.57 thf(fact_6790_sgn__mult,axiom,
% 5.27/5.57 ! [A: complex,B: complex] :
% 5.27/5.57 ( ( sgn_sgn_complex @ ( times_times_complex @ A @ B ) )
% 5.27/5.57 = ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( sgn_sgn_complex @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult
% 5.27/5.57 thf(fact_6791_sgn__mult,axiom,
% 5.27/5.57 ! [A: real,B: real] :
% 5.27/5.57 ( ( sgn_sgn_real @ ( times_times_real @ A @ B ) )
% 5.27/5.57 = ( times_times_real @ ( sgn_sgn_real @ A ) @ ( sgn_sgn_real @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult
% 5.27/5.57 thf(fact_6792_sgn__mult,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( sgn_sgn_int @ ( times_times_int @ A @ B ) )
% 5.27/5.57 = ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult
% 5.27/5.57 thf(fact_6793_same__sgn__sgn__add,axiom,
% 5.27/5.57 ! [B: code_integer,A: code_integer] :
% 5.27/5.57 ( ( ( sgn_sgn_Code_integer @ B )
% 5.27/5.57 = ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 => ( ( sgn_sgn_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.57 = ( sgn_sgn_Code_integer @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % same_sgn_sgn_add
% 5.27/5.57 thf(fact_6794_same__sgn__sgn__add,axiom,
% 5.27/5.57 ! [B: real,A: real] :
% 5.27/5.57 ( ( ( sgn_sgn_real @ B )
% 5.27/5.57 = ( sgn_sgn_real @ A ) )
% 5.27/5.57 => ( ( sgn_sgn_real @ ( plus_plus_real @ A @ B ) )
% 5.27/5.57 = ( sgn_sgn_real @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % same_sgn_sgn_add
% 5.27/5.57 thf(fact_6795_same__sgn__sgn__add,axiom,
% 5.27/5.57 ! [B: rat,A: rat] :
% 5.27/5.57 ( ( ( sgn_sgn_rat @ B )
% 5.27/5.57 = ( sgn_sgn_rat @ A ) )
% 5.27/5.57 => ( ( sgn_sgn_rat @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.57 = ( sgn_sgn_rat @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % same_sgn_sgn_add
% 5.27/5.57 thf(fact_6796_same__sgn__sgn__add,axiom,
% 5.27/5.57 ! [B: int,A: int] :
% 5.27/5.57 ( ( ( sgn_sgn_int @ B )
% 5.27/5.57 = ( sgn_sgn_int @ A ) )
% 5.27/5.57 => ( ( sgn_sgn_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.57 = ( sgn_sgn_int @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % same_sgn_sgn_add
% 5.27/5.57 thf(fact_6797_take__bit__not__eq__mask__diff,axiom,
% 5.27/5.57 ! [N2: nat,A: int] :
% 5.27/5.57 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.27/5.57 = ( minus_minus_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_not_eq_mask_diff
% 5.27/5.57 thf(fact_6798_bit__and__iff,axiom,
% 5.27/5.57 ! [A: int,B: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ N2 )
% 5.27/5.57 = ( ( bit_se1146084159140164899it_int @ A @ N2 )
% 5.27/5.57 & ( bit_se1146084159140164899it_int @ B @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_and_iff
% 5.27/5.57 thf(fact_6799_bit__and__iff,axiom,
% 5.27/5.57 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.57 ( ( bit_se1148574629649215175it_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ N2 )
% 5.27/5.57 = ( ( bit_se1148574629649215175it_nat @ A @ N2 )
% 5.27/5.57 & ( bit_se1148574629649215175it_nat @ B @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_and_iff
% 5.27/5.57 thf(fact_6800_bit_Oconj__xor__distrib,axiom,
% 5.27/5.57 ! [X4: int,Y: int,Z: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ X4 @ ( bit_se6526347334894502574or_int @ Y @ Z ) )
% 5.27/5.57 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se725231765392027082nd_int @ X4 @ Z ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_xor_distrib
% 5.27/5.57 thf(fact_6801_bit_Oconj__xor__distrib2,axiom,
% 5.27/5.57 ! [Y: int,Z: int,X4: int] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( bit_se6526347334894502574or_int @ Y @ Z ) @ X4 )
% 5.27/5.57 = ( bit_se6526347334894502574or_int @ ( bit_se725231765392027082nd_int @ Y @ X4 ) @ ( bit_se725231765392027082nd_int @ Z @ X4 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit.conj_xor_distrib2
% 5.27/5.57 thf(fact_6802_div__eq__sgn__abs,axiom,
% 5.27/5.57 ! [K: int,L: int] :
% 5.27/5.57 ( ( ( sgn_sgn_int @ K )
% 5.27/5.57 = ( sgn_sgn_int @ L ) )
% 5.27/5.57 => ( ( divide_divide_int @ K @ L )
% 5.27/5.57 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % div_eq_sgn_abs
% 5.27/5.57 thf(fact_6803_take__bit__not__iff,axiom,
% 5.27/5.57 ! [N2: nat,A: int,B: int] :
% 5.27/5.57 ( ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) )
% 5.27/5.57 = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ B ) ) )
% 5.27/5.57 = ( ( bit_se2923211474154528505it_int @ N2 @ A )
% 5.27/5.57 = ( bit_se2923211474154528505it_int @ N2 @ B ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_not_iff
% 5.27/5.57 thf(fact_6804_take__bit__not__take__bit,axiom,
% 5.27/5.57 ! [N2: nat,A: int] :
% 5.27/5.57 ( ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se2923211474154528505it_int @ N2 @ A ) ) )
% 5.27/5.57 = ( bit_se2923211474154528505it_int @ N2 @ ( bit_ri7919022796975470100ot_int @ A ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_not_take_bit
% 5.27/5.57 thf(fact_6805_bit__not__int__iff,axiom,
% 5.27/5.57 ! [K: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N2 )
% 5.27/5.57 = ( ~ ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_not_int_iff
% 5.27/5.57 thf(fact_6806_bit__and__int__iff,axiom,
% 5.27/5.57 ! [K: int,L: int,N2: nat] :
% 5.27/5.57 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ N2 )
% 5.27/5.57 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.27/5.57 & ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % bit_and_int_iff
% 5.27/5.57 thf(fact_6807_less__eq__mask,axiom,
% 5.27/5.57 ! [N2: nat] : ( ord_less_eq_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.27/5.57
% 5.27/5.57 % less_eq_mask
% 5.27/5.57 thf(fact_6808_and__not__numerals_I2_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.57 = one_one_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(2)
% 5.27/5.57 thf(fact_6809_and__not__numerals_I4_J,axiom,
% 5.27/5.57 ! [M: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.57 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(4)
% 5.27/5.57 thf(fact_6810_take__bit__not__mask__eq__0,axiom,
% 5.27/5.57 ! [M: nat,N2: nat] :
% 5.27/5.57 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.57 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) )
% 5.27/5.57 = zero_zero_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % take_bit_not_mask_eq_0
% 5.27/5.57 thf(fact_6811_and__not__numerals_I5_J,axiom,
% 5.27/5.57 ! [M: num,N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.57 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(5)
% 5.27/5.57 thf(fact_6812_and__not__numerals_I7_J,axiom,
% 5.27/5.57 ! [M: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.57 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(7)
% 5.27/5.57 thf(fact_6813_and__not__numerals_I3_J,axiom,
% 5.27/5.57 ! [N2: num] :
% 5.27/5.57 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.57 = zero_zero_int ) ).
% 5.27/5.57
% 5.27/5.57 % and_not_numerals(3)
% 5.27/5.57 thf(fact_6814_and__eq__minus__1__iff,axiom,
% 5.27/5.57 ! [A: code_integer,B: code_integer] :
% 5.27/5.57 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = ( ( A
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 & ( B
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_eq_minus_1_iff
% 5.27/5.57 thf(fact_6815_and__eq__minus__1__iff,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = ( ( A
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 & ( B
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % and_eq_minus_1_iff
% 5.27/5.57 thf(fact_6816_exp__total,axiom,
% 5.27/5.57 ! [Y: real] :
% 5.27/5.57 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.57 => ? [X5: real] :
% 5.27/5.57 ( ( exp_real @ X5 )
% 5.27/5.57 = Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_total
% 5.27/5.57 thf(fact_6817_exp__gt__zero,axiom,
% 5.27/5.57 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_gt_zero
% 5.27/5.57 thf(fact_6818_not__exp__less__zero,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ~ ( ord_less_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 5.27/5.57
% 5.27/5.57 % not_exp_less_zero
% 5.27/5.57 thf(fact_6819_exp__ge__zero,axiom,
% 5.27/5.57 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % exp_ge_zero
% 5.27/5.57 thf(fact_6820_not__exp__le__zero,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ~ ( ord_less_eq_real @ ( exp_real @ X4 ) @ zero_zero_real ) ).
% 5.27/5.57
% 5.27/5.57 % not_exp_le_zero
% 5.27/5.57 thf(fact_6821_sgn__not__eq__imp,axiom,
% 5.27/5.57 ! [B: real,A: real] :
% 5.27/5.57 ( ( ( sgn_sgn_real @ B )
% 5.27/5.57 != ( sgn_sgn_real @ A ) )
% 5.27/5.57 => ( ( ( sgn_sgn_real @ A )
% 5.27/5.57 != zero_zero_real )
% 5.27/5.57 => ( ( ( sgn_sgn_real @ B )
% 5.27/5.57 != zero_zero_real )
% 5.27/5.57 => ( ( sgn_sgn_real @ A )
% 5.27/5.57 = ( uminus_uminus_real @ ( sgn_sgn_real @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_not_eq_imp
% 5.27/5.57 thf(fact_6822_sgn__not__eq__imp,axiom,
% 5.27/5.57 ! [B: int,A: int] :
% 5.27/5.57 ( ( ( sgn_sgn_int @ B )
% 5.27/5.57 != ( sgn_sgn_int @ A ) )
% 5.27/5.57 => ( ( ( sgn_sgn_int @ A )
% 5.27/5.57 != zero_zero_int )
% 5.27/5.57 => ( ( ( sgn_sgn_int @ B )
% 5.27/5.57 != zero_zero_int )
% 5.27/5.57 => ( ( sgn_sgn_int @ A )
% 5.27/5.57 = ( uminus_uminus_int @ ( sgn_sgn_int @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_not_eq_imp
% 5.27/5.57 thf(fact_6823_sgn__not__eq__imp,axiom,
% 5.27/5.57 ! [B: code_integer,A: code_integer] :
% 5.27/5.57 ( ( ( sgn_sgn_Code_integer @ B )
% 5.27/5.57 != ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 => ( ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 != zero_z3403309356797280102nteger )
% 5.27/5.57 => ( ( ( sgn_sgn_Code_integer @ B )
% 5.27/5.57 != zero_z3403309356797280102nteger )
% 5.27/5.57 => ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ ( sgn_sgn_Code_integer @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_not_eq_imp
% 5.27/5.57 thf(fact_6824_sgn__not__eq__imp,axiom,
% 5.27/5.57 ! [B: rat,A: rat] :
% 5.27/5.57 ( ( ( sgn_sgn_rat @ B )
% 5.27/5.57 != ( sgn_sgn_rat @ A ) )
% 5.27/5.57 => ( ( ( sgn_sgn_rat @ A )
% 5.27/5.57 != zero_zero_rat )
% 5.27/5.57 => ( ( ( sgn_sgn_rat @ B )
% 5.27/5.57 != zero_zero_rat )
% 5.27/5.57 => ( ( sgn_sgn_rat @ A )
% 5.27/5.57 = ( uminus_uminus_rat @ ( sgn_sgn_rat @ B ) ) ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_not_eq_imp
% 5.27/5.57 thf(fact_6825_sgn__minus__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.57 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_minus_1
% 5.27/5.57 thf(fact_6826_sgn__minus__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.57 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_minus_1
% 5.27/5.57 thf(fact_6827_sgn__minus__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.57 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_minus_1
% 5.27/5.57 thf(fact_6828_sgn__minus__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.57 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_minus_1
% 5.27/5.57 thf(fact_6829_sgn__minus__1,axiom,
% 5.27/5.57 ( ( sgn_sgn_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.57 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_minus_1
% 5.27/5.57 thf(fact_6830_AND__upper2_H,axiom,
% 5.27/5.57 ! [Y: int,Z: int,X4: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.57 => ( ( ord_less_eq_int @ Y @ Z )
% 5.27/5.57 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % AND_upper2'
% 5.27/5.57 thf(fact_6831_AND__upper1_H,axiom,
% 5.27/5.57 ! [Y: int,Z: int,Ya: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.57 => ( ( ord_less_eq_int @ Y @ Z )
% 5.27/5.57 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % AND_upper1'
% 5.27/5.57 thf(fact_6832_AND__upper2,axiom,
% 5.27/5.57 ! [Y: int,X4: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.57 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Y ) ) ).
% 5.27/5.57
% 5.27/5.57 % AND_upper2
% 5.27/5.57 thf(fact_6833_AND__upper1,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.57 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ X4 ) ) ).
% 5.27/5.57
% 5.27/5.57 % AND_upper1
% 5.27/5.57 thf(fact_6834_AND__lower,axiom,
% 5.27/5.57 ! [X4: int,Y: int] :
% 5.27/5.57 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.57 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % AND_lower
% 5.27/5.57 thf(fact_6835_not__diff__distrib,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A @ B ) )
% 5.27/5.57 = ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_diff_distrib
% 5.27/5.57 thf(fact_6836_not__add__distrib,axiom,
% 5.27/5.57 ! [A: int,B: int] :
% 5.27/5.57 ( ( bit_ri7919022796975470100ot_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.57 = ( minus_minus_int @ ( bit_ri7919022796975470100ot_int @ A ) @ B ) ) ).
% 5.27/5.57
% 5.27/5.57 % not_add_distrib
% 5.27/5.57 thf(fact_6837_linordered__idom__class_Oabs__sgn,axiom,
% 5.27/5.57 ( abs_abs_Code_integer
% 5.27/5.57 = ( ^ [K3: code_integer] : ( times_3573771949741848930nteger @ K3 @ ( sgn_sgn_Code_integer @ K3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % linordered_idom_class.abs_sgn
% 5.27/5.57 thf(fact_6838_linordered__idom__class_Oabs__sgn,axiom,
% 5.27/5.57 ( abs_abs_rat
% 5.27/5.57 = ( ^ [K3: rat] : ( times_times_rat @ K3 @ ( sgn_sgn_rat @ K3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % linordered_idom_class.abs_sgn
% 5.27/5.57 thf(fact_6839_linordered__idom__class_Oabs__sgn,axiom,
% 5.27/5.57 ( abs_abs_real
% 5.27/5.57 = ( ^ [K3: real] : ( times_times_real @ K3 @ ( sgn_sgn_real @ K3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % linordered_idom_class.abs_sgn
% 5.27/5.57 thf(fact_6840_linordered__idom__class_Oabs__sgn,axiom,
% 5.27/5.57 ( abs_abs_int
% 5.27/5.57 = ( ^ [K3: int] : ( times_times_int @ K3 @ ( sgn_sgn_int @ K3 ) ) ) ) ).
% 5.27/5.57
% 5.27/5.57 % linordered_idom_class.abs_sgn
% 5.27/5.57 thf(fact_6841_abs__mult__sgn,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_sgn
% 5.27/5.57 thf(fact_6842_abs__mult__sgn,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( sgn_sgn_rat @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_sgn
% 5.27/5.57 thf(fact_6843_abs__mult__sgn,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( times_times_complex @ ( abs_abs_complex @ A ) @ ( sgn_sgn_complex @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_sgn
% 5.27/5.57 thf(fact_6844_abs__mult__sgn,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( sgn_sgn_real @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_sgn
% 5.27/5.57 thf(fact_6845_abs__mult__sgn,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( sgn_sgn_int @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % abs_mult_sgn
% 5.27/5.57 thf(fact_6846_sgn__mult__abs,axiom,
% 5.27/5.57 ! [A: code_integer] :
% 5.27/5.57 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_abs
% 5.27/5.57 thf(fact_6847_sgn__mult__abs,axiom,
% 5.27/5.57 ! [A: rat] :
% 5.27/5.57 ( ( times_times_rat @ ( sgn_sgn_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_abs
% 5.27/5.57 thf(fact_6848_sgn__mult__abs,axiom,
% 5.27/5.57 ! [A: complex] :
% 5.27/5.57 ( ( times_times_complex @ ( sgn_sgn_complex @ A ) @ ( abs_abs_complex @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_abs
% 5.27/5.57 thf(fact_6849_sgn__mult__abs,axiom,
% 5.27/5.57 ! [A: real] :
% 5.27/5.57 ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( abs_abs_real @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_abs
% 5.27/5.57 thf(fact_6850_sgn__mult__abs,axiom,
% 5.27/5.57 ! [A: int] :
% 5.27/5.57 ( ( times_times_int @ ( sgn_sgn_int @ A ) @ ( abs_abs_int @ A ) )
% 5.27/5.57 = A ) ).
% 5.27/5.57
% 5.27/5.57 % sgn_mult_abs
% 5.27/5.57 thf(fact_6851_mult__sgn__abs,axiom,
% 5.27/5.57 ! [X4: code_integer] :
% 5.27/5.57 ( ( times_3573771949741848930nteger @ ( sgn_sgn_Code_integer @ X4 ) @ ( abs_abs_Code_integer @ X4 ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % mult_sgn_abs
% 5.27/5.57 thf(fact_6852_mult__sgn__abs,axiom,
% 5.27/5.57 ! [X4: rat] :
% 5.27/5.57 ( ( times_times_rat @ ( sgn_sgn_rat @ X4 ) @ ( abs_abs_rat @ X4 ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % mult_sgn_abs
% 5.27/5.57 thf(fact_6853_mult__sgn__abs,axiom,
% 5.27/5.57 ! [X4: real] :
% 5.27/5.57 ( ( times_times_real @ ( sgn_sgn_real @ X4 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % mult_sgn_abs
% 5.27/5.57 thf(fact_6854_mult__sgn__abs,axiom,
% 5.27/5.57 ! [X4: int] :
% 5.27/5.57 ( ( times_times_int @ ( sgn_sgn_int @ X4 ) @ ( abs_abs_int @ X4 ) )
% 5.27/5.57 = X4 ) ).
% 5.27/5.57
% 5.27/5.57 % mult_sgn_abs
% 5.27/5.57 thf(fact_6855_same__sgn__abs__add,axiom,
% 5.27/5.57 ! [B: code_integer,A: code_integer] :
% 5.27/5.57 ( ( ( sgn_sgn_Code_integer @ B )
% 5.27/5.57 = ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.57 => ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.27/5.57 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % same_sgn_abs_add
% 5.27/5.58 thf(fact_6856_same__sgn__abs__add,axiom,
% 5.27/5.58 ! [B: real,A: real] :
% 5.27/5.58 ( ( ( sgn_sgn_real @ B )
% 5.27/5.58 = ( sgn_sgn_real @ A ) )
% 5.27/5.58 => ( ( abs_abs_real @ ( plus_plus_real @ A @ B ) )
% 5.27/5.58 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % same_sgn_abs_add
% 5.27/5.58 thf(fact_6857_same__sgn__abs__add,axiom,
% 5.27/5.58 ! [B: rat,A: rat] :
% 5.27/5.58 ( ( ( sgn_sgn_rat @ B )
% 5.27/5.58 = ( sgn_sgn_rat @ A ) )
% 5.27/5.58 => ( ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) )
% 5.27/5.58 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % same_sgn_abs_add
% 5.27/5.58 thf(fact_6858_same__sgn__abs__add,axiom,
% 5.27/5.58 ! [B: int,A: int] :
% 5.27/5.58 ( ( ( sgn_sgn_int @ B )
% 5.27/5.58 = ( sgn_sgn_int @ A ) )
% 5.27/5.58 => ( ( abs_abs_int @ ( plus_plus_int @ A @ B ) )
% 5.27/5.58 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % same_sgn_abs_add
% 5.27/5.58 thf(fact_6859_exp__add__commuting,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( ( times_times_complex @ X4 @ Y )
% 5.27/5.58 = ( times_times_complex @ Y @ X4 ) )
% 5.27/5.58 => ( ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.58 = ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_add_commuting
% 5.27/5.58 thf(fact_6860_exp__add__commuting,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ( times_times_real @ X4 @ Y )
% 5.27/5.58 = ( times_times_real @ Y @ X4 ) )
% 5.27/5.58 => ( ( exp_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.58 = ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_add_commuting
% 5.27/5.58 thf(fact_6861_mult__exp__exp,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) )
% 5.27/5.58 = ( exp_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mult_exp_exp
% 5.27/5.58 thf(fact_6862_mult__exp__exp,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) )
% 5.27/5.58 = ( exp_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mult_exp_exp
% 5.27/5.58 thf(fact_6863_exp__diff,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( exp_real @ ( minus_minus_real @ X4 @ Y ) )
% 5.27/5.58 = ( divide_divide_real @ ( exp_real @ X4 ) @ ( exp_real @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_diff
% 5.27/5.58 thf(fact_6864_exp__diff,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( exp_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 5.27/5.58 = ( divide1717551699836669952omplex @ ( exp_complex @ X4 ) @ ( exp_complex @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_diff
% 5.27/5.58 thf(fact_6865_and__not__numerals_I6_J,axiom,
% 5.27/5.58 ! [M: num,N2: num] :
% 5.27/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_not_numerals(6)
% 5.27/5.58 thf(fact_6866_and__not__numerals_I9_J,axiom,
% 5.27/5.58 ! [M: num,N2: num] :
% 5.27/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.58 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_not_numerals(9)
% 5.27/5.58 thf(fact_6867_mask__nonnegative__int,axiom,
% 5.27/5.58 ! [N2: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_nonnegative_int
% 5.27/5.58 thf(fact_6868_not__mask__negative__int,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ zero_zero_int ) ).
% 5.27/5.58
% 5.27/5.58 % not_mask_negative_int
% 5.27/5.58 thf(fact_6869_minus__exp__eq__not__mask,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_exp_eq_not_mask
% 5.27/5.58 thf(fact_6870_minus__exp__eq__not__mask,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_exp_eq_not_mask
% 5.27/5.58 thf(fact_6871_exp__gt__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_real @ one_one_real @ ( exp_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_gt_one
% 5.27/5.58 thf(fact_6872_sgn__1__pos,axiom,
% 5.27/5.58 ! [A: code_integer] :
% 5.27/5.58 ( ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.58 = one_one_Code_integer )
% 5.27/5.58 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_pos
% 5.27/5.58 thf(fact_6873_sgn__1__pos,axiom,
% 5.27/5.58 ! [A: real] :
% 5.27/5.58 ( ( ( sgn_sgn_real @ A )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_pos
% 5.27/5.58 thf(fact_6874_sgn__1__pos,axiom,
% 5.27/5.58 ! [A: rat] :
% 5.27/5.58 ( ( ( sgn_sgn_rat @ A )
% 5.27/5.58 = one_one_rat )
% 5.27/5.58 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_pos
% 5.27/5.58 thf(fact_6875_sgn__1__pos,axiom,
% 5.27/5.58 ! [A: int] :
% 5.27/5.58 ( ( ( sgn_sgn_int @ A )
% 5.27/5.58 = one_one_int )
% 5.27/5.58 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_pos
% 5.27/5.58 thf(fact_6876_exp__ge__add__one__self,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_ge_add_one_self
% 5.27/5.58 thf(fact_6877_abs__sgn__eq,axiom,
% 5.27/5.58 ! [A: code_integer] :
% 5.27/5.58 ( ( ( A = zero_z3403309356797280102nteger )
% 5.27/5.58 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.58 = zero_z3403309356797280102nteger ) )
% 5.27/5.58 & ( ( A != zero_z3403309356797280102nteger )
% 5.27/5.58 => ( ( abs_abs_Code_integer @ ( sgn_sgn_Code_integer @ A ) )
% 5.27/5.58 = one_one_Code_integer ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sgn_eq
% 5.27/5.58 thf(fact_6878_abs__sgn__eq,axiom,
% 5.27/5.58 ! [A: real] :
% 5.27/5.58 ( ( ( A = zero_zero_real )
% 5.27/5.58 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.58 = zero_zero_real ) )
% 5.27/5.58 & ( ( A != zero_zero_real )
% 5.27/5.58 => ( ( abs_abs_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.58 = one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sgn_eq
% 5.27/5.58 thf(fact_6879_abs__sgn__eq,axiom,
% 5.27/5.58 ! [A: rat] :
% 5.27/5.58 ( ( ( A = zero_zero_rat )
% 5.27/5.58 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.58 = zero_zero_rat ) )
% 5.27/5.58 & ( ( A != zero_zero_rat )
% 5.27/5.58 => ( ( abs_abs_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.58 = one_one_rat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sgn_eq
% 5.27/5.58 thf(fact_6880_abs__sgn__eq,axiom,
% 5.27/5.58 ! [A: int] :
% 5.27/5.58 ( ( ( A = zero_zero_int )
% 5.27/5.58 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.58 = zero_zero_int ) )
% 5.27/5.58 & ( ( A != zero_zero_int )
% 5.27/5.58 => ( ( abs_abs_int @ ( sgn_sgn_int @ A ) )
% 5.27/5.58 = one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sgn_eq
% 5.27/5.58 thf(fact_6881_and__less__eq,axiom,
% 5.27/5.58 ! [L: int,K: int] :
% 5.27/5.58 ( ( ord_less_int @ L @ zero_zero_int )
% 5.27/5.58 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L ) @ K ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_less_eq
% 5.27/5.58 thf(fact_6882_AND__upper1_H_H,axiom,
% 5.27/5.58 ! [Y: int,Z: int,Ya: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.58 => ( ( ord_less_int @ Y @ Z )
% 5.27/5.58 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % AND_upper1''
% 5.27/5.58 thf(fact_6883_AND__upper2_H_H,axiom,
% 5.27/5.58 ! [Y: int,Z: int,X4: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.58 => ( ( ord_less_int @ Y @ Z )
% 5.27/5.58 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % AND_upper2''
% 5.27/5.58 thf(fact_6884_minus__eq__not__plus__1,axiom,
% 5.27/5.58 ( uminus1351360451143612070nteger
% 5.27/5.58 = ( ^ [A3: code_integer] : ( plus_p5714425477246183910nteger @ ( bit_ri7632146776885996613nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_eq_not_plus_1
% 5.27/5.58 thf(fact_6885_minus__eq__not__plus__1,axiom,
% 5.27/5.58 ( uminus_uminus_int
% 5.27/5.58 = ( ^ [A3: int] : ( plus_plus_int @ ( bit_ri7919022796975470100ot_int @ A3 ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_eq_not_plus_1
% 5.27/5.58 thf(fact_6886_not__eq__complement,axiom,
% 5.27/5.58 ( bit_ri7632146776885996613nteger
% 5.27/5.58 = ( ^ [A3: code_integer] : ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A3 ) @ one_one_Code_integer ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_eq_complement
% 5.27/5.58 thf(fact_6887_not__eq__complement,axiom,
% 5.27/5.58 ( bit_ri7919022796975470100ot_int
% 5.27/5.58 = ( ^ [A3: int] : ( minus_minus_int @ ( uminus_uminus_int @ A3 ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_eq_complement
% 5.27/5.58 thf(fact_6888_minus__eq__not__minus__1,axiom,
% 5.27/5.58 ( uminus1351360451143612070nteger
% 5.27/5.58 = ( ^ [A3: code_integer] : ( bit_ri7632146776885996613nteger @ ( minus_8373710615458151222nteger @ A3 @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_eq_not_minus_1
% 5.27/5.58 thf(fact_6889_minus__eq__not__minus__1,axiom,
% 5.27/5.58 ( uminus_uminus_int
% 5.27/5.58 = ( ^ [A3: int] : ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_eq_not_minus_1
% 5.27/5.58 thf(fact_6890_div__sgn__abs__cancel,axiom,
% 5.27/5.58 ! [V: int,K: int,L: int] :
% 5.27/5.58 ( ( V != zero_zero_int )
% 5.27/5.58 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L ) ) )
% 5.27/5.58 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % div_sgn_abs_cancel
% 5.27/5.58 thf(fact_6891_not__int__def,axiom,
% 5.27/5.58 ( bit_ri7919022796975470100ot_int
% 5.27/5.58 = ( ^ [K3: int] : ( minus_minus_int @ ( uminus_uminus_int @ K3 ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_int_def
% 5.27/5.58 thf(fact_6892_exp__minus__inverse,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( times_times_real @ ( exp_real @ X4 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % exp_minus_inverse
% 5.27/5.58 thf(fact_6893_exp__minus__inverse,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( times_times_complex @ ( exp_complex @ X4 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X4 ) ) )
% 5.27/5.58 = one_one_complex ) ).
% 5.27/5.58
% 5.27/5.58 % exp_minus_inverse
% 5.27/5.58 thf(fact_6894_exp__of__nat2__mult,axiom,
% 5.27/5.58 ! [X4: complex,N2: nat] :
% 5.27/5.58 ( ( exp_complex @ ( times_times_complex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.27/5.58 = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_of_nat2_mult
% 5.27/5.58 thf(fact_6895_exp__of__nat2__mult,axiom,
% 5.27/5.58 ! [X4: real,N2: nat] :
% 5.27/5.58 ( ( exp_real @ ( times_times_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.58 = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_of_nat2_mult
% 5.27/5.58 thf(fact_6896_exp__of__nat__mult,axiom,
% 5.27/5.58 ! [N2: nat,X4: complex] :
% 5.27/5.58 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ X4 ) )
% 5.27/5.58 = ( power_power_complex @ ( exp_complex @ X4 ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_of_nat_mult
% 5.27/5.58 thf(fact_6897_exp__of__nat__mult,axiom,
% 5.27/5.58 ! [N2: nat,X4: real] :
% 5.27/5.58 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 ) )
% 5.27/5.58 = ( power_power_real @ ( exp_real @ X4 ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_of_nat_mult
% 5.27/5.58 thf(fact_6898_div__dvd__sgn__abs,axiom,
% 5.27/5.58 ! [L: int,K: int] :
% 5.27/5.58 ( ( dvd_dvd_int @ L @ K )
% 5.27/5.58 => ( ( divide_divide_int @ K @ L )
% 5.27/5.58 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % div_dvd_sgn_abs
% 5.27/5.58 thf(fact_6899_sgn__mod,axiom,
% 5.27/5.58 ! [L: int,K: int] :
% 5.27/5.58 ( ( L != zero_zero_int )
% 5.27/5.58 => ( ~ ( dvd_dvd_int @ L @ K )
% 5.27/5.58 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L ) )
% 5.27/5.58 = ( sgn_sgn_int @ L ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_mod
% 5.27/5.58 thf(fact_6900_and__not__numerals_I8_J,axiom,
% 5.27/5.58 ! [M: num,N2: num] :
% 5.27/5.58 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.58 = ( 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 @ N2 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_not_numerals(8)
% 5.27/5.58 thf(fact_6901_minus__numeral__inc__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N2 ) ) )
% 5.27/5.58 = ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_numeral_inc_eq
% 5.27/5.58 thf(fact_6902_minus__numeral__inc__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N2 ) ) )
% 5.27/5.58 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % minus_numeral_inc_eq
% 5.27/5.58 thf(fact_6903_less__mask,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.58 => ( ord_less_nat @ N2 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % less_mask
% 5.27/5.58 thf(fact_6904_even__and__iff,axiom,
% 5.27/5.58 ! [A: code_integer,B: code_integer] :
% 5.27/5.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.27/5.58 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.27/5.58 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_and_iff
% 5.27/5.58 thf(fact_6905_even__and__iff,axiom,
% 5.27/5.58 ! [A: int,B: int] :
% 5.27/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.27/5.58 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.27/5.58 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_and_iff
% 5.27/5.58 thf(fact_6906_even__and__iff,axiom,
% 5.27/5.58 ! [A: nat,B: nat] :
% 5.27/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.27/5.58 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.27/5.58 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_and_iff
% 5.27/5.58 thf(fact_6907_sgn__1__neg,axiom,
% 5.27/5.58 ! [A: real] :
% 5.27/5.58 ( ( ( sgn_sgn_real @ A )
% 5.27/5.58 = ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.58 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_neg
% 5.27/5.58 thf(fact_6908_sgn__1__neg,axiom,
% 5.27/5.58 ! [A: int] :
% 5.27/5.58 ( ( ( sgn_sgn_int @ A )
% 5.27/5.58 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.58 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_neg
% 5.27/5.58 thf(fact_6909_sgn__1__neg,axiom,
% 5.27/5.58 ! [A: code_integer] :
% 5.27/5.58 ( ( ( sgn_sgn_Code_integer @ A )
% 5.27/5.58 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.58 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_neg
% 5.27/5.58 thf(fact_6910_sgn__1__neg,axiom,
% 5.27/5.58 ! [A: rat] :
% 5.27/5.58 ( ( ( sgn_sgn_rat @ A )
% 5.27/5.58 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.27/5.58 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_1_neg
% 5.27/5.58 thf(fact_6911_sgn__if,axiom,
% 5.27/5.58 ( sgn_sgn_real
% 5.27/5.58 = ( ^ [X: real] : ( if_real @ ( X = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ X ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_if
% 5.27/5.58 thf(fact_6912_sgn__if,axiom,
% 5.27/5.58 ( sgn_sgn_int
% 5.27/5.58 = ( ^ [X: int] : ( if_int @ ( X = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ X ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_if
% 5.27/5.58 thf(fact_6913_sgn__if,axiom,
% 5.27/5.58 ( sgn_sgn_Code_integer
% 5.27/5.58 = ( ^ [X: code_integer] : ( if_Code_integer @ ( X = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ X ) @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_if
% 5.27/5.58 thf(fact_6914_sgn__if,axiom,
% 5.27/5.58 ( sgn_sgn_rat
% 5.27/5.58 = ( ^ [X: rat] : ( if_rat @ ( X = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ X ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_if
% 5.27/5.58 thf(fact_6915_not__int__div__2,axiom,
% 5.27/5.58 ! [K: int] :
% 5.27/5.58 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_int_div_2
% 5.27/5.58 thf(fact_6916_even__not__iff__int,axiom,
% 5.27/5.58 ! [K: int] :
% 5.27/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.27/5.58 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_not_iff_int
% 5.27/5.58 thf(fact_6917_exp__ge__add__one__self__aux,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( exp_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_ge_add_one_self_aux
% 5.27/5.58 thf(fact_6918_even__and__iff__int,axiom,
% 5.27/5.58 ! [K: int,L: int] :
% 5.27/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.27/5.58 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.27/5.58 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_and_iff_int
% 5.27/5.58 thf(fact_6919_lemma__exp__total,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.27/5.58 => ? [X5: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.27/5.58 & ( ord_less_eq_real @ X5 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.27/5.58 & ( ( exp_real @ X5 )
% 5.27/5.58 = Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % lemma_exp_total
% 5.27/5.58 thf(fact_6920_ln__ge__iff,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X4 ) )
% 5.27/5.58 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ln_ge_iff
% 5.27/5.58 thf(fact_6921_zsgn__def,axiom,
% 5.27/5.58 ( sgn_sgn_int
% 5.27/5.58 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % zsgn_def
% 5.27/5.58 thf(fact_6922_ln__x__over__x__mono,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X4 ) @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ln_x_over_x_mono
% 5.27/5.58 thf(fact_6923_not__numeral__Bit0__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) )
% 5.27/5.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_numeral_Bit0_eq
% 5.27/5.58 thf(fact_6924_not__numeral__Bit0__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_numeral_Bit0_eq
% 5.27/5.58 thf(fact_6925_norm__sgn,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( X4 = zero_zero_real )
% 5.27/5.58 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 5.27/5.58 = zero_zero_real ) )
% 5.27/5.58 & ( ( X4 != zero_zero_real )
% 5.27/5.58 => ( ( real_V7735802525324610683m_real @ ( sgn_sgn_real @ X4 ) )
% 5.27/5.58 = one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % norm_sgn
% 5.27/5.58 thf(fact_6926_norm__sgn,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( ( X4 = zero_zero_complex )
% 5.27/5.58 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 5.27/5.58 = zero_zero_real ) )
% 5.27/5.58 & ( ( X4 != zero_zero_complex )
% 5.27/5.58 => ( ( real_V1022390504157884413omplex @ ( sgn_sgn_complex @ X4 ) )
% 5.27/5.58 = one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % norm_sgn
% 5.27/5.58 thf(fact_6927_bit__minus__int__iff,axiom,
% 5.27/5.58 ! [K: int,N2: nat] :
% 5.27/5.58 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N2 )
% 5.27/5.58 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % bit_minus_int_iff
% 5.27/5.58 thf(fact_6928_not__numeral__BitM__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( bit_ri7632146776885996613nteger @ ( numera6620942414471956472nteger @ ( bitM @ N2 ) ) )
% 5.27/5.58 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_numeral_BitM_eq
% 5.27/5.58 thf(fact_6929_not__numeral__BitM__eq,axiom,
% 5.27/5.58 ! [N2: num] :
% 5.27/5.58 ( ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bitM @ N2 ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_numeral_BitM_eq
% 5.27/5.58 thf(fact_6930_one__and__eq,axiom,
% 5.27/5.58 ! [A: code_integer] :
% 5.27/5.58 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.27/5.58 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_and_eq
% 5.27/5.58 thf(fact_6931_one__and__eq,axiom,
% 5.27/5.58 ! [A: int] :
% 5.27/5.58 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.27/5.58 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_and_eq
% 5.27/5.58 thf(fact_6932_one__and__eq,axiom,
% 5.27/5.58 ! [A: nat] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.27/5.58 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_and_eq
% 5.27/5.58 thf(fact_6933_and__one__eq,axiom,
% 5.27/5.58 ! [A: code_integer] :
% 5.27/5.58 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.27/5.58 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_one_eq
% 5.27/5.58 thf(fact_6934_and__one__eq,axiom,
% 5.27/5.58 ! [A: int] :
% 5.27/5.58 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.27/5.58 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_one_eq
% 5.27/5.58 thf(fact_6935_and__one__eq,axiom,
% 5.27/5.58 ! [A: nat] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.27/5.58 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_one_eq
% 5.27/5.58 thf(fact_6936_exp__le,axiom,
% 5.27/5.58 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_le
% 5.27/5.58 thf(fact_6937_take__bit__eq__mask__iff,axiom,
% 5.27/5.58 ! [N2: nat,K: int] :
% 5.27/5.58 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.58 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.58 = ( ( bit_se2923211474154528505it_int @ N2 @ ( plus_plus_int @ K @ one_one_int ) )
% 5.27/5.58 = zero_zero_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % take_bit_eq_mask_iff
% 5.27/5.58 thf(fact_6938_exp__divide__power__eq,axiom,
% 5.27/5.58 ! [N2: nat,X4: complex] :
% 5.27/5.58 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.58 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X4 @ ( semiri8010041392384452111omplex @ N2 ) ) ) @ N2 )
% 5.27/5.58 = ( exp_complex @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_divide_power_eq
% 5.27/5.58 thf(fact_6939_exp__divide__power__eq,axiom,
% 5.27/5.58 ! [N2: nat,X4: real] :
% 5.27/5.58 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.58 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.27/5.58 = ( exp_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_divide_power_eq
% 5.27/5.58 thf(fact_6940_eucl__rel__int__remainderI,axiom,
% 5.27/5.58 ! [R3: int,L: int,K: int,Q3: int] :
% 5.27/5.58 ( ( ( sgn_sgn_int @ R3 )
% 5.27/5.58 = ( sgn_sgn_int @ L ) )
% 5.27/5.58 => ( ( ord_less_int @ ( abs_abs_int @ R3 ) @ ( abs_abs_int @ L ) )
% 5.27/5.58 => ( ( K
% 5.27/5.58 = ( plus_plus_int @ ( times_times_int @ Q3 @ L ) @ R3 ) )
% 5.27/5.58 => ( eucl_rel_int @ K @ L @ ( product_Pair_int_int @ Q3 @ R3 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % eucl_rel_int_remainderI
% 5.27/5.58 thf(fact_6941_tanh__altdef,axiom,
% 5.27/5.58 ( tanh_real
% 5.27/5.58 = ( ^ [X: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % tanh_altdef
% 5.27/5.58 thf(fact_6942_tanh__altdef,axiom,
% 5.27/5.58 ( tanh_complex
% 5.27/5.58 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % tanh_altdef
% 5.27/5.58 thf(fact_6943_and__exp__eq__0__iff__not__bit,axiom,
% 5.27/5.58 ! [A: int,N2: nat] :
% 5.27/5.58 ( ( ( bit_se725231765392027082nd_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 = zero_zero_int )
% 5.27/5.58 = ( ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_exp_eq_0_iff_not_bit
% 5.27/5.58 thf(fact_6944_and__exp__eq__0__iff__not__bit,axiom,
% 5.27/5.58 ! [A: nat,N2: nat] :
% 5.27/5.58 ( ( ( bit_se727722235901077358nd_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 = zero_zero_nat )
% 5.27/5.58 = ( ~ ( bit_se1148574629649215175it_nat @ A @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_exp_eq_0_iff_not_bit
% 5.27/5.58 thf(fact_6945_exp__half__le2,axiom,
% 5.27/5.58 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_half_le2
% 5.27/5.58 thf(fact_6946_Suc__mask__eq__exp,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.27/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % Suc_mask_eq_exp
% 5.27/5.58 thf(fact_6947_mask__nat__less__exp,axiom,
% 5.27/5.58 ! [N2: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N2 ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_nat_less_exp
% 5.27/5.58 thf(fact_6948_bit__not__iff__eq,axiom,
% 5.27/5.58 ! [A: int,N2: nat] :
% 5.27/5.58 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ A ) @ N2 )
% 5.27/5.58 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.58 != zero_zero_int )
% 5.27/5.58 & ~ ( bit_se1146084159140164899it_int @ A @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % bit_not_iff_eq
% 5.27/5.58 thf(fact_6949_exp__double,axiom,
% 5.27/5.58 ! [Z: complex] :
% 5.27/5.58 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.27/5.58 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_double
% 5.27/5.58 thf(fact_6950_exp__double,axiom,
% 5.27/5.58 ! [Z: real] :
% 5.27/5.58 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.27/5.58 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_double
% 5.27/5.58 thf(fact_6951_eucl__rel__int_Osimps,axiom,
% 5.27/5.58 ( eucl_rel_int
% 5.27/5.58 = ( ^ [A1: int,A22: int,A32: product_prod_int_int] :
% 5.27/5.58 ( ? [K3: int] :
% 5.27/5.58 ( ( A1 = K3 )
% 5.27/5.58 & ( A22 = zero_zero_int )
% 5.27/5.58 & ( A32
% 5.27/5.58 = ( product_Pair_int_int @ zero_zero_int @ K3 ) ) )
% 5.27/5.58 | ? [L2: int,K3: int,Q5: int] :
% 5.27/5.58 ( ( A1 = K3 )
% 5.27/5.58 & ( A22 = L2 )
% 5.27/5.58 & ( A32
% 5.27/5.58 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 5.27/5.58 & ( L2 != zero_zero_int )
% 5.27/5.58 & ( K3
% 5.27/5.58 = ( times_times_int @ Q5 @ L2 ) ) )
% 5.27/5.58 | ? [R5: int,L2: int,K3: int,Q5: int] :
% 5.27/5.58 ( ( A1 = K3 )
% 5.27/5.58 & ( A22 = L2 )
% 5.27/5.58 & ( A32
% 5.27/5.58 = ( product_Pair_int_int @ Q5 @ R5 ) )
% 5.27/5.58 & ( ( sgn_sgn_int @ R5 )
% 5.27/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.27/5.58 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L2 ) )
% 5.27/5.58 & ( K3
% 5.27/5.58 = ( plus_plus_int @ ( times_times_int @ Q5 @ L2 ) @ R5 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % eucl_rel_int.simps
% 5.27/5.58 thf(fact_6952_eucl__rel__int_Ocases,axiom,
% 5.27/5.58 ! [A12: int,A23: int,A33: product_prod_int_int] :
% 5.27/5.58 ( ( eucl_rel_int @ A12 @ A23 @ A33 )
% 5.27/5.58 => ( ( ( A23 = zero_zero_int )
% 5.27/5.58 => ( A33
% 5.27/5.58 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.27/5.58 => ( ! [Q2: int] :
% 5.27/5.58 ( ( A33
% 5.27/5.58 = ( product_Pair_int_int @ Q2 @ zero_zero_int ) )
% 5.27/5.58 => ( ( A23 != zero_zero_int )
% 5.27/5.58 => ( A12
% 5.27/5.58 != ( times_times_int @ Q2 @ A23 ) ) ) )
% 5.27/5.58 => ~ ! [R2: int,Q2: int] :
% 5.27/5.58 ( ( A33
% 5.27/5.58 = ( product_Pair_int_int @ Q2 @ R2 ) )
% 5.27/5.58 => ( ( ( sgn_sgn_int @ R2 )
% 5.27/5.58 = ( sgn_sgn_int @ A23 ) )
% 5.27/5.58 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 5.27/5.58 => ( A12
% 5.27/5.58 != ( plus_plus_int @ ( times_times_int @ Q2 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % eucl_rel_int.cases
% 5.27/5.58 thf(fact_6953_div__noneq__sgn__abs,axiom,
% 5.27/5.58 ! [L: int,K: int] :
% 5.27/5.58 ( ( L != zero_zero_int )
% 5.27/5.58 => ( ( ( sgn_sgn_int @ K )
% 5.27/5.58 != ( sgn_sgn_int @ L ) )
% 5.27/5.58 => ( ( divide_divide_int @ K @ L )
% 5.27/5.58 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) ) )
% 5.27/5.58 @ ( zero_n2684676970156552555ol_int
% 5.27/5.58 @ ~ ( dvd_dvd_int @ L @ K ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % div_noneq_sgn_abs
% 5.27/5.58 thf(fact_6954_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N2 ) )
% 5.27/5.58 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.58
% 5.27/5.58 % semiring_bit_operations_class.even_mask_iff
% 5.27/5.58 thf(fact_6955_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N2 ) )
% 5.27/5.58 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.58
% 5.27/5.58 % semiring_bit_operations_class.even_mask_iff
% 5.27/5.58 thf(fact_6956_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.58 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.58
% 5.27/5.58 % semiring_bit_operations_class.even_mask_iff
% 5.27/5.58 thf(fact_6957_mask__half__int,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N2 ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_half_int
% 5.27/5.58 thf(fact_6958_mask__nat__def,axiom,
% 5.27/5.58 ( bit_se2002935070580805687sk_nat
% 5.27/5.58 = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_nat_def
% 5.27/5.58 thf(fact_6959_mask__int__def,axiom,
% 5.27/5.58 ( bit_se2000444600071755411sk_int
% 5.27/5.58 = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_int_def
% 5.27/5.58 thf(fact_6960_exp__bound__half,axiom,
% 5.27/5.58 ! [Z: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_bound_half
% 5.27/5.58 thf(fact_6961_exp__bound__half,axiom,
% 5.27/5.58 ! [Z: complex] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_bound_half
% 5.27/5.58 thf(fact_6962_mask__eq__exp__minus__1,axiom,
% 5.27/5.58 ( bit_se2002935070580805687sk_nat
% 5.27/5.58 = ( ^ [N: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_eq_exp_minus_1
% 5.27/5.58 thf(fact_6963_mask__eq__exp__minus__1,axiom,
% 5.27/5.58 ( bit_se2000444600071755411sk_int
% 5.27/5.58 = ( ^ [N: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mask_eq_exp_minus_1
% 5.27/5.58 thf(fact_6964_exp__bound,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.58 => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_bound
% 5.27/5.58 thf(fact_6965_not__int__rec,axiom,
% 5.27/5.58 ( bit_ri7919022796975470100ot_int
% 5.27/5.58 = ( ^ [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 ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % not_int_rec
% 5.27/5.58 thf(fact_6966_and__int__rec,axiom,
% 5.27/5.58 ( bit_se725231765392027082nd_int
% 5.27/5.58 = ( ^ [K3: int,L2: int] :
% 5.27/5.58 ( plus_plus_int
% 5.27/5.58 @ ( zero_n2684676970156552555ol_int
% 5.27/5.58 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.27/5.58 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.27/5.58 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_int_rec
% 5.27/5.58 thf(fact_6967_real__exp__bound__lemma,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( exp_real @ X4 ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_exp_bound_lemma
% 5.27/5.58 thf(fact_6968_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.27/5.58 ! [N2: nat,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ X4 )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.58 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_ge_one_plus_x_over_n_power_n
% 5.27/5.58 thf(fact_6969_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.27/5.58 ! [X4: real,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.58 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 ) @ ( exp_real @ ( uminus_uminus_real @ X4 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_ge_one_minus_x_over_n_power_n
% 5.27/5.58 thf(fact_6970_exp__bound__lemma,axiom,
% 5.27/5.58 ! [Z: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_bound_lemma
% 5.27/5.58 thf(fact_6971_exp__bound__lemma,axiom,
% 5.27/5.58 ! [Z: complex] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_bound_lemma
% 5.27/5.58 thf(fact_6972_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.27/5.58 ! [N2: nat,K: int] :
% 5.27/5.58 ( ( ( bit_se2923211474154528505it_int @ N2 @ K )
% 5.27/5.58 = ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.58 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % take_bit_eq_mask_iff_exp_dvd
% 5.27/5.58 thf(fact_6973_exp__lower__Taylor__quadratic,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X4 ) @ ( divide_divide_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % exp_lower_Taylor_quadratic
% 5.27/5.58 thf(fact_6974_log__base__10__eq1,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.58 = ( 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 @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_base_10_eq1
% 5.27/5.58 thf(fact_6975_modulo__int__def,axiom,
% 5.27/5.58 ( modulo_modulo_int
% 5.27/5.58 = ( ^ [K3: int,L2: int] :
% 5.27/5.58 ( if_int @ ( L2 = zero_zero_int ) @ K3
% 5.27/5.58 @ ( if_int
% 5.27/5.58 @ ( ( sgn_sgn_int @ K3 )
% 5.27/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.27/5.58 @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) )
% 5.27/5.58 @ ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.27/5.58 @ ( minus_minus_int
% 5.27/5.58 @ ( times_times_int @ ( abs_abs_int @ L2 )
% 5.27/5.58 @ ( zero_n2684676970156552555ol_int
% 5.27/5.58 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) )
% 5.27/5.58 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % modulo_int_def
% 5.27/5.58 thf(fact_6976_divide__int__def,axiom,
% 5.27/5.58 ( divide_divide_int
% 5.27/5.58 = ( ^ [K3: int,L2: int] :
% 5.27/5.58 ( if_int @ ( L2 = zero_zero_int ) @ zero_zero_int
% 5.27/5.58 @ ( if_int
% 5.27/5.58 @ ( ( sgn_sgn_int @ K3 )
% 5.27/5.58 = ( sgn_sgn_int @ L2 ) )
% 5.27/5.58 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) )
% 5.27/5.58 @ ( uminus_uminus_int
% 5.27/5.58 @ ( semiri1314217659103216013at_int
% 5.27/5.58 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K3 ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) )
% 5.27/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.58 @ ~ ( dvd_dvd_int @ L2 @ K3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % divide_int_def
% 5.27/5.58 thf(fact_6977_arctan__half,axiom,
% 5.27/5.58 ( arctan
% 5.27/5.58 = ( ^ [X: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_half
% 5.27/5.58 thf(fact_6978_log__base__10__eq2,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.58 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_base_10_eq2
% 5.27/5.58 thf(fact_6979_machin,axiom,
% 5.27/5.58 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % machin
% 5.27/5.58 thf(fact_6980_zero__le__sgn__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X4 ) )
% 5.27/5.58 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_le_sgn_iff
% 5.27/5.58 thf(fact_6981_sgn__le__0__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X4 ) @ zero_zero_real )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_le_0_iff
% 5.27/5.58 thf(fact_6982_real__sqrt__less__iff,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_less_iff
% 5.27/5.58 thf(fact_6983_real__sqrt__le__iff,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_le_iff
% 5.27/5.58 thf(fact_6984_real__sqrt__one,axiom,
% 5.27/5.58 ( ( sqrt @ one_one_real )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_one
% 5.27/5.58 thf(fact_6985_real__sqrt__eq__1__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( sqrt @ X4 )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 = ( X4 = one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_eq_1_iff
% 5.27/5.58 thf(fact_6986_real__sqrt__lt__0__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 5.27/5.58 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_lt_0_iff
% 5.27/5.58 thf(fact_6987_real__sqrt__gt__0__iff,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_gt_0_iff
% 5.27/5.58 thf(fact_6988_nat__numeral,axiom,
% 5.27/5.58 ! [K: num] :
% 5.27/5.58 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.27/5.58 = ( numeral_numeral_nat @ K ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_numeral
% 5.27/5.58 thf(fact_6989_real__sqrt__le__0__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ zero_zero_real )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_le_0_iff
% 5.27/5.58 thf(fact_6990_real__sqrt__ge__0__iff,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_0_iff
% 5.27/5.58 thf(fact_6991_real__sqrt__lt__1__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ ( sqrt @ X4 ) @ one_one_real )
% 5.27/5.58 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_lt_1_iff
% 5.27/5.58 thf(fact_6992_real__sqrt__gt__1__iff,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_gt_1_iff
% 5.27/5.58 thf(fact_6993_real__sqrt__le__1__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ one_one_real )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_le_1_iff
% 5.27/5.58 thf(fact_6994_real__sqrt__ge__1__iff,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.27/5.58 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_1_iff
% 5.27/5.58 thf(fact_6995_log__one,axiom,
% 5.27/5.58 ! [A: real] :
% 5.27/5.58 ( ( log @ A @ one_one_real )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % log_one
% 5.27/5.58 thf(fact_6996_real__sqrt__four,axiom,
% 5.27/5.58 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_four
% 5.27/5.58 thf(fact_6997_nat__1,axiom,
% 5.27/5.58 ( ( nat2 @ one_one_int )
% 5.27/5.58 = ( suc @ zero_zero_nat ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_1
% 5.27/5.58 thf(fact_6998_nat__0__iff,axiom,
% 5.27/5.58 ! [I2: int] :
% 5.27/5.58 ( ( ( nat2 @ I2 )
% 5.27/5.58 = zero_zero_nat )
% 5.27/5.58 = ( ord_less_eq_int @ I2 @ zero_zero_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_0_iff
% 5.27/5.58 thf(fact_6999_nat__le__0,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.27/5.58 => ( ( nat2 @ Z )
% 5.27/5.58 = zero_zero_nat ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_le_0
% 5.27/5.58 thf(fact_7000_zless__nat__conj,axiom,
% 5.27/5.58 ! [W: int,Z: int] :
% 5.27/5.58 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.58 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % zless_nat_conj
% 5.27/5.58 thf(fact_7001_log__eq__one,axiom,
% 5.27/5.58 ! [A: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( log @ A @ A )
% 5.27/5.58 = one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_eq_one
% 5.27/5.58 thf(fact_7002_log__less__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 5.27/5.58 = ( ord_less_real @ X4 @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_less_cancel_iff
% 5.27/5.58 thf(fact_7003_log__less__one__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ ( log @ A @ X4 ) @ one_one_real )
% 5.27/5.58 = ( ord_less_real @ X4 @ A ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_less_one_cancel_iff
% 5.27/5.58 thf(fact_7004_one__less__log__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ A @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_less_log_cancel_iff
% 5.27/5.58 thf(fact_7005_log__less__zero__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 5.27/5.58 = ( ord_less_real @ X4 @ one_one_real ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_less_zero_cancel_iff
% 5.27/5.58 thf(fact_7006_zero__less__log__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ one_one_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_less_log_cancel_iff
% 5.27/5.58 thf(fact_7007_int__nat__eq,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.27/5.58 = Z ) )
% 5.27/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.27/5.58 = zero_zero_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % int_nat_eq
% 5.27/5.58 thf(fact_7008_zero__less__nat__eq,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_less_nat_eq
% 5.27/5.58 thf(fact_7009_zero__le__log__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X4 ) )
% 5.27/5.58 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_le_log_cancel_iff
% 5.27/5.58 thf(fact_7010_log__le__zero__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ zero_zero_real )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_le_zero_cancel_iff
% 5.27/5.58 thf(fact_7011_one__le__log__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X4 ) )
% 5.27/5.58 = ( ord_less_eq_real @ A @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_le_log_cancel_iff
% 5.27/5.58 thf(fact_7012_log__le__one__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ one_one_real )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ A ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_le_one_cancel_iff
% 5.27/5.58 thf(fact_7013_log__le__cancel__iff,axiom,
% 5.27/5.58 ! [A: real,X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_le_cancel_iff
% 5.27/5.58 thf(fact_7014_diff__nat__numeral,axiom,
% 5.27/5.58 ! [V: num,V3: num] :
% 5.27/5.58 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.27/5.58 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % diff_nat_numeral
% 5.27/5.58 thf(fact_7015_and__nat__numerals_I3_J,axiom,
% 5.27/5.58 ! [X4: num] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.58 = zero_zero_nat ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_numerals(3)
% 5.27/5.58 thf(fact_7016_and__nat__numerals_I1_J,axiom,
% 5.27/5.58 ! [Y: num] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.58 = zero_zero_nat ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_numerals(1)
% 5.27/5.58 thf(fact_7017_nat__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.58 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.58 ( ( ( nat2 @ Y )
% 5.27/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 5.27/5.58 = ( Y
% 5.27/5.58 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_eq_numeral_power_cancel_iff
% 5.27/5.58 thf(fact_7018_numeral__power__eq__nat__cancel__iff,axiom,
% 5.27/5.58 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.58 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 )
% 5.27/5.58 = ( nat2 @ Y ) )
% 5.27/5.58 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.58 = Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_power_eq_nat_cancel_iff
% 5.27/5.58 thf(fact_7019_one__less__nat__eq,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_less_nat_eq
% 5.27/5.58 thf(fact_7020_real__sqrt__abs,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( sqrt @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = ( abs_abs_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_abs
% 5.27/5.58 thf(fact_7021_log__pow__cancel,axiom,
% 5.27/5.58 ! [A: real,B: nat] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.27/5.58 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_pow_cancel
% 5.27/5.58 thf(fact_7022_and__nat__numerals_I2_J,axiom,
% 5.27/5.58 ! [Y: num] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.58 = one_one_nat ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_numerals(2)
% 5.27/5.58 thf(fact_7023_and__nat__numerals_I4_J,axiom,
% 5.27/5.58 ! [X4: num] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.58 = one_one_nat ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_numerals(4)
% 5.27/5.58 thf(fact_7024_real__sqrt__pow2,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_pow2
% 5.27/5.58 thf(fact_7025_real__sqrt__pow2__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( power_power_real @ ( sqrt @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = X4 )
% 5.27/5.58 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_pow2_iff
% 5.27/5.58 thf(fact_7026_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.27/5.58 ! [X4: real,Y: real,Xa: real,Ya: real] :
% 5.27/5.58 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_mult_squared_eq
% 5.27/5.58 thf(fact_7027_nat__numeral__diff__1,axiom,
% 5.27/5.58 ! [V: num] :
% 5.27/5.58 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.27/5.58 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_numeral_diff_1
% 5.27/5.58 thf(fact_7028_nat__less__numeral__power__cancel__iff,axiom,
% 5.27/5.58 ! [A: int,X4: num,N2: nat] :
% 5.27/5.58 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 5.27/5.58 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_less_numeral_power_cancel_iff
% 5.27/5.58 thf(fact_7029_numeral__power__less__nat__cancel__iff,axiom,
% 5.27/5.58 ! [X4: num,N2: nat,A: int] :
% 5.27/5.58 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 5.27/5.58 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_power_less_nat_cancel_iff
% 5.27/5.58 thf(fact_7030_numeral__power__le__nat__cancel__iff,axiom,
% 5.27/5.58 ! [X4: num,N2: nat,A: int] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) @ ( nat2 @ A ) )
% 5.27/5.58 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_power_le_nat_cancel_iff
% 5.27/5.58 thf(fact_7031_nat__le__numeral__power__cancel__iff,axiom,
% 5.27/5.58 ! [A: int,X4: num,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X4 ) @ N2 ) )
% 5.27/5.58 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_le_numeral_power_cancel_iff
% 5.27/5.58 thf(fact_7032_Suc__0__and__eq,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.58 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % Suc_0_and_eq
% 5.27/5.58 thf(fact_7033_and__Suc__0__eq,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( bit_se727722235901077358nd_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.58 = ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_Suc_0_eq
% 5.27/5.58 thf(fact_7034_nat__mask__eq,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.58 = ( bit_se2002935070580805687sk_nat @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mask_eq
% 5.27/5.58 thf(fact_7035_and__nat__def,axiom,
% 5.27/5.58 ( bit_se727722235901077358nd_nat
% 5.27/5.58 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_def
% 5.27/5.58 thf(fact_7036_real__sqrt__less__mono,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ X4 @ Y )
% 5.27/5.58 => ( ord_less_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_less_mono
% 5.27/5.58 thf(fact_7037_real__sqrt__le__mono,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_le_mono
% 5.27/5.58 thf(fact_7038_real__sqrt__power,axiom,
% 5.27/5.58 ! [X4: real,K: nat] :
% 5.27/5.58 ( ( sqrt @ ( power_power_real @ X4 @ K ) )
% 5.27/5.58 = ( power_power_real @ ( sqrt @ X4 ) @ K ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_power
% 5.27/5.58 thf(fact_7039_real__sqrt__gt__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_gt_zero
% 5.27/5.58 thf(fact_7040_real__sqrt__eq__zero__cancel,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ( sqrt @ X4 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 => ( X4 = zero_zero_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_eq_zero_cancel
% 5.27/5.58 thf(fact_7041_real__sqrt__ge__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_zero
% 5.27/5.58 thf(fact_7042_real__sqrt__ge__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_one
% 5.27/5.58 thf(fact_7043_nat__numeral__as__int,axiom,
% 5.27/5.58 ( numeral_numeral_nat
% 5.27/5.58 = ( ^ [I3: num] : ( nat2 @ ( numeral_numeral_int @ I3 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_numeral_as_int
% 5.27/5.58 thf(fact_7044_nat__mono,axiom,
% 5.27/5.58 ! [X4: int,Y: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ X4 @ Y )
% 5.27/5.58 => ( ord_less_eq_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mono
% 5.27/5.58 thf(fact_7045_ex__nat,axiom,
% 5.27/5.58 ( ( ^ [P3: nat > $o] :
% 5.27/5.58 ? [X6: nat] : ( P3 @ X6 ) )
% 5.27/5.58 = ( ^ [P4: nat > $o] :
% 5.27/5.58 ? [X: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.27/5.58 & ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ex_nat
% 5.27/5.58 thf(fact_7046_all__nat,axiom,
% 5.27/5.58 ( ( ^ [P3: nat > $o] :
% 5.27/5.58 ! [X6: nat] : ( P3 @ X6 ) )
% 5.27/5.58 = ( ^ [P4: nat > $o] :
% 5.27/5.58 ! [X: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.27/5.58 => ( P4 @ ( nat2 @ X ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % all_nat
% 5.27/5.58 thf(fact_7047_eq__nat__nat__iff,axiom,
% 5.27/5.58 ! [Z: int,Z6: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.27/5.58 => ( ( ( nat2 @ Z )
% 5.27/5.58 = ( nat2 @ Z6 ) )
% 5.27/5.58 = ( Z = Z6 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % eq_nat_nat_iff
% 5.27/5.58 thf(fact_7048_nat__one__as__int,axiom,
% 5.27/5.58 ( one_one_nat
% 5.27/5.58 = ( nat2 @ one_one_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_one_as_int
% 5.27/5.58 thf(fact_7049_pi__not__less__zero,axiom,
% 5.27/5.58 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % pi_not_less_zero
% 5.27/5.58 thf(fact_7050_pi__gt__zero,axiom,
% 5.27/5.58 ord_less_real @ zero_zero_real @ pi ).
% 5.27/5.58
% 5.27/5.58 % pi_gt_zero
% 5.27/5.58 thf(fact_7051_pi__ge__zero,axiom,
% 5.27/5.58 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.27/5.58
% 5.27/5.58 % pi_ge_zero
% 5.27/5.58 thf(fact_7052_unset__bit__nat__def,axiom,
% 5.27/5.58 ( bit_se4205575877204974255it_nat
% 5.27/5.58 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M6 @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % unset_bit_nat_def
% 5.27/5.58 thf(fact_7053_real__div__sqrt,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( divide_divide_real @ X4 @ ( sqrt @ X4 ) )
% 5.27/5.58 = ( sqrt @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_div_sqrt
% 5.27/5.58 thf(fact_7054_sqrt__add__le__add__sqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X4 ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_add_le_add_sqrt
% 5.27/5.58 thf(fact_7055_le__real__sqrt__sumsq,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X4 @ X4 ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % le_real_sqrt_sumsq
% 5.27/5.58 thf(fact_7056_nat__mono__iff,axiom,
% 5.27/5.58 ! [Z: int,W: int] :
% 5.27/5.58 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mono_iff
% 5.27/5.58 thf(fact_7057_zless__nat__eq__int__zless,axiom,
% 5.27/5.58 ! [M: nat,Z: int] :
% 5.27/5.58 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.27/5.58
% 5.27/5.58 % zless_nat_eq_int_zless
% 5.27/5.58 thf(fact_7058_nat__le__iff,axiom,
% 5.27/5.58 ! [X4: int,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( nat2 @ X4 ) @ N2 )
% 5.27/5.58 = ( ord_less_eq_int @ X4 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_le_iff
% 5.27/5.58 thf(fact_7059_nat__0__le,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.27/5.58 = Z ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_0_le
% 5.27/5.58 thf(fact_7060_int__eq__iff,axiom,
% 5.27/5.58 ! [M: nat,Z: int] :
% 5.27/5.58 ( ( ( semiri1314217659103216013at_int @ M )
% 5.27/5.58 = Z )
% 5.27/5.58 = ( ( M
% 5.27/5.58 = ( nat2 @ Z ) )
% 5.27/5.58 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % int_eq_iff
% 5.27/5.58 thf(fact_7061_nat__int__add,axiom,
% 5.27/5.58 ! [A: nat,B: nat] :
% 5.27/5.58 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.27/5.58 = ( plus_plus_nat @ A @ B ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_int_add
% 5.27/5.58 thf(fact_7062_log__ln,axiom,
% 5.27/5.58 ( ln_ln_real
% 5.27/5.58 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_ln
% 5.27/5.58 thf(fact_7063_xor__nat__def,axiom,
% 5.27/5.58 ( bit_se6528837805403552850or_nat
% 5.27/5.58 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % xor_nat_def
% 5.27/5.58 thf(fact_7064_sqrt2__less__2,axiom,
% 5.27/5.58 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt2_less_2
% 5.27/5.58 thf(fact_7065_sgn__real__def,axiom,
% 5.27/5.58 ( sgn_sgn_real
% 5.27/5.58 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_real_def
% 5.27/5.58 thf(fact_7066_log__base__change,axiom,
% 5.27/5.58 ! [A: real,B: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( log @ B @ X4 )
% 5.27/5.58 = ( divide_divide_real @ ( log @ A @ X4 ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_base_change
% 5.27/5.58 thf(fact_7067_less__log__of__power,axiom,
% 5.27/5.58 ! [B: real,N2: nat,M: real] :
% 5.27/5.58 ( ( ord_less_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.58 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % less_log_of_power
% 5.27/5.58 thf(fact_7068_log__of__power__eq,axiom,
% 5.27/5.58 ! [M: nat,B: real,N2: nat] :
% 5.27/5.58 ( ( ( semiri5074537144036343181t_real @ M )
% 5.27/5.58 = ( power_power_real @ B @ N2 ) )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.58 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.27/5.58 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_of_power_eq
% 5.27/5.58 thf(fact_7069_nat__less__eq__zless,axiom,
% 5.27/5.58 ! [W: int,Z: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_less_eq_zless
% 5.27/5.58 thf(fact_7070_nat__le__eq__zle,axiom,
% 5.27/5.58 ! [W: int,Z: int] :
% 5.27/5.58 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.27/5.58 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.27/5.58 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.27/5.58 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_le_eq_zle
% 5.27/5.58 thf(fact_7071_nat__eq__iff,axiom,
% 5.27/5.58 ! [W: int,M: nat] :
% 5.27/5.58 ( ( ( nat2 @ W )
% 5.27/5.58 = M )
% 5.27/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( W
% 5.27/5.58 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.27/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_eq_iff
% 5.27/5.58 thf(fact_7072_nat__eq__iff2,axiom,
% 5.27/5.58 ! [M: nat,W: int] :
% 5.27/5.58 ( ( M
% 5.27/5.58 = ( nat2 @ W ) )
% 5.27/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( W
% 5.27/5.58 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.27/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_eq_iff2
% 5.27/5.58 thf(fact_7073_split__nat,axiom,
% 5.27/5.58 ! [P: nat > $o,I2: int] :
% 5.27/5.58 ( ( P @ ( nat2 @ I2 ) )
% 5.27/5.58 = ( ! [N: nat] :
% 5.27/5.58 ( ( I2
% 5.27/5.58 = ( semiri1314217659103216013at_int @ N ) )
% 5.27/5.58 => ( P @ N ) )
% 5.27/5.58 & ( ( ord_less_int @ I2 @ zero_zero_int )
% 5.27/5.58 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % split_nat
% 5.27/5.58 thf(fact_7074_le__nat__iff,axiom,
% 5.27/5.58 ! [K: int,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.58 => ( ( ord_less_eq_nat @ N2 @ ( nat2 @ K ) )
% 5.27/5.58 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N2 ) @ K ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % le_nat_iff
% 5.27/5.58 thf(fact_7075_nat__add__distrib,axiom,
% 5.27/5.58 ! [Z: int,Z6: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.27/5.58 => ( ( nat2 @ ( plus_plus_int @ Z @ Z6 ) )
% 5.27/5.58 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_add_distrib
% 5.27/5.58 thf(fact_7076_nat__mult__distrib,axiom,
% 5.27/5.58 ! [Z: int,Z6: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.27/5.58 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mult_distrib
% 5.27/5.58 thf(fact_7077_Suc__as__int,axiom,
% 5.27/5.58 ( suc
% 5.27/5.58 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % Suc_as_int
% 5.27/5.58 thf(fact_7078_nat__diff__distrib_H,axiom,
% 5.27/5.58 ! [X4: int,Y: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.58 => ( ( nat2 @ ( minus_minus_int @ X4 @ Y ) )
% 5.27/5.58 = ( minus_minus_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_diff_distrib'
% 5.27/5.58 thf(fact_7079_nat__diff__distrib,axiom,
% 5.27/5.58 ! [Z6: int,Z: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z6 )
% 5.27/5.58 => ( ( ord_less_eq_int @ Z6 @ Z )
% 5.27/5.58 => ( ( nat2 @ ( minus_minus_int @ Z @ Z6 ) )
% 5.27/5.58 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_diff_distrib
% 5.27/5.58 thf(fact_7080_nat__abs__triangle__ineq,axiom,
% 5.27/5.58 ! [K: int,L: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_abs_triangle_ineq
% 5.27/5.58 thf(fact_7081_nat__div__distrib,axiom,
% 5.27/5.58 ! [X4: int,Y: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.58 => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 5.27/5.58 = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_div_distrib
% 5.27/5.58 thf(fact_7082_nat__div__distrib_H,axiom,
% 5.27/5.58 ! [Y: int,X4: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.58 => ( ( nat2 @ ( divide_divide_int @ X4 @ Y ) )
% 5.27/5.58 = ( divide_divide_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_div_distrib'
% 5.27/5.58 thf(fact_7083_nat__power__eq,axiom,
% 5.27/5.58 ! [Z: int,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( nat2 @ ( power_power_int @ Z @ N2 ) )
% 5.27/5.58 = ( power_power_nat @ ( nat2 @ Z ) @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_power_eq
% 5.27/5.58 thf(fact_7084_nat__mod__distrib,axiom,
% 5.27/5.58 ! [X4: int,Y: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.58 => ( ( nat2 @ ( modulo_modulo_int @ X4 @ Y ) )
% 5.27/5.58 = ( modulo_modulo_nat @ ( nat2 @ X4 ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mod_distrib
% 5.27/5.58 thf(fact_7085_pi__less__4,axiom,
% 5.27/5.58 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_less_4
% 5.27/5.58 thf(fact_7086_pi__ge__two,axiom,
% 5.27/5.58 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.27/5.58
% 5.27/5.58 % pi_ge_two
% 5.27/5.58 thf(fact_7087_div__abs__eq__div__nat,axiom,
% 5.27/5.58 ! [K: int,L: int] :
% 5.27/5.58 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.27/5.58 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % div_abs_eq_div_nat
% 5.27/5.58 thf(fact_7088_pi__half__neq__two,axiom,
% 5.27/5.58 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_neq_two
% 5.27/5.58 thf(fact_7089_mod__abs__eq__div__nat,axiom,
% 5.27/5.58 ! [K: int,L: int] :
% 5.27/5.58 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L ) )
% 5.27/5.58 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mod_abs_eq_div_nat
% 5.27/5.58 thf(fact_7090_take__bit__nat__eq,axiom,
% 5.27/5.58 ! [K: int,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.58 => ( ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) )
% 5.27/5.58 = ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % take_bit_nat_eq
% 5.27/5.58 thf(fact_7091_nat__take__bit__eq,axiom,
% 5.27/5.58 ! [K: int,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.58 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) )
% 5.27/5.58 = ( bit_se2925701944663578781it_nat @ N2 @ ( nat2 @ K ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_take_bit_eq
% 5.27/5.58 thf(fact_7092_arctan__inverse,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( X4 != zero_zero_real )
% 5.27/5.58 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X4 ) )
% 5.27/5.58 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X4 ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_inverse
% 5.27/5.58 thf(fact_7093_bit__nat__iff,axiom,
% 5.27/5.58 ! [K: int,N2: nat] :
% 5.27/5.58 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N2 )
% 5.27/5.58 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.58 & ( bit_se1146084159140164899it_int @ K @ N2 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % bit_nat_iff
% 5.27/5.58 thf(fact_7094_real__less__rsqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.27/5.58 => ( ord_less_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_less_rsqrt
% 5.27/5.58 thf(fact_7095_sqrt__le__D,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_le_D
% 5.27/5.58 thf(fact_7096_real__le__rsqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ X4 @ ( sqrt @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_le_rsqrt
% 5.27/5.58 thf(fact_7097_nat__2,axiom,
% 5.27/5.58 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_2
% 5.27/5.58 thf(fact_7098_log__mult,axiom,
% 5.27/5.58 ! [A: real,X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( log @ A @ ( times_times_real @ X4 @ Y ) )
% 5.27/5.58 = ( plus_plus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_mult
% 5.27/5.58 thf(fact_7099_sgn__power__injE,axiom,
% 5.27/5.58 ! [A: real,N2: nat,X4: real,B: real] :
% 5.27/5.58 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N2 ) )
% 5.27/5.58 = X4 )
% 5.27/5.58 => ( ( X4
% 5.27/5.58 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N2 ) ) )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.58 => ( A = B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sgn_power_injE
% 5.27/5.58 thf(fact_7100_log__divide,axiom,
% 5.27/5.58 ! [A: real,X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( log @ A @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.58 = ( minus_minus_real @ ( log @ A @ X4 ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_divide
% 5.27/5.58 thf(fact_7101_le__log__of__power,axiom,
% 5.27/5.58 ! [B: real,N2: nat,M: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( power_power_real @ B @ N2 ) @ M )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.58 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % le_log_of_power
% 5.27/5.58 thf(fact_7102_log__base__pow,axiom,
% 5.27/5.58 ! [A: real,N2: nat,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( log @ ( power_power_real @ A @ N2 ) @ X4 )
% 5.27/5.58 = ( divide_divide_real @ ( log @ A @ X4 ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_base_pow
% 5.27/5.58 thf(fact_7103_log__nat__power,axiom,
% 5.27/5.58 ! [X4: real,B: real,N2: nat] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( log @ B @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.58 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_nat_power
% 5.27/5.58 thf(fact_7104_Suc__nat__eq__nat__zadd1,axiom,
% 5.27/5.58 ! [Z: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( ( suc @ ( nat2 @ Z ) )
% 5.27/5.58 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % Suc_nat_eq_nat_zadd1
% 5.27/5.58 thf(fact_7105_nat__less__iff,axiom,
% 5.27/5.58 ! [W: int,M: nat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.27/5.58 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.27/5.58 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_less_iff
% 5.27/5.58 thf(fact_7106_nat__mult__distrib__neg,axiom,
% 5.27/5.58 ! [Z: int,Z6: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.27/5.58 => ( ( nat2 @ ( times_times_int @ Z @ Z6 ) )
% 5.27/5.58 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z6 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_mult_distrib_neg
% 5.27/5.58 thf(fact_7107_nat__abs__int__diff,axiom,
% 5.27/5.58 ! [A: nat,B: nat] :
% 5.27/5.58 ( ( ( ord_less_eq_nat @ A @ B )
% 5.27/5.58 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.27/5.58 = ( minus_minus_nat @ B @ A ) ) )
% 5.27/5.58 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.27/5.58 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.27/5.58 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_abs_int_diff
% 5.27/5.58 thf(fact_7108_pi__half__neq__zero,axiom,
% 5.27/5.58 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 != zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_neq_zero
% 5.27/5.58 thf(fact_7109_pi__half__less__two,axiom,
% 5.27/5.58 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_less_two
% 5.27/5.58 thf(fact_7110_pi__half__le__two,axiom,
% 5.27/5.58 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_le_two
% 5.27/5.58 thf(fact_7111_real__le__lsqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_le_lsqrt
% 5.27/5.58 thf(fact_7112_real__sqrt__unique,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( sqrt @ X4 )
% 5.27/5.58 = Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_unique
% 5.27/5.58 thf(fact_7113_lemma__real__divide__sqrt__less,axiom,
% 5.27/5.58 ! [U: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ U )
% 5.27/5.58 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.27/5.58
% 5.27/5.58 % lemma_real_divide_sqrt_less
% 5.27/5.58 thf(fact_7114_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 = X4 )
% 5.27/5.58 => ( Y = zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_eq_cancel
% 5.27/5.58 thf(fact_7115_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 = Y )
% 5.27/5.58 => ( X4 = zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_eq_cancel2
% 5.27/5.58 thf(fact_7116_real__sqrt__sum__squares__ge1,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_ge1
% 5.27/5.58 thf(fact_7117_real__sqrt__sum__squares__ge2,axiom,
% 5.27/5.58 ! [Y: real,X4: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_ge2
% 5.27/5.58 thf(fact_7118_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.27/5.58 ! [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 ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_triangle_ineq
% 5.27/5.58 thf(fact_7119_sqrt__ge__absD,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ Y ) )
% 5.27/5.58 => ( ord_less_eq_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_ge_absD
% 5.27/5.58 thf(fact_7120_log__of__power__less,axiom,
% 5.27/5.58 ! [M: nat,B: real,N2: nat] :
% 5.27/5.58 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.58 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_of_power_less
% 5.27/5.58 thf(fact_7121_log2__of__power__eq,axiom,
% 5.27/5.58 ! [M: nat,N2: nat] :
% 5.27/5.58 ( ( M
% 5.27/5.58 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 => ( ( semiri5074537144036343181t_real @ N2 )
% 5.27/5.58 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log2_of_power_eq
% 5.27/5.58 thf(fact_7122_log__eq__div__ln__mult__log,axiom,
% 5.27/5.58 ! [A: real,B: real,X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( A != one_one_real )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.58 => ( ( B != one_one_real )
% 5.27/5.58 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( log @ A @ X4 )
% 5.27/5.58 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X4 ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_eq_div_ln_mult_log
% 5.27/5.58 thf(fact_7123_nat__dvd__iff,axiom,
% 5.27/5.58 ! [Z: int,M: nat] :
% 5.27/5.58 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.27/5.58 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.27/5.58 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.58 => ( M = zero_zero_nat ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_dvd_iff
% 5.27/5.58 thf(fact_7124_pi__half__gt__zero,axiom,
% 5.27/5.58 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_gt_zero
% 5.27/5.58 thf(fact_7125_pi__half__ge__zero,axiom,
% 5.27/5.58 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % pi_half_ge_zero
% 5.27/5.58 thf(fact_7126_m2pi__less__pi,axiom,
% 5.27/5.58 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.27/5.58
% 5.27/5.58 % m2pi_less_pi
% 5.27/5.58 thf(fact_7127_arctan__ubound,axiom,
% 5.27/5.58 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_ubound
% 5.27/5.58 thf(fact_7128_arctan__one,axiom,
% 5.27/5.58 ( ( arctan @ one_one_real )
% 5.27/5.58 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_one
% 5.27/5.58 thf(fact_7129_real__less__lsqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_real @ X4 @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ord_less_real @ ( sqrt @ X4 ) @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_less_lsqrt
% 5.27/5.58 thf(fact_7130_sqrt__sum__squares__le__sum,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_sum_squares_le_sum
% 5.27/5.58 thf(fact_7131_log__of__power__le,axiom,
% 5.27/5.58 ! [M: nat,B: real,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N2 ) )
% 5.27/5.58 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.58 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log_of_power_le
% 5.27/5.58 thf(fact_7132_sqrt__sum__squares__le__sum__abs,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_sum_squares_le_sum_abs
% 5.27/5.58 thf(fact_7133_real__sqrt__ge__abs2,axiom,
% 5.27/5.58 ! [Y: real,X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_abs2
% 5.27/5.58 thf(fact_7134_real__sqrt__ge__abs1,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_ge_abs1
% 5.27/5.58 thf(fact_7135_ln__sqrt,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ln_ln_real @ ( sqrt @ X4 ) )
% 5.27/5.58 = ( divide_divide_real @ ( ln_ln_real @ X4 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ln_sqrt
% 5.27/5.58 thf(fact_7136_sqrt__even__pow2,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.58 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_even_pow2
% 5.27/5.58 thf(fact_7137_minus__pi__half__less__zero,axiom,
% 5.27/5.58 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.27/5.58
% 5.27/5.58 % minus_pi_half_less_zero
% 5.27/5.58 thf(fact_7138_arctan__bounded,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.27/5.58 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_bounded
% 5.27/5.58 thf(fact_7139_arctan__lbound,axiom,
% 5.27/5.58 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % arctan_lbound
% 5.27/5.58 thf(fact_7140_and__nat__unfold,axiom,
% 5.27/5.58 ( bit_se727722235901077358nd_nat
% 5.27/5.58 = ( ^ [M6: nat,N: nat] :
% 5.27/5.58 ( if_nat
% 5.27/5.58 @ ( ( M6 = zero_zero_nat )
% 5.27/5.58 | ( N = zero_zero_nat ) )
% 5.27/5.58 @ zero_zero_nat
% 5.27/5.58 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_unfold
% 5.27/5.58 thf(fact_7141_arsinh__real__aux,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arsinh_real_aux
% 5.27/5.58 thf(fact_7142_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.27/5.58 ! [X4: real,Y: real,Xa: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_mult_ge_zero
% 5.27/5.58 thf(fact_7143_real__sqrt__power__even,axiom,
% 5.27/5.58 ! [N2: nat,X4: real] :
% 5.27/5.58 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( power_power_real @ ( sqrt @ X4 ) @ N2 )
% 5.27/5.58 = ( power_power_real @ X4 @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_power_even
% 5.27/5.58 thf(fact_7144_arith__geo__mean__sqrt,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X4 @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X4 @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arith_geo_mean_sqrt
% 5.27/5.58 thf(fact_7145_less__log2__of__power,axiom,
% 5.27/5.58 ! [N2: nat,M: nat] :
% 5.27/5.58 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.27/5.58 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % less_log2_of_power
% 5.27/5.58 thf(fact_7146_le__log2__of__power,axiom,
% 5.27/5.58 ! [N2: nat,M: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ M )
% 5.27/5.58 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % le_log2_of_power
% 5.27/5.58 thf(fact_7147_and__nat__rec,axiom,
% 5.27/5.58 ( bit_se727722235901077358nd_nat
% 5.27/5.58 = ( ^ [M6: nat,N: nat] :
% 5.27/5.58 ( plus_plus_nat
% 5.27/5.58 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.58 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.27/5.58 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.58 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % and_nat_rec
% 5.27/5.58 thf(fact_7148_even__nat__iff,axiom,
% 5.27/5.58 ! [K: int] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.58 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.27/5.58 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % even_nat_iff
% 5.27/5.58 thf(fact_7149_log2__of__power__less,axiom,
% 5.27/5.58 ! [M: nat,N2: nat] :
% 5.27/5.58 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.58 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log2_of_power_less
% 5.27/5.58 thf(fact_7150_cos__x__y__le__one,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_x_y_le_one
% 5.27/5.58 thf(fact_7151_real__sqrt__sum__squares__less,axiom,
% 5.27/5.58 ! [X4: real,U: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_sqrt_sum_squares_less
% 5.27/5.58 thf(fact_7152_arcosh__real__def,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.58 => ( ( arcosh_real @ X4 )
% 5.27/5.58 = ( ln_ln_real @ ( plus_plus_real @ X4 @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arcosh_real_def
% 5.27/5.58 thf(fact_7153_sqrt__sum__squares__half__less,axiom,
% 5.27/5.58 ! [X4: real,U: real,Y: real] :
% 5.27/5.58 ( ( ord_less_real @ X4 @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sqrt_sum_squares_half_less
% 5.27/5.58 thf(fact_7154_log2__of__power__le,axiom,
% 5.27/5.58 ! [M: nat,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.58 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % log2_of_power_le
% 5.27/5.58 thf(fact_7155_machin__Euler,axiom,
% 5.27/5.58 ( ( 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 ) ) ) ) ) ) ) ) ) ) )
% 5.27/5.58 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % machin_Euler
% 5.27/5.58 thf(fact_7156_sin__cos__npi,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_npi
% 5.27/5.58 thf(fact_7157_ceiling__log__nat__eq__powr__iff,axiom,
% 5.27/5.58 ! [B: nat,K: nat,N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.27/5.58 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.58 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.27/5.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) )
% 5.27/5.58 = ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.27/5.58 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_log_nat_eq_powr_iff
% 5.27/5.58 thf(fact_7158_arsinh__real__def,axiom,
% 5.27/5.58 ( arsinh_real
% 5.27/5.58 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % arsinh_real_def
% 5.27/5.58 thf(fact_7159_cos__pi__eq__zero,axiom,
% 5.27/5.58 ! [M: nat] :
% 5.27/5.58 ( ( 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 ) ) ) )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_pi_eq_zero
% 5.27/5.58 thf(fact_7160_ceiling__log__nat__eq__if,axiom,
% 5.27/5.58 ! [B: nat,N2: nat,K: nat] :
% 5.27/5.58 ( ( ord_less_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.27/5.58 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.27/5.58 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.27/5.58 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.27/5.58 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_log_nat_eq_if
% 5.27/5.58 thf(fact_7161_ceiling__log2__div2,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.58 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.58 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_log2_div2
% 5.27/5.58 thf(fact_7162_cos__zero,axiom,
% 5.27/5.58 ( ( cos_complex @ zero_zero_complex )
% 5.27/5.58 = one_one_complex ) ).
% 5.27/5.58
% 5.27/5.58 % cos_zero
% 5.27/5.58 thf(fact_7163_cos__zero,axiom,
% 5.27/5.58 ( ( cos_real @ zero_zero_real )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_zero
% 5.27/5.58 thf(fact_7164_ceiling__numeral,axiom,
% 5.27/5.58 ! [V: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( numeral_numeral_real @ V ) )
% 5.27/5.58 = ( numeral_numeral_int @ V ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_numeral
% 5.27/5.58 thf(fact_7165_ceiling__one,axiom,
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ one_one_rat )
% 5.27/5.58 = one_one_int ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_one
% 5.27/5.58 thf(fact_7166_ceiling__one,axiom,
% 5.27/5.58 ( ( archim7802044766580827645g_real @ one_one_real )
% 5.27/5.58 = one_one_int ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_one
% 5.27/5.58 thf(fact_7167_cos__pi,axiom,
% 5.27/5.58 ( ( cos_real @ pi )
% 5.27/5.58 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_pi
% 5.27/5.58 thf(fact_7168_sin__cos__squared__add3,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ X4 ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ X4 ) ) )
% 5.27/5.58 = one_one_complex ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add3
% 5.27/5.58 thf(fact_7169_sin__cos__squared__add3,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ X4 ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ X4 ) ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add3
% 5.27/5.58 thf(fact_7170_ceiling__le__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_zero
% 5.27/5.58 thf(fact_7171_ceiling__le__zero,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_zero
% 5.27/5.58 thf(fact_7172_zero__less__ceiling,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_less_ceiling
% 5.27/5.58 thf(fact_7173_zero__less__ceiling,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_less_ceiling
% 5.27/5.58 thf(fact_7174_ceiling__le__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_numeral
% 5.27/5.58 thf(fact_7175_ceiling__le__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_numeral
% 5.27/5.58 thf(fact_7176_ceiling__less__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_one
% 5.27/5.58 thf(fact_7177_ceiling__less__one,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ zero_zero_rat ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_one
% 5.27/5.58 thf(fact_7178_one__le__ceiling,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ zero_zero_rat @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_le_ceiling
% 5.27/5.58 thf(fact_7179_one__le__ceiling,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_le_ceiling
% 5.27/5.58 thf(fact_7180_numeral__less__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_less_ceiling
% 5.27/5.58 thf(fact_7181_numeral__less__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: real] :
% 5.27/5.58 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_less_ceiling
% 5.27/5.58 thf(fact_7182_ceiling__le__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_one
% 5.27/5.58 thf(fact_7183_ceiling__le__one,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_one
% 5.27/5.58 thf(fact_7184_one__less__ceiling,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ one_one_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ one_one_rat @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_less_ceiling
% 5.27/5.58 thf(fact_7185_one__less__ceiling,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_int @ one_one_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ one_one_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % one_less_ceiling
% 5.27/5.58 thf(fact_7186_ceiling__add__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.27/5.58 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_numeral
% 5.27/5.58 thf(fact_7187_ceiling__add__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.27/5.58 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_numeral
% 5.27/5.58 thf(fact_7188_ceiling__neg__numeral,axiom,
% 5.27/5.58 ! [V: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_neg_numeral
% 5.27/5.58 thf(fact_7189_ceiling__neg__numeral,axiom,
% 5.27/5.58 ! [V: num] :
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_neg_numeral
% 5.27/5.58 thf(fact_7190_ceiling__add__one,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 5.27/5.58 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_one
% 5.27/5.58 thf(fact_7191_ceiling__add__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 5.27/5.58 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_one
% 5.27/5.58 thf(fact_7192_ceiling__diff__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.27/5.58 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_diff_numeral
% 5.27/5.58 thf(fact_7193_ceiling__diff__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.27/5.58 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_diff_numeral
% 5.27/5.58 thf(fact_7194_ceiling__diff__one,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( archim2889992004027027881ng_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 5.27/5.58 = ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ one_one_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_diff_one
% 5.27/5.58 thf(fact_7195_ceiling__diff__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 5.27/5.58 = ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ one_one_int ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_diff_one
% 5.27/5.58 thf(fact_7196_ceiling__numeral__power,axiom,
% 5.27/5.58 ! [X4: num,N2: nat] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.58 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_numeral_power
% 5.27/5.58 thf(fact_7197_nat__ceiling__le__eq,axiom,
% 5.27/5.58 ! [X4: real,A: nat] :
% 5.27/5.58 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) @ A )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % nat_ceiling_le_eq
% 5.27/5.58 thf(fact_7198_ceiling__less__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ zero_zero_int )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_zero
% 5.27/5.58 thf(fact_7199_ceiling__less__zero,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ zero_zero_int )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_zero
% 5.27/5.58 thf(fact_7200_zero__le__ceiling,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_le_ceiling
% 5.27/5.58 thf(fact_7201_zero__le__ceiling,axiom,
% 5.27/5.58 ! [X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ zero_zero_int @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % zero_le_ceiling
% 5.27/5.58 thf(fact_7202_ceiling__divide__eq__div__numeral,axiom,
% 5.27/5.58 ! [A: num,B: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_divide_eq_div_numeral
% 5.27/5.58 thf(fact_7203_ceiling__less__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_numeral
% 5.27/5.58 thf(fact_7204_ceiling__less__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_numeral
% 5.27/5.58 thf(fact_7205_numeral__le__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ ( minus_minus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_le_ceiling
% 5.27/5.58 thf(fact_7206_numeral__le__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ ( minus_minus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % numeral_le_ceiling
% 5.27/5.58 thf(fact_7207_ceiling__le__neg__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_neg_numeral
% 5.27/5.58 thf(fact_7208_ceiling__le__neg__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_le_neg_numeral
% 5.27/5.58 thf(fact_7209_neg__numeral__less__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: real] :
% 5.27/5.58 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % neg_numeral_less_ceiling
% 5.27/5.58 thf(fact_7210_neg__numeral__less__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: rat] :
% 5.27/5.58 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % neg_numeral_less_ceiling
% 5.27/5.58 thf(fact_7211_cos__pi__half,axiom,
% 5.27/5.58 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_pi_half
% 5.27/5.58 thf(fact_7212_sin__two__pi,axiom,
% 5.27/5.58 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_two_pi
% 5.27/5.58 thf(fact_7213_sin__pi__half,axiom,
% 5.27/5.58 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_pi_half
% 5.27/5.58 thf(fact_7214_cos__two__pi,axiom,
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_two_pi
% 5.27/5.58 thf(fact_7215_cos__periodic,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( cos_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.27/5.58 = ( cos_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_periodic
% 5.27/5.58 thf(fact_7216_sin__periodic,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( sin_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.27/5.58 = ( sin_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_periodic
% 5.27/5.58 thf(fact_7217_cos__2pi__minus,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 5.27/5.58 = ( cos_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_2pi_minus
% 5.27/5.58 thf(fact_7218_cos__npi,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ pi ) )
% 5.27/5.58 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_npi
% 5.27/5.58 thf(fact_7219_cos__npi2,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.58 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_npi2
% 5.27/5.58 thf(fact_7220_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.27/5.58 ! [A: num,B: num] :
% 5.27/5.58 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.27/5.58 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_minus_divide_eq_div_numeral
% 5.27/5.58 thf(fact_7221_sin__cos__squared__add2,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( plus_plus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add2
% 5.27/5.58 thf(fact_7222_sin__cos__squared__add2,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( plus_plus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_complex ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add2
% 5.27/5.58 thf(fact_7223_sin__cos__squared__add,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( plus_plus_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add
% 5.27/5.58 thf(fact_7224_sin__cos__squared__add,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( plus_plus_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_complex ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_squared_add
% 5.27/5.58 thf(fact_7225_sin__2npi,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_2npi
% 5.27/5.58 thf(fact_7226_cos__2npi,axiom,
% 5.27/5.58 ! [N2: nat] :
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) @ pi ) )
% 5.27/5.58 = one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_2npi
% 5.27/5.58 thf(fact_7227_sin__2pi__minus,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X4 ) )
% 5.27/5.58 = ( uminus_uminus_real @ ( sin_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_2pi_minus
% 5.27/5.58 thf(fact_7228_ceiling__less__neg__numeral,axiom,
% 5.27/5.58 ! [X4: real,V: num] :
% 5.27/5.58 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.58 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_neg_numeral
% 5.27/5.58 thf(fact_7229_ceiling__less__neg__numeral,axiom,
% 5.27/5.58 ! [X4: rat,V: num] :
% 5.27/5.58 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.58 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_neg_numeral
% 5.27/5.58 thf(fact_7230_neg__numeral__le__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.58 = ( ord_less_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % neg_numeral_le_ceiling
% 5.27/5.58 thf(fact_7231_neg__numeral__le__ceiling,axiom,
% 5.27/5.58 ! [V: num,X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.58 = ( ord_less_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % neg_numeral_le_ceiling
% 5.27/5.58 thf(fact_7232_cos__3over2__pi,axiom,
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.27/5.58 = zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_3over2_pi
% 5.27/5.58 thf(fact_7233_sin__3over2__pi,axiom,
% 5.27/5.58 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.27/5.58 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_3over2_pi
% 5.27/5.58 thf(fact_7234_cos__one__sin__zero,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( ( cos_complex @ X4 )
% 5.27/5.58 = one_one_complex )
% 5.27/5.58 => ( ( sin_complex @ X4 )
% 5.27/5.58 = zero_zero_complex ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_one_sin_zero
% 5.27/5.58 thf(fact_7235_cos__one__sin__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( cos_real @ X4 )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 => ( ( sin_real @ X4 )
% 5.27/5.58 = zero_zero_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_one_sin_zero
% 5.27/5.58 thf(fact_7236_sin__add,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.58 = ( plus_plus_complex @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_add
% 5.27/5.58 thf(fact_7237_sin__add,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( sin_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.58 = ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_add
% 5.27/5.58 thf(fact_7238_cos__diff,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 5.27/5.58 = ( plus_plus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_diff
% 5.27/5.58 thf(fact_7239_cos__diff,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 5.27/5.58 = ( plus_plus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_diff
% 5.27/5.58 thf(fact_7240_cos__add,axiom,
% 5.27/5.58 ! [X4: complex,Y: complex] :
% 5.27/5.58 ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.58 = ( minus_minus_complex @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_add
% 5.27/5.58 thf(fact_7241_cos__add,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.58 = ( minus_minus_real @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_add
% 5.27/5.58 thf(fact_7242_sin__zero__norm__cos__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( sin_real @ X4 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 => ( ( real_V7735802525324610683m_real @ ( cos_real @ X4 ) )
% 5.27/5.58 = one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_zero_norm_cos_one
% 5.27/5.58 thf(fact_7243_sin__zero__norm__cos__one,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( ( sin_complex @ X4 )
% 5.27/5.58 = zero_zero_complex )
% 5.27/5.58 => ( ( real_V1022390504157884413omplex @ ( cos_complex @ X4 ) )
% 5.27/5.58 = one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_zero_norm_cos_one
% 5.27/5.58 thf(fact_7244_sin__zero__abs__cos__one,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ( sin_real @ X4 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 => ( ( abs_abs_real @ ( cos_real @ X4 ) )
% 5.27/5.58 = one_one_real ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_zero_abs_cos_one
% 5.27/5.58 thf(fact_7245_sin__double,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.58 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sin_complex @ X4 ) ) @ ( cos_complex @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_double
% 5.27/5.58 thf(fact_7246_sin__double,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.58 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sin_real @ X4 ) ) @ ( cos_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_double
% 5.27/5.58 thf(fact_7247_sincos__principal__value,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ? [Y3: real] :
% 5.27/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y3 )
% 5.27/5.58 & ( ord_less_eq_real @ Y3 @ pi )
% 5.27/5.58 & ( ( sin_real @ Y3 )
% 5.27/5.58 = ( sin_real @ X4 ) )
% 5.27/5.58 & ( ( cos_real @ Y3 )
% 5.27/5.58 = ( cos_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sincos_principal_value
% 5.27/5.58 thf(fact_7248_ceiling__mono,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ Y @ X4 )
% 5.27/5.58 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ Y ) @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_mono
% 5.27/5.58 thf(fact_7249_ceiling__mono,axiom,
% 5.27/5.58 ! [Y: rat,X4: rat] :
% 5.27/5.58 ( ( ord_less_eq_rat @ Y @ X4 )
% 5.27/5.58 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ Y ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_mono
% 5.27/5.58 thf(fact_7250_sin__x__le__x,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ ( sin_real @ X4 ) @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_x_le_x
% 5.27/5.58 thf(fact_7251_ceiling__less__cancel,axiom,
% 5.27/5.58 ! [X4: rat,Y: rat] :
% 5.27/5.58 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) )
% 5.27/5.58 => ( ord_less_rat @ X4 @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_cancel
% 5.27/5.58 thf(fact_7252_ceiling__less__cancel,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) )
% 5.27/5.58 => ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_less_cancel
% 5.27/5.58 thf(fact_7253_sin__le__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( sin_real @ X4 ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_le_one
% 5.27/5.58 thf(fact_7254_cos__le__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( cos_real @ X4 ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_le_one
% 5.27/5.58 thf(fact_7255_abs__sin__x__le__abs__x,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ ( abs_abs_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sin_x_le_abs_x
% 5.27/5.58 thf(fact_7256_sin__cos__le1,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_le1
% 5.27/5.58 thf(fact_7257_sin__squared__eq,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_squared_eq
% 5.27/5.58 thf(fact_7258_sin__squared__eq,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_squared_eq
% 5.27/5.58 thf(fact_7259_cos__squared__eq,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_squared_eq
% 5.27/5.58 thf(fact_7260_cos__squared__eq,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.58 = ( minus_minus_real @ one_one_real @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_squared_eq
% 5.27/5.58 thf(fact_7261_of__nat__ceiling,axiom,
% 5.27/5.58 ! [R3: real] : ( ord_less_eq_real @ R3 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ R3 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % of_nat_ceiling
% 5.27/5.58 thf(fact_7262_of__nat__ceiling,axiom,
% 5.27/5.58 ! [R3: rat] : ( ord_less_eq_rat @ R3 @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim2889992004027027881ng_rat @ R3 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % of_nat_ceiling
% 5.27/5.58 thf(fact_7263_sin__gt__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ X4 @ pi )
% 5.27/5.58 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_gt_zero
% 5.27/5.58 thf(fact_7264_sin__x__ge__neg__x,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ord_less_eq_real @ ( uminus_uminus_real @ X4 ) @ ( sin_real @ X4 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_x_ge_neg_x
% 5.27/5.58 thf(fact_7265_sin__ge__zero,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_ge_zero
% 5.27/5.58 thf(fact_7266_ceiling__add__le,axiom,
% 5.27/5.58 ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_le
% 5.27/5.58 thf(fact_7267_ceiling__add__le,axiom,
% 5.27/5.58 ! [X4: real,Y: real] : ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim7802044766580827645g_real @ Y ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % ceiling_add_le
% 5.27/5.58 thf(fact_7268_real__nat__ceiling__ge,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ X4 @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % real_nat_ceiling_ge
% 5.27/5.58 thf(fact_7269_sin__ge__minus__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_ge_minus_one
% 5.27/5.58 thf(fact_7270_cos__inj__pi,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ pi )
% 5.27/5.58 => ( ( ( cos_real @ X4 )
% 5.27/5.58 = ( cos_real @ Y ) )
% 5.27/5.58 => ( X4 = Y ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_inj_pi
% 5.27/5.58 thf(fact_7271_cos__mono__le__eq,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ pi )
% 5.27/5.58 => ( ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 5.27/5.58 = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_mono_le_eq
% 5.27/5.58 thf(fact_7272_cos__monotone__0__pi__le,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ord_less_eq_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_monotone_0_pi_le
% 5.27/5.58 thf(fact_7273_cos__ge__minus__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X4 ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_ge_minus_one
% 5.27/5.58 thf(fact_7274_abs__sin__le__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X4 ) ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % abs_sin_le_one
% 5.27/5.58 thf(fact_7275_abs__cos__le__one,axiom,
% 5.27/5.58 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X4 ) ) @ one_one_real ) ).
% 5.27/5.58
% 5.27/5.58 % abs_cos_le_one
% 5.27/5.58 thf(fact_7276_sin__times__sin,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( times_times_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_times_sin
% 5.27/5.58 thf(fact_7277_sin__times__sin,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( times_times_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.27/5.58 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_times_sin
% 5.27/5.58 thf(fact_7278_sin__times__cos,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( times_times_real @ ( sin_real @ W ) @ ( cos_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_times_cos
% 5.27/5.58 thf(fact_7279_sin__times__cos,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( times_times_complex @ ( sin_complex @ W ) @ ( cos_complex @ Z ) )
% 5.27/5.58 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_times_cos
% 5.27/5.58 thf(fact_7280_cos__times__sin,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( times_times_real @ ( cos_real @ W ) @ ( sin_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_times_sin
% 5.27/5.58 thf(fact_7281_cos__times__sin,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( times_times_complex @ ( cos_complex @ W ) @ ( sin_complex @ Z ) )
% 5.27/5.58 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( sin_complex @ ( plus_plus_complex @ W @ Z ) ) @ ( sin_complex @ ( minus_minus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_times_sin
% 5.27/5.58 thf(fact_7282_sin__plus__sin,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( plus_plus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_plus_sin
% 5.27/5.58 thf(fact_7283_sin__plus__sin,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( plus_plus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_plus_sin
% 5.27/5.58 thf(fact_7284_sin__diff__sin,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( minus_minus_real @ ( sin_real @ W ) @ ( sin_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_diff_sin
% 5.27/5.58 thf(fact_7285_sin__diff__sin,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( minus_minus_complex @ ( sin_complex @ W ) @ ( sin_complex @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_diff_sin
% 5.27/5.58 thf(fact_7286_cos__diff__cos,axiom,
% 5.27/5.58 ! [W: real,Z: real] :
% 5.27/5.58 ( ( minus_minus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_diff_cos
% 5.27/5.58 thf(fact_7287_cos__diff__cos,axiom,
% 5.27/5.58 ! [W: complex,Z: complex] :
% 5.27/5.58 ( ( minus_minus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_diff_cos
% 5.27/5.58 thf(fact_7288_cos__double,axiom,
% 5.27/5.58 ! [X4: complex] :
% 5.27/5.58 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.58 = ( minus_minus_complex @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sin_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_double
% 5.27/5.58 thf(fact_7289_cos__double,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.58 = ( minus_minus_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sin_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_double
% 5.27/5.58 thf(fact_7290_cos__double__sin,axiom,
% 5.27/5.58 ! [W: complex] :
% 5.27/5.58 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.27/5.58 = ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( sin_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_double_sin
% 5.27/5.58 thf(fact_7291_cos__double__sin,axiom,
% 5.27/5.58 ! [W: real] :
% 5.27/5.58 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.27/5.58 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_double_sin
% 5.27/5.58 thf(fact_7292_cos__two__neq__zero,axiom,
% 5.27/5.58 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 != zero_zero_real ) ).
% 5.27/5.58
% 5.27/5.58 % cos_two_neq_zero
% 5.27/5.58 thf(fact_7293_cos__monotone__0__pi,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_real @ Y @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_monotone_0_pi
% 5.27/5.58 thf(fact_7294_cos__mono__less__eq,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ pi )
% 5.27/5.58 => ( ( ord_less_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) )
% 5.27/5.58 = ( ord_less_real @ Y @ X4 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_mono_less_eq
% 5.27/5.58 thf(fact_7295_sin__eq__0__pi,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ X4 @ pi )
% 5.27/5.58 => ( ( ( sin_real @ X4 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 => ( X4 = zero_zero_real ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_eq_0_pi
% 5.27/5.58 thf(fact_7296_sin__zero__pi__iff,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ pi )
% 5.27/5.58 => ( ( ( sin_real @ X4 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 = ( X4 = zero_zero_real ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_zero_pi_iff
% 5.27/5.58 thf(fact_7297_cos__monotone__minus__pi__0_H,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.58 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_monotone_minus_pi_0'
% 5.27/5.58 thf(fact_7298_sincos__total__pi,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 => ? [T3: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.58 & ( ord_less_eq_real @ T3 @ pi )
% 5.27/5.58 & ( X4
% 5.27/5.58 = ( cos_real @ T3 ) )
% 5.27/5.58 & ( Y
% 5.27/5.58 = ( sin_real @ T3 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sincos_total_pi
% 5.27/5.58 thf(fact_7299_sin__cos__sqrt,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X4 ) )
% 5.27/5.58 => ( ( sin_real @ X4 )
% 5.27/5.58 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_cos_sqrt
% 5.27/5.58 thf(fact_7300_sin__expansion__lemma,axiom,
% 5.27/5.58 ! [X4: real,M: nat] :
% 5.27/5.58 ( ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_expansion_lemma
% 5.27/5.58 thf(fact_7301_cos__expansion__lemma,axiom,
% 5.27/5.58 ! [X4: real,M: nat] :
% 5.27/5.58 ( ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.58 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_expansion_lemma
% 5.27/5.58 thf(fact_7302_mult__ceiling__le,axiom,
% 5.27/5.58 ! [A: real,B: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.27/5.58 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mult_ceiling_le
% 5.27/5.58 thf(fact_7303_mult__ceiling__le,axiom,
% 5.27/5.58 ! [A: rat,B: rat] :
% 5.27/5.58 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.58 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.27/5.58 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % mult_ceiling_le
% 5.27/5.58 thf(fact_7304_sin__gt__zero__02,axiom,
% 5.27/5.58 ! [X4: real] :
% 5.27/5.58 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sin_gt_zero_02
% 5.27/5.58 thf(fact_7305_cos__two__less__zero,axiom,
% 5.27/5.58 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.27/5.58
% 5.27/5.58 % cos_two_less_zero
% 5.27/5.58 thf(fact_7306_cos__is__zero,axiom,
% 5.27/5.58 ? [X5: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.27/5.58 & ( ord_less_eq_real @ X5 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 & ( ( cos_real @ X5 )
% 5.27/5.58 = zero_zero_real )
% 5.27/5.58 & ! [Y4: real] :
% 5.27/5.58 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.27/5.58 & ( ord_less_eq_real @ Y4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.58 & ( ( cos_real @ Y4 )
% 5.27/5.58 = zero_zero_real ) )
% 5.27/5.58 => ( Y4 = X5 ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_is_zero
% 5.27/5.58 thf(fact_7307_cos__two__le__zero,axiom,
% 5.27/5.58 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.27/5.58
% 5.27/5.58 % cos_two_le_zero
% 5.27/5.58 thf(fact_7308_cos__monotone__minus__pi__0,axiom,
% 5.27/5.58 ! [Y: real,X4: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.27/5.58 => ( ( ord_less_real @ Y @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.58 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X4 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_monotone_minus_pi_0
% 5.27/5.58 thf(fact_7309_cos__total,axiom,
% 5.27/5.58 ! [Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.58 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.58 => ? [X5: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.27/5.58 & ( ord_less_eq_real @ X5 @ pi )
% 5.27/5.58 & ( ( cos_real @ X5 )
% 5.27/5.58 = Y )
% 5.27/5.58 & ! [Y4: real] :
% 5.27/5.58 ( ( ( ord_less_eq_real @ zero_zero_real @ Y4 )
% 5.27/5.58 & ( ord_less_eq_real @ Y4 @ pi )
% 5.27/5.58 & ( ( cos_real @ Y4 )
% 5.27/5.58 = Y ) )
% 5.27/5.58 => ( Y4 = X5 ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % cos_total
% 5.27/5.58 thf(fact_7310_sincos__total__pi__half,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.58 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.58 => ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 => ? [T3: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.58 & ( ord_less_eq_real @ T3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.58 & ( X4
% 5.27/5.58 = ( cos_real @ T3 ) )
% 5.27/5.58 & ( Y
% 5.27/5.58 = ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sincos_total_pi_half
% 5.27/5.58 thf(fact_7311_sincos__total__2pi__le,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 => ? [T3: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.58 & ( ord_less_eq_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.58 & ( X4
% 5.27/5.58 = ( cos_real @ T3 ) )
% 5.27/5.58 & ( Y
% 5.27/5.58 = ( sin_real @ T3 ) ) ) ) ).
% 5.27/5.58
% 5.27/5.58 % sincos_total_2pi_le
% 5.27/5.58 thf(fact_7312_sincos__total__2pi,axiom,
% 5.27/5.58 ! [X4: real,Y: real] :
% 5.27/5.58 ( ( ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.58 = one_one_real )
% 5.27/5.58 => ~ ! [T3: real] :
% 5.27/5.58 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.58 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.58 => ( ( X4
% 5.27/5.58 = ( cos_real @ T3 ) )
% 5.27/5.58 => ( Y
% 5.27/5.59 != ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sincos_total_2pi
% 5.27/5.59 thf(fact_7313_sin__pi__divide__n__ge__0,axiom,
% 5.27/5.59 ! [N2: nat] :
% 5.27/5.59 ( ( N2 != zero_zero_nat )
% 5.27/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_pi_divide_n_ge_0
% 5.27/5.59 thf(fact_7314_sin__45,axiom,
% 5.27/5.59 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_45
% 5.27/5.59 thf(fact_7315_cos__45,axiom,
% 5.27/5.59 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_45
% 5.27/5.59 thf(fact_7316_cos__times__cos,axiom,
% 5.27/5.59 ! [W: real,Z: real] :
% 5.27/5.59 ( ( times_times_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.27/5.59 = ( 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 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_times_cos
% 5.27/5.59 thf(fact_7317_cos__times__cos,axiom,
% 5.27/5.59 ! [W: complex,Z: complex] :
% 5.27/5.59 ( ( times_times_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( cos_complex @ ( minus_minus_complex @ W @ Z ) ) @ ( cos_complex @ ( plus_plus_complex @ W @ Z ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_times_cos
% 5.27/5.59 thf(fact_7318_cos__plus__cos,axiom,
% 5.27/5.59 ! [W: real,Z: real] :
% 5.27/5.59 ( ( plus_plus_real @ ( cos_real @ W ) @ ( cos_real @ Z ) )
% 5.27/5.59 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_plus_cos
% 5.27/5.59 thf(fact_7319_cos__plus__cos,axiom,
% 5.27/5.59 ! [W: complex,Z: complex] :
% 5.27/5.59 ( ( plus_plus_complex @ ( cos_complex @ W ) @ ( cos_complex @ Z ) )
% 5.27/5.59 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_plus_cos
% 5.27/5.59 thf(fact_7320_sin__gt__zero2,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_gt_zero2
% 5.27/5.59 thf(fact_7321_sin__lt__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ pi @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.59 => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_lt_zero
% 5.27/5.59 thf(fact_7322_cos__double__less__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.59 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_double_less_one
% 5.27/5.59 thf(fact_7323_sin__30,axiom,
% 5.27/5.59 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_30
% 5.27/5.59 thf(fact_7324_cos__gt__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_gt_zero
% 5.27/5.59 thf(fact_7325_sin__inj__pi,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ( sin_real @ X4 )
% 5.27/5.59 = ( sin_real @ Y ) )
% 5.27/5.59 => ( X4 = Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_inj_pi
% 5.27/5.59 thf(fact_7326_sin__mono__le__eq,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_mono_le_eq
% 5.27/5.59 thf(fact_7327_sin__monotone__2pi__le,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_monotone_2pi_le
% 5.27/5.59 thf(fact_7328_cos__60,axiom,
% 5.27/5.59 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_60
% 5.27/5.59 thf(fact_7329_sin__60,axiom,
% 5.27/5.59 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_60
% 5.27/5.59 thf(fact_7330_cos__30,axiom,
% 5.27/5.59 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_30
% 5.27/5.59 thf(fact_7331_cos__double__cos,axiom,
% 5.27/5.59 ! [W: complex] :
% 5.27/5.59 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ W ) )
% 5.27/5.59 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( power_power_complex @ ( cos_complex @ W ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_complex ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_double_cos
% 5.27/5.59 thf(fact_7332_cos__double__cos,axiom,
% 5.27/5.59 ! [W: real] :
% 5.27/5.59 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ W ) )
% 5.27/5.59 = ( 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 ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_double_cos
% 5.27/5.59 thf(fact_7333_cos__treble__cos,axiom,
% 5.27/5.59 ! [X4: complex] :
% 5.27/5.59 ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ X4 ) )
% 5.27/5.59 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( cos_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) @ ( cos_complex @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_treble_cos
% 5.27/5.59 thf(fact_7334_cos__treble__cos,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ X4 ) )
% 5.27/5.59 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( cos_real @ X4 ) @ ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( cos_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_treble_cos
% 5.27/5.59 thf(fact_7335_sin__le__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ pi @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.59 => ( ord_less_eq_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_le_zero
% 5.27/5.59 thf(fact_7336_sin__less__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.59 => ( ord_less_real @ ( sin_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_less_zero
% 5.27/5.59 thf(fact_7337_sin__mono__less__eq,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_mono_less_eq
% 5.27/5.59 thf(fact_7338_sin__monotone__2pi,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_monotone_2pi
% 5.27/5.59 thf(fact_7339_sin__total,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ? [X5: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.27/5.59 & ( ord_less_eq_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( sin_real @ X5 )
% 5.27/5.59 = Y )
% 5.27/5.59 & ! [Y4: real] :
% 5.27/5.59 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.27/5.59 & ( ord_less_eq_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( sin_real @ Y4 )
% 5.27/5.59 = Y ) )
% 5.27/5.59 => ( Y4 = X5 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_total
% 5.27/5.59 thf(fact_7340_cos__gt__zero__pi,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_gt_zero_pi
% 5.27/5.59 thf(fact_7341_cos__ge__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_ge_zero
% 5.27/5.59 thf(fact_7342_cos__one__2pi,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 = one_one_real )
% 5.27/5.59 = ( ? [X: nat] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.27/5.59 | ? [X: nat] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_one_2pi
% 5.27/5.59 thf(fact_7343_sin__pi__divide__n__gt__0,axiom,
% 5.27/5.59 ! [N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.59 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_pi_divide_n_gt_0
% 5.27/5.59 thf(fact_7344_sin__arctan,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( sin_real @ ( arctan @ X4 ) )
% 5.27/5.59 = ( divide_divide_real @ X4 @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_arctan
% 5.27/5.59 thf(fact_7345_cos__arctan,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( cos_real @ ( arctan @ X4 ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_arctan
% 5.27/5.59 thf(fact_7346_sin__zero__lemma,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ( sin_real @ X4 )
% 5.27/5.59 = zero_zero_real )
% 5.27/5.59 => ? [N3: nat] :
% 5.27/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_zero_lemma
% 5.27/5.59 thf(fact_7347_sin__zero__iff,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( sin_real @ X4 )
% 5.27/5.59 = zero_zero_real )
% 5.27/5.59 = ( ? [N: nat] :
% 5.27/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.59 | ? [N: nat] :
% 5.27/5.59 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_zero_iff
% 5.27/5.59 thf(fact_7348_cos__zero__lemma,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ( cos_real @ X4 )
% 5.27/5.59 = zero_zero_real )
% 5.27/5.59 => ? [N3: nat] :
% 5.27/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_zero_lemma
% 5.27/5.59 thf(fact_7349_cos__zero__iff,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 = zero_zero_real )
% 5.27/5.59 = ( ? [N: nat] :
% 5.27/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.59 | ? [N: nat] :
% 5.27/5.59 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.27/5.59 & ( X4
% 5.27/5.59 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_zero_iff
% 5.27/5.59 thf(fact_7350_tan__double,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( tan_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.59 = ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( tan_real @ X4 ) ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_double
% 5.27/5.59 thf(fact_7351_tan__double,axiom,
% 5.27/5.59 ! [X4: complex] :
% 5.27/5.59 ( ( ( cos_complex @ X4 )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( tan_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( tan_complex @ X4 ) ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_double
% 5.27/5.59 thf(fact_7352_sin__tan,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( sin_real @ X4 )
% 5.27/5.59 = ( divide_divide_real @ ( tan_real @ X4 ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_tan
% 5.27/5.59 thf(fact_7353_cos__tan,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( cos_real @ X4 )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_tan
% 5.27/5.59 thf(fact_7354_complex__unimodular__polar,axiom,
% 5.27/5.59 ! [Z: complex] :
% 5.27/5.59 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.27/5.59 = one_one_real )
% 5.27/5.59 => ~ ! [T3: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.59 => ( ( ord_less_real @ T3 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.59 => ( Z
% 5.27/5.59 != ( complex2 @ ( cos_real @ T3 ) @ ( sin_real @ T3 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % complex_unimodular_polar
% 5.27/5.59 thf(fact_7355_ceiling__log__eq__powr__iff,axiom,
% 5.27/5.59 ! [X4: real,B: real,K: nat] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X4 ) )
% 5.27/5.59 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.27/5.59 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X4 )
% 5.27/5.59 & ( ord_less_eq_real @ X4 @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_log_eq_powr_iff
% 5.27/5.59 thf(fact_7356_powr__one__eq__one,axiom,
% 5.27/5.59 ! [A: real] :
% 5.27/5.59 ( ( powr_real @ one_one_real @ A )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % powr_one_eq_one
% 5.27/5.59 thf(fact_7357_powr__zero__eq__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( X4 = zero_zero_real )
% 5.27/5.59 => ( ( powr_real @ X4 @ zero_zero_real )
% 5.27/5.59 = zero_zero_real ) )
% 5.27/5.59 & ( ( X4 != zero_zero_real )
% 5.27/5.59 => ( ( powr_real @ X4 @ zero_zero_real )
% 5.27/5.59 = one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_zero_eq_one
% 5.27/5.59 thf(fact_7358_powr__gt__zero,axiom,
% 5.27/5.59 ! [X4: real,A: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X4 @ A ) )
% 5.27/5.59 = ( X4 != zero_zero_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_gt_zero
% 5.27/5.59 thf(fact_7359_powr__nonneg__iff,axiom,
% 5.27/5.59 ! [A: real,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( powr_real @ A @ X4 ) @ zero_zero_real )
% 5.27/5.59 = ( A = zero_zero_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_nonneg_iff
% 5.27/5.59 thf(fact_7360_powr__less__cancel__iff,axiom,
% 5.27/5.59 ! [X4: real,A: real,B: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 5.27/5.59 = ( ord_less_real @ A @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_cancel_iff
% 5.27/5.59 thf(fact_7361_powr__eq__one__iff,axiom,
% 5.27/5.59 ! [A: real,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ A )
% 5.27/5.59 => ( ( ( powr_real @ A @ X4 )
% 5.27/5.59 = one_one_real )
% 5.27/5.59 = ( X4 = zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_eq_one_iff
% 5.27/5.59 thf(fact_7362_powr__one__gt__zero__iff,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( powr_real @ X4 @ one_one_real )
% 5.27/5.59 = X4 )
% 5.27/5.59 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_one_gt_zero_iff
% 5.27/5.59 thf(fact_7363_powr__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ one_one_real )
% 5.27/5.59 = X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_one
% 5.27/5.59 thf(fact_7364_powr__le__cancel__iff,axiom,
% 5.27/5.59 ! [X4: real,A: real,B: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 5.27/5.59 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_le_cancel_iff
% 5.27/5.59 thf(fact_7365_numeral__powr__numeral__real,axiom,
% 5.27/5.59 ! [M: num,N2: num] :
% 5.27/5.59 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.59 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_powr_numeral_real
% 5.27/5.59 thf(fact_7366_log__powr__cancel,axiom,
% 5.27/5.59 ! [A: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( A != one_one_real )
% 5.27/5.59 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.27/5.59 = Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % log_powr_cancel
% 5.27/5.59 thf(fact_7367_powr__log__cancel,axiom,
% 5.27/5.59 ! [A: real,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( A != one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ A @ ( log @ A @ X4 ) )
% 5.27/5.59 = X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_log_cancel
% 5.27/5.59 thf(fact_7368_tan__periodic__n,axiom,
% 5.27/5.59 ! [X4: real,N2: num] :
% 5.27/5.59 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ N2 ) @ pi ) ) )
% 5.27/5.59 = ( tan_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_periodic_n
% 5.27/5.59 thf(fact_7369_norm__cos__sin,axiom,
% 5.27/5.59 ! [T2: real] :
% 5.27/5.59 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T2 ) @ ( sin_real @ T2 ) ) )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % norm_cos_sin
% 5.27/5.59 thf(fact_7370_powr__numeral,axiom,
% 5.27/5.59 ! [X4: real,N2: num] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.59 = ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_numeral
% 5.27/5.59 thf(fact_7371_tan__periodic,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( tan_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.27/5.59 = ( tan_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_periodic
% 5.27/5.59 thf(fact_7372_square__powr__half,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( powr_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = ( abs_abs_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % square_powr_half
% 5.27/5.59 thf(fact_7373_powr__non__neg,axiom,
% 5.27/5.59 ! [A: real,X4: real] :
% 5.27/5.59 ~ ( ord_less_real @ ( powr_real @ A @ X4 ) @ zero_zero_real ) ).
% 5.27/5.59
% 5.27/5.59 % powr_non_neg
% 5.27/5.59 thf(fact_7374_powr__less__mono2__neg,axiom,
% 5.27/5.59 ! [A: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_mono2_neg
% 5.27/5.59 thf(fact_7375_powr__ge__pzero,axiom,
% 5.27/5.59 ! [X4: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X4 @ Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_ge_pzero
% 5.27/5.59 thf(fact_7376_powr__mono2,axiom,
% 5.27/5.59 ! [A: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mono2
% 5.27/5.59 thf(fact_7377_powr__less__cancel,axiom,
% 5.27/5.59 ! [X4: real,A: real,B: real] :
% 5.27/5.59 ( ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) )
% 5.27/5.59 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ord_less_real @ A @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_cancel
% 5.27/5.59 thf(fact_7378_powr__less__mono,axiom,
% 5.27/5.59 ! [A: real,B: real,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ A @ B )
% 5.27/5.59 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_mono
% 5.27/5.59 thf(fact_7379_powr__mono,axiom,
% 5.27/5.59 ! [A: real,B: real,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.59 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mono
% 5.27/5.59 thf(fact_7380_one__complex_Ocode,axiom,
% 5.27/5.59 ( one_one_complex
% 5.27/5.59 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % one_complex.code
% 5.27/5.59 thf(fact_7381_Complex__eq__1,axiom,
% 5.27/5.59 ! [A: real,B: real] :
% 5.27/5.59 ( ( ( complex2 @ A @ B )
% 5.27/5.59 = one_one_complex )
% 5.27/5.59 = ( ( A = one_one_real )
% 5.27/5.59 & ( B = zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % Complex_eq_1
% 5.27/5.59 thf(fact_7382_Complex__eq__numeral,axiom,
% 5.27/5.59 ! [A: real,B: real,W: num] :
% 5.27/5.59 ( ( ( complex2 @ A @ B )
% 5.27/5.59 = ( numera6690914467698888265omplex @ W ) )
% 5.27/5.59 = ( ( A
% 5.27/5.59 = ( numeral_numeral_real @ W ) )
% 5.27/5.59 & ( B = zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % Complex_eq_numeral
% 5.27/5.59 thf(fact_7383_powr__mono2_H,axiom,
% 5.27/5.59 ! [A: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X4 @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mono2'
% 5.27/5.59 thf(fact_7384_powr__less__mono2,axiom,
% 5.27/5.59 ! [A: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_mono2
% 5.27/5.59 thf(fact_7385_powr__inj,axiom,
% 5.27/5.59 ! [A: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( A != one_one_real )
% 5.27/5.59 => ( ( ( powr_real @ A @ X4 )
% 5.27/5.59 = ( powr_real @ A @ Y ) )
% 5.27/5.59 = ( X4 = Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_inj
% 5.27/5.59 thf(fact_7386_gr__one__powr,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.59 => ( ord_less_real @ one_one_real @ ( powr_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % gr_one_powr
% 5.27/5.59 thf(fact_7387_ge__one__powr__ge__zero,axiom,
% 5.27/5.59 ! [X4: real,A: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ge_one_powr_ge_zero
% 5.27/5.59 thf(fact_7388_powr__mono__both,axiom,
% 5.27/5.59 ! [A: real,B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( ord_less_eq_real @ A @ B )
% 5.27/5.59 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mono_both
% 5.27/5.59 thf(fact_7389_powr__le1,axiom,
% 5.27/5.59 ! [A: real,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ X4 @ A ) @ one_one_real ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_le1
% 5.27/5.59 thf(fact_7390_powr__divide,axiom,
% 5.27/5.59 ! [X4: real,Y: real,A: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.59 => ( ( powr_real @ ( divide_divide_real @ X4 @ Y ) @ A )
% 5.27/5.59 = ( divide_divide_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_divide
% 5.27/5.59 thf(fact_7391_powr__mult,axiom,
% 5.27/5.59 ! [X4: real,Y: real,A: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.59 => ( ( powr_real @ ( times_times_real @ X4 @ Y ) @ A )
% 5.27/5.59 = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mult
% 5.27/5.59 thf(fact_7392_Complex__eq__neg__1,axiom,
% 5.27/5.59 ! [A: real,B: real] :
% 5.27/5.59 ( ( ( complex2 @ A @ B )
% 5.27/5.59 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.27/5.59 = ( ( A
% 5.27/5.59 = ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.59 & ( B = zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % Complex_eq_neg_1
% 5.27/5.59 thf(fact_7393_Complex__eq__neg__numeral,axiom,
% 5.27/5.59 ! [A: real,B: real,W: num] :
% 5.27/5.59 ( ( ( complex2 @ A @ B )
% 5.27/5.59 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.59 = ( ( A
% 5.27/5.59 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.59 & ( B = zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % Complex_eq_neg_numeral
% 5.27/5.59 thf(fact_7394_powr__add,axiom,
% 5.27/5.59 ! [X4: real,A: real,B: real] :
% 5.27/5.59 ( ( powr_real @ X4 @ ( plus_plus_real @ A @ B ) )
% 5.27/5.59 = ( times_times_real @ ( powr_real @ X4 @ A ) @ ( powr_real @ X4 @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_add
% 5.27/5.59 thf(fact_7395_powr__diff,axiom,
% 5.27/5.59 ! [W: real,Z1: real,Z22: real] :
% 5.27/5.59 ( ( powr_real @ W @ ( minus_minus_real @ Z1 @ Z22 ) )
% 5.27/5.59 = ( divide_divide_real @ ( powr_real @ W @ Z1 ) @ ( powr_real @ W @ Z22 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_diff
% 5.27/5.59 thf(fact_7396_tan__def,axiom,
% 5.27/5.59 ( tan_real
% 5.27/5.59 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ X ) @ ( cos_real @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_def
% 5.27/5.59 thf(fact_7397_tan__def,axiom,
% 5.27/5.59 ( tan_complex
% 5.27/5.59 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ X ) @ ( cos_complex @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_def
% 5.27/5.59 thf(fact_7398_powr__realpow,axiom,
% 5.27/5.59 ! [X4: real,N2: nat] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.27/5.59 = ( power_power_real @ X4 @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_realpow
% 5.27/5.59 thf(fact_7399_less__log__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ Y @ ( log @ B @ X4 ) )
% 5.27/5.59 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_log_iff
% 5.27/5.59 thf(fact_7400_log__less__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ ( log @ B @ X4 ) @ Y )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % log_less_iff
% 5.27/5.59 thf(fact_7401_less__powr__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( powr_real @ B @ Y ) )
% 5.27/5.59 = ( ord_less_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_powr_iff
% 5.27/5.59 thf(fact_7402_powr__less__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X4 )
% 5.27/5.59 = ( ord_less_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_less_iff
% 5.27/5.59 thf(fact_7403_powr__minus__divide,axiom,
% 5.27/5.59 ! [X4: real,A: real] :
% 5.27/5.59 ( ( powr_real @ X4 @ ( uminus_uminus_real @ A ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( powr_real @ X4 @ A ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_minus_divide
% 5.27/5.59 thf(fact_7404_powr__neg__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_neg_one
% 5.27/5.59 thf(fact_7405_powr__mult__base,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( times_times_real @ X4 @ ( powr_real @ X4 @ Y ) )
% 5.27/5.59 = ( powr_real @ X4 @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_mult_base
% 5.27/5.59 thf(fact_7406_le__log__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_log_iff
% 5.27/5.59 thf(fact_7407_log__le__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % log_le_iff
% 5.27/5.59 thf(fact_7408_le__powr__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( powr_real @ B @ Y ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( log @ B @ X4 ) @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_powr_iff
% 5.27/5.59 thf(fact_7409_powr__le__iff,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X4 )
% 5.27/5.59 = ( ord_less_eq_real @ Y @ ( log @ B @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_le_iff
% 5.27/5.59 thf(fact_7410_ln__powr__bound,axiom,
% 5.27/5.59 ! [X4: real,A: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ord_less_eq_real @ ( ln_ln_real @ X4 ) @ ( divide_divide_real @ ( powr_real @ X4 @ A ) @ A ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ln_powr_bound
% 5.27/5.59 thf(fact_7411_ln__powr__bound2,axiom,
% 5.27/5.59 ! [X4: real,A: real] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.59 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X4 ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ln_powr_bound2
% 5.27/5.59 thf(fact_7412_tan__45,axiom,
% 5.27/5.59 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % tan_45
% 5.27/5.59 thf(fact_7413_log__add__eq__powr,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.59 => ( ( B != one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( plus_plus_real @ ( log @ B @ X4 ) @ Y )
% 5.27/5.59 = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % log_add_eq_powr
% 5.27/5.59 thf(fact_7414_add__log__eq__powr,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.59 => ( ( B != one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( plus_plus_real @ Y @ ( log @ B @ X4 ) )
% 5.27/5.59 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % add_log_eq_powr
% 5.27/5.59 thf(fact_7415_minus__log__eq__powr,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.59 => ( ( B != one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( minus_minus_real @ Y @ ( log @ B @ X4 ) )
% 5.27/5.59 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X4 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % minus_log_eq_powr
% 5.27/5.59 thf(fact_7416_tan__60,axiom,
% 5.27/5.59 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.27/5.59 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_60
% 5.27/5.59 thf(fact_7417_lemma__tan__total,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.27/5.59 => ? [X5: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X5 )
% 5.27/5.59 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ord_less_real @ Y @ ( tan_real @ X5 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % lemma_tan_total
% 5.27/5.59 thf(fact_7418_tan__gt__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_gt_zero
% 5.27/5.59 thf(fact_7419_tan__total,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ? [X5: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.27/5.59 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( tan_real @ X5 )
% 5.27/5.59 = Y )
% 5.27/5.59 & ! [Y4: real] :
% 5.27/5.59 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y4 )
% 5.27/5.59 & ( ord_less_real @ Y4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( tan_real @ Y4 )
% 5.27/5.59 = Y ) )
% 5.27/5.59 => ( Y4 = X5 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_total
% 5.27/5.59 thf(fact_7420_tan__monotone,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_monotone
% 5.27/5.59 thf(fact_7421_tan__monotone_H,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ Y @ X4 )
% 5.27/5.59 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_monotone'
% 5.27/5.59 thf(fact_7422_tan__mono__lt__eq,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_mono_lt_eq
% 5.27/5.59 thf(fact_7423_lemma__tan__total1,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ? [X5: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X5 )
% 5.27/5.59 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( tan_real @ X5 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % lemma_tan_total1
% 5.27/5.59 thf(fact_7424_tan__minus__45,axiom,
% 5.27/5.59 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.59 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_minus_45
% 5.27/5.59 thf(fact_7425_tan__inverse,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.27/5.59 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_inverse
% 5.27/5.59 thf(fact_7426_log__minus__eq__powr,axiom,
% 5.27/5.59 ! [B: real,X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.59 => ( ( B != one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( minus_minus_real @ ( log @ B @ X4 ) @ Y )
% 5.27/5.59 = ( log @ B @ ( times_times_real @ X4 @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % log_minus_eq_powr
% 5.27/5.59 thf(fact_7427_complex__norm,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( real_V1022390504157884413omplex @ ( complex2 @ X4 @ Y ) )
% 5.27/5.59 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % complex_norm
% 5.27/5.59 thf(fact_7428_add__tan__eq,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ Y )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 5.27/5.59 = ( divide_divide_real @ ( sin_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % add_tan_eq
% 5.27/5.59 thf(fact_7429_add__tan__eq,axiom,
% 5.27/5.59 ! [X4: complex,Y: complex] :
% 5.27/5.59 ( ( ( cos_complex @ X4 )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ Y )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( sin_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % add_tan_eq
% 5.27/5.59 thf(fact_7430_powr__half__sqrt,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = ( sqrt @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_half_sqrt
% 5.27/5.59 thf(fact_7431_powr__neg__numeral,axiom,
% 5.27/5.59 ! [X4: real,N2: num] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( powr_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % powr_neg_numeral
% 5.27/5.59 thf(fact_7432_tan__total__pos,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.59 => ? [X5: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X5 )
% 5.27/5.59 & ( ord_less_real @ X5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( tan_real @ X5 )
% 5.27/5.59 = Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_total_pos
% 5.27/5.59 thf(fact_7433_tan__pos__pi2__le,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_pos_pi2_le
% 5.27/5.59 thf(fact_7434_tan__less__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.59 => ( ord_less_real @ ( tan_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_less_zero
% 5.27/5.59 thf(fact_7435_tan__mono__le__eq,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_mono_le_eq
% 5.27/5.59 thf(fact_7436_tan__mono__le,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ord_less_eq_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_mono_le
% 5.27/5.59 thf(fact_7437_tan__bound__pi2,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.27/5.59 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X4 ) ) @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_bound_pi2
% 5.27/5.59 thf(fact_7438_tan__30,axiom,
% 5.27/5.59 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.27/5.59 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_30
% 5.27/5.59 thf(fact_7439_arctan__unique,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ( tan_real @ X4 )
% 5.27/5.59 = Y )
% 5.27/5.59 => ( ( arctan @ Y )
% 5.27/5.59 = X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arctan_unique
% 5.27/5.59 thf(fact_7440_arctan__tan,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( arctan @ ( tan_real @ X4 ) )
% 5.27/5.59 = X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arctan_tan
% 5.27/5.59 thf(fact_7441_arctan,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.27/5.59 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( tan_real @ ( arctan @ Y ) )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % arctan
% 5.27/5.59 thf(fact_7442_lemma__tan__add1,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ Y )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) )
% 5.27/5.59 = ( divide_divide_real @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % lemma_tan_add1
% 5.27/5.59 thf(fact_7443_lemma__tan__add1,axiom,
% 5.27/5.59 ! [X4: complex,Y: complex] :
% 5.27/5.59 ( ( ( cos_complex @ X4 )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ Y )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % lemma_tan_add1
% 5.27/5.59 thf(fact_7444_tan__diff,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ Y )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ ( minus_minus_real @ X4 @ Y ) )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( tan_real @ ( minus_minus_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide_divide_real @ ( minus_minus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_diff
% 5.27/5.59 thf(fact_7445_tan__diff,axiom,
% 5.27/5.59 ! [X4: complex,Y: complex] :
% 5.27/5.59 ( ( ( cos_complex @ X4 )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ Y )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( tan_complex @ ( minus_minus_complex @ X4 @ Y ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_diff
% 5.27/5.59 thf(fact_7446_tan__add,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ( cos_real @ X4 )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ Y )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( ( cos_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.59 != zero_zero_real )
% 5.27/5.59 => ( ( tan_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide_divide_real @ ( plus_plus_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ ( tan_real @ X4 ) @ ( tan_real @ Y ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_add
% 5.27/5.59 thf(fact_7447_tan__add,axiom,
% 5.27/5.59 ! [X4: complex,Y: complex] :
% 5.27/5.59 ( ( ( cos_complex @ X4 )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ Y )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.59 != zero_zero_complex )
% 5.27/5.59 => ( ( tan_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) @ ( minus_minus_complex @ one_one_complex @ ( times_times_complex @ ( tan_complex @ X4 ) @ ( tan_complex @ Y ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_add
% 5.27/5.59 thf(fact_7448_tan__total__pi4,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ? [Z2: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z2 )
% 5.27/5.59 & ( ord_less_real @ Z2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.27/5.59 & ( ( tan_real @ Z2 )
% 5.27/5.59 = X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_total_pi4
% 5.27/5.59 thf(fact_7449_tan__half,axiom,
% 5.27/5.59 ( tan_real
% 5.27/5.59 = ( ^ [X: real] : ( divide_divide_real @ ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_half
% 5.27/5.59 thf(fact_7450_tan__half,axiom,
% 5.27/5.59 ( tan_complex
% 5.27/5.59 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sin_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ ( plus_plus_complex @ ( cos_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) ) @ one_one_complex ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % tan_half
% 5.27/5.59 thf(fact_7451_arcosh__def,axiom,
% 5.27/5.59 ( arcosh_real
% 5.27/5.59 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcosh_def
% 5.27/5.59 thf(fact_7452_cos__arcsin,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( cos_real @ ( arcsin @ X4 ) )
% 5.27/5.59 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_arcsin
% 5.27/5.59 thf(fact_7453_sin__arccos__abs,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( sin_real @ ( arccos @ Y ) )
% 5.27/5.59 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_arccos_abs
% 5.27/5.59 thf(fact_7454_sin__arccos,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( sin_real @ ( arccos @ X4 ) )
% 5.27/5.59 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_arccos
% 5.27/5.59 thf(fact_7455_arsinh__def,axiom,
% 5.27/5.59 ( arsinh_real
% 5.27/5.59 = ( ^ [X: real] : ( ln_ln_real @ ( plus_plus_real @ X @ ( powr_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( real_V1803761363581548252l_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arsinh_def
% 5.27/5.59 thf(fact_7456_of__real__eq__1__iff,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( real_V1803761363581548252l_real @ X4 )
% 5.27/5.59 = one_one_real )
% 5.27/5.59 = ( X4 = one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_eq_1_iff
% 5.27/5.59 thf(fact_7457_of__real__eq__1__iff,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( real_V4546457046886955230omplex @ X4 )
% 5.27/5.59 = one_one_complex )
% 5.27/5.59 = ( X4 = one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_eq_1_iff
% 5.27/5.59 thf(fact_7458_of__real__1,axiom,
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ one_one_real )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_1
% 5.27/5.59 thf(fact_7459_of__real__1,axiom,
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ one_one_real )
% 5.27/5.59 = one_one_complex ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_1
% 5.27/5.59 thf(fact_7460_of__real__numeral,axiom,
% 5.27/5.59 ! [W: num] :
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.59 = ( numeral_numeral_real @ W ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_numeral
% 5.27/5.59 thf(fact_7461_of__real__numeral,axiom,
% 5.27/5.59 ! [W: num] :
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ ( numeral_numeral_real @ W ) )
% 5.27/5.59 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_numeral
% 5.27/5.59 thf(fact_7462_of__real__divide,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_divide
% 5.27/5.59 thf(fact_7463_of__real__divide,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_divide
% 5.27/5.59 thf(fact_7464_of__real__add,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.59 = ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_add
% 5.27/5.59 thf(fact_7465_of__real__add,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.59 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_add
% 5.27/5.59 thf(fact_7466_of__real__power,axiom,
% 5.27/5.59 ! [X4: real,N2: nat] :
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.59 = ( power_power_real @ ( real_V1803761363581548252l_real @ X4 ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_power
% 5.27/5.59 thf(fact_7467_of__real__power,axiom,
% 5.27/5.59 ! [X4: real,N2: nat] :
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.59 = ( power_power_complex @ ( real_V4546457046886955230omplex @ X4 ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_power
% 5.27/5.59 thf(fact_7468_arccos__1,axiom,
% 5.27/5.59 ( ( arccos @ one_one_real )
% 5.27/5.59 = zero_zero_real ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_1
% 5.27/5.59 thf(fact_7469_arccos__minus__1,axiom,
% 5.27/5.59 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.59 = pi ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_minus_1
% 5.27/5.59 thf(fact_7470_of__real__neg__numeral,axiom,
% 5.27/5.59 ! [W: num] :
% 5.27/5.59 ( ( real_V1803761363581548252l_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.59 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_neg_numeral
% 5.27/5.59 thf(fact_7471_of__real__neg__numeral,axiom,
% 5.27/5.59 ! [W: num] :
% 5.27/5.59 ( ( real_V4546457046886955230omplex @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.59 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_real_neg_numeral
% 5.27/5.59 thf(fact_7472_cos__of__real__pi,axiom,
% 5.27/5.59 ( ( cos_real @ ( real_V1803761363581548252l_real @ pi ) )
% 5.27/5.59 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_of_real_pi
% 5.27/5.59 thf(fact_7473_cos__of__real__pi,axiom,
% 5.27/5.59 ( ( cos_complex @ ( real_V4546457046886955230omplex @ pi ) )
% 5.27/5.59 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_of_real_pi
% 5.27/5.59 thf(fact_7474_cos__arccos,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( cos_real @ ( arccos @ Y ) )
% 5.27/5.59 = Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_arccos
% 5.27/5.59 thf(fact_7475_sin__arcsin,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.27/5.59 = Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_arcsin
% 5.27/5.59 thf(fact_7476_norm__of__real__add1,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ one_one_real ) )
% 5.27/5.59 = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_add1
% 5.27/5.59 thf(fact_7477_norm__of__real__add1,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ one_one_complex ) )
% 5.27/5.59 = ( abs_abs_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_add1
% 5.27/5.59 thf(fact_7478_norm__of__real__addn,axiom,
% 5.27/5.59 ! [X4: real,B: num] :
% 5.27/5.59 ( ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( numeral_numeral_real @ B ) ) )
% 5.27/5.59 = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_addn
% 5.27/5.59 thf(fact_7479_norm__of__real__addn,axiom,
% 5.27/5.59 ! [X4: real,B: num] :
% 5.27/5.59 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ X4 ) @ ( numera6690914467698888265omplex @ B ) ) )
% 5.27/5.59 = ( abs_abs_real @ ( plus_plus_real @ X4 @ ( numeral_numeral_real @ B ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_addn
% 5.27/5.59 thf(fact_7480_arccos__0,axiom,
% 5.27/5.59 ( ( arccos @ zero_zero_real )
% 5.27/5.59 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_0
% 5.27/5.59 thf(fact_7481_arcsin__1,axiom,
% 5.27/5.59 ( ( arcsin @ one_one_real )
% 5.27/5.59 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_1
% 5.27/5.59 thf(fact_7482_cos__of__real__pi__half,axiom,
% 5.27/5.59 ( ( cos_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = zero_zero_real ) ).
% 5.27/5.59
% 5.27/5.59 % cos_of_real_pi_half
% 5.27/5.59 thf(fact_7483_cos__of__real__pi__half,axiom,
% 5.27/5.59 ( ( cos_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = zero_zero_complex ) ).
% 5.27/5.59
% 5.27/5.59 % cos_of_real_pi_half
% 5.27/5.59 thf(fact_7484_sin__of__real__pi__half,axiom,
% 5.27/5.59 ( ( sin_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % sin_of_real_pi_half
% 5.27/5.59 thf(fact_7485_sin__of__real__pi__half,axiom,
% 5.27/5.59 ( ( sin_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.27/5.59 = one_one_complex ) ).
% 5.27/5.59
% 5.27/5.59 % sin_of_real_pi_half
% 5.27/5.59 thf(fact_7486_arcsin__minus__1,axiom,
% 5.27/5.59 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.27/5.59 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_minus_1
% 5.27/5.59 thf(fact_7487_nonzero__of__real__divide,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( Y != zero_zero_real )
% 5.27/5.59 => ( ( real_V1803761363581548252l_real @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide_divide_real @ ( real_V1803761363581548252l_real @ X4 ) @ ( real_V1803761363581548252l_real @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % nonzero_of_real_divide
% 5.27/5.59 thf(fact_7488_nonzero__of__real__divide,axiom,
% 5.27/5.59 ! [Y: real,X4: real] :
% 5.27/5.59 ( ( Y != zero_zero_real )
% 5.27/5.59 => ( ( real_V4546457046886955230omplex @ ( divide_divide_real @ X4 @ Y ) )
% 5.27/5.59 = ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ X4 ) @ ( real_V4546457046886955230omplex @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % nonzero_of_real_divide
% 5.27/5.59 thf(fact_7489_arccos__le__arccos,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_le_arccos
% 5.27/5.59 thf(fact_7490_arccos__le__mono,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 5.27/5.59 = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_le_mono
% 5.27/5.59 thf(fact_7491_arccos__eq__iff,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.27/5.59 => ( ( ( arccos @ X4 )
% 5.27/5.59 = ( arccos @ Y ) )
% 5.27/5.59 = ( X4 = Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_eq_iff
% 5.27/5.59 thf(fact_7492_arcsin__minus,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( arcsin @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.59 = ( uminus_uminus_real @ ( arcsin @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_minus
% 5.27/5.59 thf(fact_7493_arcsin__le__arcsin,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_le_arcsin
% 5.27/5.59 thf(fact_7494_arcsin__le__mono,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_le_mono
% 5.27/5.59 thf(fact_7495_arcsin__eq__iff,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( ( arcsin @ X4 )
% 5.27/5.59 = ( arcsin @ Y ) )
% 5.27/5.59 = ( X4 = Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_eq_iff
% 5.27/5.59 thf(fact_7496_norm__less__p1,axiom,
% 5.27/5.59 ! [X4: real] : ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ ( real_V1803761363581548252l_real @ ( real_V7735802525324610683m_real @ X4 ) ) @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_less_p1
% 5.27/5.59 thf(fact_7497_norm__less__p1,axiom,
% 5.27/5.59 ! [X4: complex] : ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( real_V1022390504157884413omplex @ X4 ) ) @ one_one_complex ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_less_p1
% 5.27/5.59 thf(fact_7498_arccos__lbound,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_lbound
% 5.27/5.59 thf(fact_7499_arccos__less__arccos,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_less_arccos
% 5.27/5.59 thf(fact_7500_arccos__less__mono,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ ( arccos @ X4 ) @ ( arccos @ Y ) )
% 5.27/5.59 = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_less_mono
% 5.27/5.59 thf(fact_7501_arccos__ubound,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_ubound
% 5.27/5.59 thf(fact_7502_arccos__cos,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.59 => ( ( arccos @ ( cos_real @ X4 ) )
% 5.27/5.59 = X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_cos
% 5.27/5.59 thf(fact_7503_arcsin__less__arcsin,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_less_arcsin
% 5.27/5.59 thf(fact_7504_arcsin__less__mono,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ ( arcsin @ X4 ) @ ( arcsin @ Y ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_less_mono
% 5.27/5.59 thf(fact_7505_cos__arccos__abs,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.27/5.59 => ( ( cos_real @ ( arccos @ Y ) )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_arccos_abs
% 5.27/5.59 thf(fact_7506_norm__of__real__diff,axiom,
% 5.27/5.59 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( real_V1803761363581548252l_real @ B ) @ ( real_V1803761363581548252l_real @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_diff
% 5.27/5.59 thf(fact_7507_norm__of__real__diff,axiom,
% 5.27/5.59 ! [B: real,A: real] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( real_V4546457046886955230omplex @ B ) @ ( real_V4546457046886955230omplex @ A ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % norm_of_real_diff
% 5.27/5.59 thf(fact_7508_arccos__cos__eq__abs,axiom,
% 5.27/5.59 ! [Theta: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.27/5.59 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.27/5.59 = ( abs_abs_real @ Theta ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_cos_eq_abs
% 5.27/5.59 thf(fact_7509_arccos__lt__bounded,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.27/5.59 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_lt_bounded
% 5.27/5.59 thf(fact_7510_arccos__bounded,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.27/5.59 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_bounded
% 5.27/5.59 thf(fact_7511_sin__arccos__nonzero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( sin_real @ ( arccos @ X4 ) )
% 5.27/5.59 != zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_arccos_nonzero
% 5.27/5.59 thf(fact_7512_arccos__cos2,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.27/5.59 => ( ( arccos @ ( cos_real @ X4 ) )
% 5.27/5.59 = ( uminus_uminus_real @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_cos2
% 5.27/5.59 thf(fact_7513_arccos__minus,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.59 = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_minus
% 5.27/5.59 thf(fact_7514_cos__arcsin__nonzero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( cos_real @ ( arcsin @ X4 ) )
% 5.27/5.59 != zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_arcsin_nonzero
% 5.27/5.59 thf(fact_7515_arccos,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.27/5.59 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.27/5.59 & ( ( cos_real @ ( arccos @ Y ) )
% 5.27/5.59 = Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos
% 5.27/5.59 thf(fact_7516_arccos__minus__abs,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.59 => ( ( arccos @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.59 = ( minus_minus_real @ pi @ ( arccos @ X4 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_minus_abs
% 5.27/5.59 thf(fact_7517_cos__sin__eq,axiom,
% 5.27/5.59 ( cos_real
% 5.27/5.59 = ( ^ [X: real] : ( sin_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_sin_eq
% 5.27/5.59 thf(fact_7518_cos__sin__eq,axiom,
% 5.27/5.59 ( cos_complex
% 5.27/5.59 = ( ^ [X: complex] : ( sin_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_sin_eq
% 5.27/5.59 thf(fact_7519_sin__cos__eq,axiom,
% 5.27/5.59 ( sin_real
% 5.27/5.59 = ( ^ [X: real] : ( cos_real @ ( minus_minus_real @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_cos_eq
% 5.27/5.59 thf(fact_7520_sin__cos__eq,axiom,
% 5.27/5.59 ( sin_complex
% 5.27/5.59 = ( ^ [X: complex] : ( cos_complex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ X ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % sin_cos_eq
% 5.27/5.59 thf(fact_7521_minus__sin__cos__eq,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( uminus_uminus_real @ ( sin_real @ X4 ) )
% 5.27/5.59 = ( cos_real @ ( plus_plus_real @ X4 @ ( divide_divide_real @ ( real_V1803761363581548252l_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % minus_sin_cos_eq
% 5.27/5.59 thf(fact_7522_minus__sin__cos__eq,axiom,
% 5.27/5.59 ! [X4: complex] :
% 5.27/5.59 ( ( uminus1482373934393186551omplex @ ( sin_complex @ X4 ) )
% 5.27/5.59 = ( cos_complex @ ( plus_plus_complex @ X4 @ ( divide1717551699836669952omplex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % minus_sin_cos_eq
% 5.27/5.59 thf(fact_7523_arccos__le__pi2,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arccos_le_pi2
% 5.27/5.59 thf(fact_7524_arcsin__lt__bounded,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.27/5.59 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_lt_bounded
% 5.27/5.59 thf(fact_7525_arcsin__bounded,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.27/5.59 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_bounded
% 5.27/5.59 thf(fact_7526_arcsin__ubound,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_ubound
% 5.27/5.59 thf(fact_7527_arcsin__lbound,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_lbound
% 5.27/5.59 thf(fact_7528_arcsin__sin,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( arcsin @ ( sin_real @ X4 ) )
% 5.27/5.59 = X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_sin
% 5.27/5.59 thf(fact_7529_arcsin,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.27/5.59 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.27/5.59 = Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin
% 5.27/5.59 thf(fact_7530_arcsin__pi,axiom,
% 5.27/5.59 ! [Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.27/5.59 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.27/5.59 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.27/5.59 = Y ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_pi
% 5.27/5.59 thf(fact_7531_arcsin__le__iff,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( arcsin @ X4 ) @ Y )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % arcsin_le_iff
% 5.27/5.59 thf(fact_7532_le__arcsin__iff,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.59 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.59 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.59 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X4 ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_arcsin_iff
% 5.27/5.59 thf(fact_7533_floor__log__nat__eq__powr__iff,axiom,
% 5.27/5.59 ! [B: nat,K: nat,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.27/5.59 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.59 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.27/5.59 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.27/5.59 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.27/5.59 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_log_nat_eq_powr_iff
% 5.27/5.59 thf(fact_7534_cos__npi__int,axiom,
% 5.27/5.59 ! [N2: int] :
% 5.27/5.59 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.59 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.27/5.59 = one_one_real ) )
% 5.27/5.59 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.59 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N2 ) ) )
% 5.27/5.59 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cos_npi_int
% 5.27/5.59 thf(fact_7535_cot__less__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.59 => ( ord_less_real @ ( cot_real @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % cot_less_zero
% 5.27/5.59 thf(fact_7536_floor__log__nat__eq__if,axiom,
% 5.27/5.59 ! [B: nat,N2: nat,K: nat] :
% 5.27/5.59 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N2 ) @ K )
% 5.27/5.59 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N2 @ one_one_nat ) ) )
% 5.27/5.59 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.27/5.59 = ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_log_nat_eq_if
% 5.27/5.59 thf(fact_7537_cot__periodic,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( cot_real @ ( plus_plus_real @ X4 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.27/5.59 = ( cot_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % cot_periodic
% 5.27/5.59 thf(fact_7538_of__int__floor__cancel,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = X4 )
% 5.27/5.59 = ( ? [N: int] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( ring_1_of_int_real @ N ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_floor_cancel
% 5.27/5.59 thf(fact_7539_of__int__floor__cancel,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = X4 )
% 5.27/5.59 = ( ? [N: int] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_floor_cancel
% 5.27/5.59 thf(fact_7540_of__int__ceiling__cancel,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.59 = X4 )
% 5.27/5.59 = ( ? [N: int] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( ring_1_of_int_rat @ N ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_ceiling_cancel
% 5.27/5.59 thf(fact_7541_of__int__ceiling__cancel,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.59 = X4 )
% 5.27/5.59 = ( ? [N: int] :
% 5.27/5.59 ( X4
% 5.27/5.59 = ( ring_1_of_int_real @ N ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_ceiling_cancel
% 5.27/5.59 thf(fact_7542_of__int__le__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_iff
% 5.27/5.59 thf(fact_7543_of__int__le__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_iff
% 5.27/5.59 thf(fact_7544_of__int__le__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_iff
% 5.27/5.59 thf(fact_7545_of__int__numeral,axiom,
% 5.27/5.59 ! [K: num] :
% 5.27/5.59 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.27/5.59 = ( numeral_numeral_rat @ K ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral
% 5.27/5.59 thf(fact_7546_of__int__numeral,axiom,
% 5.27/5.59 ! [K: num] :
% 5.27/5.59 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.27/5.59 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral
% 5.27/5.59 thf(fact_7547_of__int__numeral,axiom,
% 5.27/5.59 ! [K: num] :
% 5.27/5.59 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.27/5.59 = ( numeral_numeral_real @ K ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral
% 5.27/5.59 thf(fact_7548_of__int__numeral,axiom,
% 5.27/5.59 ! [K: num] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.27/5.59 = ( numeral_numeral_int @ K ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral
% 5.27/5.59 thf(fact_7549_of__int__eq__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ Z )
% 5.27/5.59 = ( numeral_numeral_rat @ N2 ) )
% 5.27/5.59 = ( Z
% 5.27/5.59 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_iff
% 5.27/5.59 thf(fact_7550_of__int__eq__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.27/5.59 = ( numera6690914467698888265omplex @ N2 ) )
% 5.27/5.59 = ( Z
% 5.27/5.59 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_iff
% 5.27/5.59 thf(fact_7551_of__int__eq__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ Z )
% 5.27/5.59 = ( numeral_numeral_real @ N2 ) )
% 5.27/5.59 = ( Z
% 5.27/5.59 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_iff
% 5.27/5.59 thf(fact_7552_of__int__eq__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ( ring_1_of_int_int @ Z )
% 5.27/5.59 = ( numeral_numeral_int @ N2 ) )
% 5.27/5.59 = ( Z
% 5.27/5.59 = ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_iff
% 5.27/5.59 thf(fact_7553_of__int__less__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_iff
% 5.27/5.59 thf(fact_7554_of__int__less__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_iff
% 5.27/5.59 thf(fact_7555_of__int__less__iff,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_int @ W @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_iff
% 5.27/5.59 thf(fact_7556_of__int__1,axiom,
% 5.27/5.59 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.27/5.59 = one_one_complex ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1
% 5.27/5.59 thf(fact_7557_of__int__1,axiom,
% 5.27/5.59 ( ( ring_1_of_int_int @ one_one_int )
% 5.27/5.59 = one_one_int ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1
% 5.27/5.59 thf(fact_7558_of__int__1,axiom,
% 5.27/5.59 ( ( ring_1_of_int_real @ one_one_int )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1
% 5.27/5.59 thf(fact_7559_of__int__1,axiom,
% 5.27/5.59 ( ( ring_1_of_int_rat @ one_one_int )
% 5.27/5.59 = one_one_rat ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1
% 5.27/5.59 thf(fact_7560_of__int__eq__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.27/5.59 = one_one_complex )
% 5.27/5.59 = ( Z = one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_1_iff
% 5.27/5.59 thf(fact_7561_of__int__eq__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ( ring_1_of_int_int @ Z )
% 5.27/5.59 = one_one_int )
% 5.27/5.59 = ( Z = one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_1_iff
% 5.27/5.59 thf(fact_7562_of__int__eq__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ Z )
% 5.27/5.59 = one_one_real )
% 5.27/5.59 = ( Z = one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_1_iff
% 5.27/5.59 thf(fact_7563_of__int__eq__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ Z )
% 5.27/5.59 = one_one_rat )
% 5.27/5.59 = ( Z = one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_1_iff
% 5.27/5.59 thf(fact_7564_of__int__add,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.27/5.59 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_add
% 5.27/5.59 thf(fact_7565_of__int__add,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.27/5.59 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_add
% 5.27/5.59 thf(fact_7566_of__int__add,axiom,
% 5.27/5.59 ! [W: int,Z: int] :
% 5.27/5.59 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.27/5.59 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_add
% 5.27/5.59 thf(fact_7567_floor__numeral,axiom,
% 5.27/5.59 ! [V: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( numeral_numeral_real @ V ) )
% 5.27/5.59 = ( numeral_numeral_int @ V ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_numeral
% 5.27/5.59 thf(fact_7568_floor__numeral,axiom,
% 5.27/5.59 ! [V: num] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( numeral_numeral_rat @ V ) )
% 5.27/5.59 = ( numeral_numeral_int @ V ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_numeral
% 5.27/5.59 thf(fact_7569_floor__one,axiom,
% 5.27/5.59 ( ( archim6058952711729229775r_real @ one_one_real )
% 5.27/5.59 = one_one_int ) ).
% 5.27/5.59
% 5.27/5.59 % floor_one
% 5.27/5.59 thf(fact_7570_floor__one,axiom,
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ one_one_rat )
% 5.27/5.59 = one_one_int ) ).
% 5.27/5.59
% 5.27/5.59 % floor_one
% 5.27/5.59 thf(fact_7571_of__int__power,axiom,
% 5.27/5.59 ! [Z: int,N2: nat] :
% 5.27/5.59 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N2 ) )
% 5.27/5.59 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power
% 5.27/5.59 thf(fact_7572_of__int__power,axiom,
% 5.27/5.59 ! [Z: int,N2: nat] :
% 5.27/5.59 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N2 ) )
% 5.27/5.59 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power
% 5.27/5.59 thf(fact_7573_of__int__power,axiom,
% 5.27/5.59 ! [Z: int,N2: nat] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N2 ) )
% 5.27/5.59 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power
% 5.27/5.59 thf(fact_7574_of__int__power,axiom,
% 5.27/5.59 ! [Z: int,N2: nat] :
% 5.27/5.59 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N2 ) )
% 5.27/5.59 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power
% 5.27/5.59 thf(fact_7575_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.27/5.59 = ( ring_1_of_int_rat @ X4 ) )
% 5.27/5.59 = ( ( power_power_int @ B @ W )
% 5.27/5.59 = X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7576_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.27/5.59 = ( ring_1_of_int_real @ X4 ) )
% 5.27/5.59 = ( ( power_power_int @ B @ W )
% 5.27/5.59 = X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7577_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.27/5.59 = ( ring_1_of_int_int @ X4 ) )
% 5.27/5.59 = ( ( power_power_int @ B @ W )
% 5.27/5.59 = X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7578_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.27/5.59 = ( ring_17405671764205052669omplex @ X4 ) )
% 5.27/5.59 = ( ( power_power_int @ B @ W )
% 5.27/5.59 = X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7579_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ X4 )
% 5.27/5.59 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.27/5.59 = ( X4
% 5.27/5.59 = ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7580_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ X4 )
% 5.27/5.59 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.27/5.59 = ( X4
% 5.27/5.59 = ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7581_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_int @ X4 )
% 5.27/5.59 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.27/5.59 = ( X4
% 5.27/5.59 = ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7582_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ( ring_17405671764205052669omplex @ X4 )
% 5.27/5.59 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.27/5.59 = ( X4
% 5.27/5.59 = ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7583_ceiling__add__of__int,axiom,
% 5.27/5.59 ! [X4: rat,Z: int] :
% 5.27/5.59 ( ( archim2889992004027027881ng_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) )
% 5.27/5.59 = ( plus_plus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_add_of_int
% 5.27/5.59 thf(fact_7584_ceiling__add__of__int,axiom,
% 5.27/5.59 ! [X4: real,Z: int] :
% 5.27/5.59 ( ( archim7802044766580827645g_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) )
% 5.27/5.59 = ( plus_plus_int @ ( archim7802044766580827645g_real @ X4 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_add_of_int
% 5.27/5.59 thf(fact_7585_of__nat__nat__take__bit__eq,axiom,
% 5.27/5.59 ! [N2: nat,K: int] :
% 5.27/5.59 ( ( semiri681578069525770553at_rat @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.27/5.59 = ( ring_1_of_int_rat @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat_take_bit_eq
% 5.27/5.59 thf(fact_7586_of__nat__nat__take__bit__eq,axiom,
% 5.27/5.59 ! [N2: nat,K: int] :
% 5.27/5.59 ( ( semiri5074537144036343181t_real @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.27/5.59 = ( ring_1_of_int_real @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat_take_bit_eq
% 5.27/5.59 thf(fact_7587_of__nat__nat__take__bit__eq,axiom,
% 5.27/5.59 ! [N2: nat,K: int] :
% 5.27/5.59 ( ( semiri1314217659103216013at_int @ ( nat2 @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) )
% 5.27/5.59 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat_take_bit_eq
% 5.27/5.59 thf(fact_7588_of__int__0__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_le_iff
% 5.27/5.59 thf(fact_7589_of__int__0__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_le_iff
% 5.27/5.59 thf(fact_7590_of__int__0__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_le_iff
% 5.27/5.59 thf(fact_7591_of__int__le__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_0_iff
% 5.27/5.59 thf(fact_7592_of__int__le__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_0_iff
% 5.27/5.59 thf(fact_7593_of__int__le__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_0_iff
% 5.27/5.59 thf(fact_7594_of__int__0__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_less_iff
% 5.27/5.59 thf(fact_7595_of__int__0__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_less_iff
% 5.27/5.59 thf(fact_7596_of__int__0__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_0_less_iff
% 5.27/5.59 thf(fact_7597_of__int__less__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.27/5.59 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_0_iff
% 5.27/5.59 thf(fact_7598_of__int__less__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.27/5.59 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_0_iff
% 5.27/5.59 thf(fact_7599_of__int__less__0__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_0_iff
% 5.27/5.59 thf(fact_7600_of__int__numeral__le__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_le_iff
% 5.27/5.59 thf(fact_7601_of__int__numeral__le__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_le_iff
% 5.27/5.59 thf(fact_7602_of__int__numeral__le__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_le_iff
% 5.27/5.59 thf(fact_7603_of__int__le__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_iff
% 5.27/5.59 thf(fact_7604_of__int__le__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_iff
% 5.27/5.59 thf(fact_7605_of__int__le__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_iff
% 5.27/5.59 thf(fact_7606_of__int__less__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_iff
% 5.27/5.59 thf(fact_7607_of__int__less__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_iff
% 5.27/5.59 thf(fact_7608_of__int__less__numeral__iff,axiom,
% 5.27/5.59 ! [Z: int,N2: num] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_iff
% 5.27/5.59 thf(fact_7609_of__int__numeral__less__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( numeral_numeral_rat @ N2 ) @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_less_iff
% 5.27/5.59 thf(fact_7610_of__int__numeral__less__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_real @ ( numeral_numeral_real @ N2 ) @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_less_iff
% 5.27/5.59 thf(fact_7611_of__int__numeral__less__iff,axiom,
% 5.27/5.59 ! [N2: num,Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_int @ ( numeral_numeral_int @ N2 ) @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_numeral_less_iff
% 5.27/5.59 thf(fact_7612_of__int__le__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_1_iff
% 5.27/5.59 thf(fact_7613_of__int__le__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_1_iff
% 5.27/5.59 thf(fact_7614_of__int__le__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.27/5.59 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_1_iff
% 5.27/5.59 thf(fact_7615_of__int__1__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_le_iff
% 5.27/5.59 thf(fact_7616_of__int__1__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_le_iff
% 5.27/5.59 thf(fact_7617_of__int__1__le__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_le_iff
% 5.27/5.59 thf(fact_7618_zero__le__floor,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % zero_le_floor
% 5.27/5.59 thf(fact_7619_zero__le__floor,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ zero_zero_rat @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % zero_le_floor
% 5.27/5.59 thf(fact_7620_of__int__1__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.59 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_less_iff
% 5.27/5.59 thf(fact_7621_of__int__1__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.59 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_less_iff
% 5.27/5.59 thf(fact_7622_of__int__1__less__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.27/5.59 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_1_less_iff
% 5.27/5.59 thf(fact_7623_of__int__less__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.27/5.59 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_1_iff
% 5.27/5.59 thf(fact_7624_of__int__less__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.27/5.59 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_1_iff
% 5.27/5.59 thf(fact_7625_of__int__less__1__iff,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.27/5.59 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_1_iff
% 5.27/5.59 thf(fact_7626_floor__less__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_zero
% 5.27/5.59 thf(fact_7627_floor__less__zero,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_rat @ X4 @ zero_zero_rat ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_zero
% 5.27/5.59 thf(fact_7628_numeral__le__floor,axiom,
% 5.27/5.59 ! [V: num,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( numeral_numeral_real @ V ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_le_floor
% 5.27/5.59 thf(fact_7629_numeral__le__floor,axiom,
% 5.27/5.59 ! [V: num,X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ V ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_le_floor
% 5.27/5.59 thf(fact_7630_zero__less__floor,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_int @ zero_zero_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % zero_less_floor
% 5.27/5.59 thf(fact_7631_zero__less__floor,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ zero_zero_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % zero_less_floor
% 5.27/5.59 thf(fact_7632_floor__le__zero,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_zero
% 5.27/5.59 thf(fact_7633_floor__le__zero,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ zero_zero_int )
% 5.27/5.59 = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_zero
% 5.27/5.59 thf(fact_7634_floor__less__numeral,axiom,
% 5.27/5.59 ! [X4: real,V: num] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( numeral_numeral_real @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_numeral
% 5.27/5.59 thf(fact_7635_floor__less__numeral,axiom,
% 5.27/5.59 ! [X4: rat,V: num] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_numeral
% 5.27/5.59 thf(fact_7636_one__le__floor,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ one_one_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % one_le_floor
% 5.27/5.59 thf(fact_7637_one__le__floor,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % one_le_floor
% 5.27/5.59 thf(fact_7638_floor__less__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.27/5.59 = ( ord_less_real @ X4 @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_one
% 5.27/5.59 thf(fact_7639_floor__less__one,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.27/5.59 = ( ord_less_rat @ X4 @ one_one_rat ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_one
% 5.27/5.59 thf(fact_7640_floor__neg__numeral,axiom,
% 5.27/5.59 ! [V: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.27/5.59 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_neg_numeral
% 5.27/5.59 thf(fact_7641_floor__neg__numeral,axiom,
% 5.27/5.59 ! [V: num] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.27/5.59 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_neg_numeral
% 5.27/5.59 thf(fact_7642_floor__diff__numeral,axiom,
% 5.27/5.59 ! [X4: real,V: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ ( numeral_numeral_real @ V ) ) )
% 5.27/5.59 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_diff_numeral
% 5.27/5.59 thf(fact_7643_floor__diff__numeral,axiom,
% 5.27/5.59 ! [X4: rat,V: num] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ ( numeral_numeral_rat @ V ) ) )
% 5.27/5.59 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_diff_numeral
% 5.27/5.59 thf(fact_7644_of__int__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7645_of__int__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7646_of__int__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_eq_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7647_of__int__le__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7648_of__int__le__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7649_of__int__le__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7650_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_rat @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7651_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 )
% 5.27/5.59 = ( ring_17405671764205052669omplex @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7652_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_real @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7653_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_int @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7654_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ Y )
% 5.27/5.59 = ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7655_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.27/5.59 = ( power_power_complex @ ( numera6690914467698888265omplex @ X4 ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7656_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ Y )
% 5.27/5.59 = ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7657_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_int @ Y )
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7658_floor__diff__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( minus_minus_real @ X4 @ one_one_real ) )
% 5.27/5.59 = ( minus_minus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_diff_one
% 5.27/5.59 thf(fact_7659_floor__diff__one,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) )
% 5.27/5.59 = ( minus_minus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_diff_one
% 5.27/5.59 thf(fact_7660_of__int__less__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X4 ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7661_of__int__less__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7662_of__int__less__of__int__power__cancel__iff,axiom,
% 5.27/5.59 ! [B: int,W: nat,X4: int] :
% 5.27/5.59 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X4 ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_of_int_power_cancel_iff
% 5.27/5.59 thf(fact_7663_of__int__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ X4 ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7664_of__int__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X4 ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7665_of__int__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: int,B: int,W: nat] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ X4 ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.27/5.59 = ( ord_less_int @ X4 @ ( power_power_int @ B @ W ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7666_of__nat__nat,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.59 => ( ( semiri681578069525770553at_rat @ ( nat2 @ Z ) )
% 5.27/5.59 = ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat
% 5.27/5.59 thf(fact_7667_of__nat__nat,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.59 => ( ( semiri5074537144036343181t_real @ ( nat2 @ Z ) )
% 5.27/5.59 = ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat
% 5.27/5.59 thf(fact_7668_of__nat__nat,axiom,
% 5.27/5.59 ! [Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.59 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.27/5.59 = ( ring_1_of_int_int @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_nat
% 5.27/5.59 thf(fact_7669_floor__numeral__power,axiom,
% 5.27/5.59 ! [X4: num,N2: nat] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_numeral_power
% 5.27/5.59 thf(fact_7670_floor__numeral__power,axiom,
% 5.27/5.59 ! [X4: num,N2: nat] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 5.27/5.59 = ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_numeral_power
% 5.27/5.59 thf(fact_7671_floor__divide__eq__div__numeral,axiom,
% 5.27/5.59 ! [A: num,B: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.27/5.59 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_eq_div_numeral
% 5.27/5.59 thf(fact_7672_numeral__less__floor,axiom,
% 5.27/5.59 ! [V: num,X4: real] :
% 5.27/5.59 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_less_floor
% 5.27/5.59 thf(fact_7673_numeral__less__floor,axiom,
% 5.27/5.59 ! [V: num,X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ ( numeral_numeral_int @ V ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_less_floor
% 5.27/5.59 thf(fact_7674_floor__le__numeral,axiom,
% 5.27/5.59 ! [X4: real,V: num] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( numeral_numeral_real @ V ) @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_numeral
% 5.27/5.59 thf(fact_7675_floor__le__numeral,axiom,
% 5.27/5.59 ! [X4: rat,V: num] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( numeral_numeral_int @ V ) )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ one_one_rat ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_numeral
% 5.27/5.59 thf(fact_7676_one__less__floor,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_int @ one_one_int @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % one_less_floor
% 5.27/5.59 thf(fact_7677_one__less__floor,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ one_one_int @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % one_less_floor
% 5.27/5.59 thf(fact_7678_floor__le__one,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_one
% 5.27/5.59 thf(fact_7679_floor__le__one,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_one
% 5.27/5.59 thf(fact_7680_neg__numeral__le__floor,axiom,
% 5.27/5.59 ! [V: num,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_le_floor
% 5.27/5.59 thf(fact_7681_neg__numeral__le__floor,axiom,
% 5.27/5.59 ! [V: num,X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_le_floor
% 5.27/5.59 thf(fact_7682_floor__less__neg__numeral,axiom,
% 5.27/5.59 ! [X4: real,V: num] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_neg_numeral
% 5.27/5.59 thf(fact_7683_floor__less__neg__numeral,axiom,
% 5.27/5.59 ! [X4: rat,V: num] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_neg_numeral
% 5.27/5.59 thf(fact_7684_numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7685_numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7686_numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7687_of__int__le__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7688_of__int__le__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7689_of__int__le__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7690_numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7691_numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7692_numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7693_of__int__less__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7694_of__int__less__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7695_of__int__less__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7696_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_real @ Y )
% 5.27/5.59 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7697_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_int @ Y )
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7698_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.27/5.59 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7699_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.27/5.59 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7700_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [Y: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ( ring_1_of_int_rat @ Y )
% 5.27/5.59 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( Y
% 5.27/5.59 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_eq_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7701_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_real @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7702_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_int @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7703_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X4 ) ) @ N2 )
% 5.27/5.59 = ( ring_17405671764205052669omplex @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7704_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 )
% 5.27/5.59 = ( ring_18347121197199848620nteger @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7705_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,Y: int] :
% 5.27/5.59 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 )
% 5.27/5.59 = ( ring_1_of_int_rat @ Y ) )
% 5.27/5.59 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 )
% 5.27/5.59 = Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_eq_of_int_cancel_iff
% 5.27/5.59 thf(fact_7706_floor__one__divide__eq__div__numeral,axiom,
% 5.27/5.59 ! [B: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.27/5.59 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_one_divide_eq_div_numeral
% 5.27/5.59 thf(fact_7707_floor__minus__divide__eq__div__numeral,axiom,
% 5.27/5.59 ! [A: num,B: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.27/5.59 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_minus_divide_eq_div_numeral
% 5.27/5.59 thf(fact_7708_sin__int__2pin,axiom,
% 5.27/5.59 ! [N2: int] :
% 5.27/5.59 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.27/5.59 = zero_zero_real ) ).
% 5.27/5.59
% 5.27/5.59 % sin_int_2pin
% 5.27/5.59 thf(fact_7709_cos__int__2pin,axiom,
% 5.27/5.59 ! [N2: int] :
% 5.27/5.59 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N2 ) ) )
% 5.27/5.59 = one_one_real ) ).
% 5.27/5.59
% 5.27/5.59 % cos_int_2pin
% 5.27/5.59 thf(fact_7710_neg__numeral__less__floor,axiom,
% 5.27/5.59 ! [V: num,X4: real] :
% 5.27/5.59 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_less_floor
% 5.27/5.59 thf(fact_7711_neg__numeral__less__floor,axiom,
% 5.27/5.59 ! [V: num,X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_less_floor
% 5.27/5.59 thf(fact_7712_floor__le__neg__numeral,axiom,
% 5.27/5.59 ! [X4: real,V: num] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_neg_numeral
% 5.27/5.59 thf(fact_7713_floor__le__neg__numeral,axiom,
% 5.27/5.59 ! [X4: rat,V: num] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ one_one_rat ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_neg_numeral
% 5.27/5.59 thf(fact_7714_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7715_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7716_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7717_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_le_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7718_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7719_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7720_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7721_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.27/5.59 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_le_of_int_cancel_iff
% 5.27/5.59 thf(fact_7722_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) @ ( ring_1_of_int_real @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7723_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ ( ring_1_of_int_int @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7724_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7725_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.27/5.59 ! [X4: num,N2: nat,A: int] :
% 5.27/5.59 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) @ ( ring_1_of_int_rat @ A ) )
% 5.27/5.59 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % neg_numeral_power_less_of_int_cancel_iff
% 5.27/5.59 thf(fact_7726_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7727_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7728_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7729_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.27/5.59 ! [A: int,X4: num,N2: nat] :
% 5.27/5.59 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X4 ) ) @ N2 ) )
% 5.27/5.59 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X4 ) ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_less_neg_numeral_power_cancel_iff
% 5.27/5.59 thf(fact_7730_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.27/5.59 ! [B: num] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.27/5.59 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_minus_one_divide_eq_div_numeral
% 5.27/5.59 thf(fact_7731_ex__le__of__int,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % ex_le_of_int
% 5.27/5.59 thf(fact_7732_ex__le__of__int,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % ex_le_of_int
% 5.27/5.59 thf(fact_7733_ex__of__int__less,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z2 ) @ X4 ) ).
% 5.27/5.59
% 5.27/5.59 % ex_of_int_less
% 5.27/5.59 thf(fact_7734_ex__of__int__less,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 ) ).
% 5.27/5.59
% 5.27/5.59 % ex_of_int_less
% 5.27/5.59 thf(fact_7735_ex__less__of__int,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % ex_less_of_int
% 5.27/5.59 thf(fact_7736_ex__less__of__int,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ? [Z2: int] : ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % ex_less_of_int
% 5.27/5.59 thf(fact_7737_int__add__floor,axiom,
% 5.27/5.59 ! [Z: int,X4: real] :
% 5.27/5.59 ( ( plus_plus_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( archim6058952711729229775r_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % int_add_floor
% 5.27/5.59 thf(fact_7738_int__add__floor,axiom,
% 5.27/5.59 ! [Z: int,X4: rat] :
% 5.27/5.59 ( ( plus_plus_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % int_add_floor
% 5.27/5.59 thf(fact_7739_floor__add__int,axiom,
% 5.27/5.59 ! [X4: real,Z: int] :
% 5.27/5.59 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.27/5.59 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_add_int
% 5.27/5.59 thf(fact_7740_floor__add__int,axiom,
% 5.27/5.59 ! [X4: rat,Z: int] :
% 5.27/5.59 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.27/5.59 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_add_int
% 5.27/5.59 thf(fact_7741_floor__divide__of__int__eq,axiom,
% 5.27/5.59 ! [K: int,L: int] :
% 5.27/5.59 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( ring_1_of_int_real @ K ) @ ( ring_1_of_int_real @ L ) ) )
% 5.27/5.59 = ( divide_divide_int @ K @ L ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_of_int_eq
% 5.27/5.59 thf(fact_7742_floor__divide__of__int__eq,axiom,
% 5.27/5.59 ! [K: int,L: int] :
% 5.27/5.59 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ K ) @ ( ring_1_of_int_rat @ L ) ) )
% 5.27/5.59 = ( divide_divide_int @ K @ L ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_of_int_eq
% 5.27/5.59 thf(fact_7743_of__int__floor__le,axiom,
% 5.27/5.59 ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_floor_le
% 5.27/5.59 thf(fact_7744_of__int__floor__le,axiom,
% 5.27/5.59 ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_floor_le
% 5.27/5.59 thf(fact_7745_floor__less__iff,axiom,
% 5.27/5.59 ! [X4: real,Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_iff
% 5.27/5.59 thf(fact_7746_floor__less__iff,axiom,
% 5.27/5.59 ! [X4: rat,Z: int] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_iff
% 5.27/5.59 thf(fact_7747_le__floor__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_floor_iff
% 5.27/5.59 thf(fact_7748_le__floor__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_floor_iff
% 5.27/5.59 thf(fact_7749_floor__power,axiom,
% 5.27/5.59 ! [X4: real,N2: nat] :
% 5.27/5.59 ( ( X4
% 5.27/5.59 = ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.59 = ( power_power_int @ ( archim6058952711729229775r_real @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_power
% 5.27/5.59 thf(fact_7750_floor__power,axiom,
% 5.27/5.59 ! [X4: rat,N2: nat] :
% 5.27/5.59 ( ( X4
% 5.27/5.59 = ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) )
% 5.27/5.59 => ( ( archim3151403230148437115or_rat @ ( power_power_rat @ X4 @ N2 ) )
% 5.27/5.59 = ( power_power_int @ ( archim3151403230148437115or_rat @ X4 ) @ N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_power
% 5.27/5.59 thf(fact_7751_real__of__int__floor__add__one__gt,axiom,
% 5.27/5.59 ! [R3: real] : ( ord_less_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_floor_add_one_gt
% 5.27/5.59 thf(fact_7752_floor__eq,axiom,
% 5.27/5.59 ! [N2: int,X4: real] :
% 5.27/5.59 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ X4 )
% 5.27/5.59 = N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_eq
% 5.27/5.59 thf(fact_7753_real__of__int__floor__add__one__ge,axiom,
% 5.27/5.59 ! [R3: real] : ( ord_less_eq_real @ R3 @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) @ one_one_real ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_floor_add_one_ge
% 5.27/5.59 thf(fact_7754_real__of__int__floor__gt__diff__one,axiom,
% 5.27/5.59 ! [R3: real] : ( ord_less_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_floor_gt_diff_one
% 5.27/5.59 thf(fact_7755_real__of__int__floor__ge__diff__one,axiom,
% 5.27/5.59 ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ R3 @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R3 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_floor_ge_diff_one
% 5.27/5.59 thf(fact_7756_floor__split,axiom,
% 5.27/5.59 ! [P: int > $o,T2: real] :
% 5.27/5.59 ( ( P @ ( archim6058952711729229775r_real @ T2 ) )
% 5.27/5.59 = ( ! [I3: int] :
% 5.27/5.59 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ I3 ) @ T2 )
% 5.27/5.59 & ( ord_less_real @ T2 @ ( plus_plus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) ) )
% 5.27/5.59 => ( P @ I3 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_split
% 5.27/5.59 thf(fact_7757_floor__split,axiom,
% 5.27/5.59 ! [P: int > $o,T2: rat] :
% 5.27/5.59 ( ( P @ ( archim3151403230148437115or_rat @ T2 ) )
% 5.27/5.59 = ( ! [I3: int] :
% 5.27/5.59 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ I3 ) @ T2 )
% 5.27/5.59 & ( ord_less_rat @ T2 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) ) )
% 5.27/5.59 => ( P @ I3 ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_split
% 5.27/5.59 thf(fact_7758_floor__eq__iff,axiom,
% 5.27/5.59 ! [X4: real,A: int] :
% 5.27/5.59 ( ( ( archim6058952711729229775r_real @ X4 )
% 5.27/5.59 = A )
% 5.27/5.59 = ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ X4 )
% 5.27/5.59 & ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_eq_iff
% 5.27/5.59 thf(fact_7759_floor__eq__iff,axiom,
% 5.27/5.59 ! [X4: rat,A: int] :
% 5.27/5.59 ( ( ( archim3151403230148437115or_rat @ X4 )
% 5.27/5.59 = A )
% 5.27/5.59 = ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ X4 )
% 5.27/5.59 & ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_eq_iff
% 5.27/5.59 thf(fact_7760_floor__unique,axiom,
% 5.27/5.59 ! [Z: int,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ X4 )
% 5.27/5.59 = Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_unique
% 5.27/5.59 thf(fact_7761_floor__unique,axiom,
% 5.27/5.59 ! [Z: int,X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ X4 )
% 5.27/5.59 => ( ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) )
% 5.27/5.59 => ( ( archim3151403230148437115or_rat @ X4 )
% 5.27/5.59 = Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_unique
% 5.27/5.59 thf(fact_7762_less__floor__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: real] :
% 5.27/5.59 ( ( ord_less_int @ Z @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_floor_iff
% 5.27/5.59 thf(fact_7763_less__floor__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ Z @ ( archim3151403230148437115or_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_floor_iff
% 5.27/5.59 thf(fact_7764_floor__le__iff,axiom,
% 5.27/5.59 ! [X4: real,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_iff
% 5.27/5.59 thf(fact_7765_floor__le__iff,axiom,
% 5.27/5.59 ! [X4: rat,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_iff
% 5.27/5.59 thf(fact_7766_floor__correct,axiom,
% 5.27/5.59 ! [X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ X4 ) ) @ X4 )
% 5.27/5.59 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_correct
% 5.27/5.59 thf(fact_7767_floor__correct,axiom,
% 5.27/5.59 ! [X4: rat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ X4 ) ) @ X4 )
% 5.27/5.59 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_correct
% 5.27/5.59 thf(fact_7768_floor__eq2,axiom,
% 5.27/5.59 ! [N2: int,X4: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 5.27/5.59 => ( ( ord_less_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ X4 )
% 5.27/5.59 = N2 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_eq2
% 5.27/5.59 thf(fact_7769_floor__divide__real__eq__div,axiom,
% 5.27/5.59 ! [B: int,A: real] :
% 5.27/5.59 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.27/5.59 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.27/5.59 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_real_eq_div
% 5.27/5.59 thf(fact_7770_floor__mono,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.59 => ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_mono
% 5.27/5.59 thf(fact_7771_floor__mono,axiom,
% 5.27/5.59 ! [X4: rat,Y: rat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.27/5.59 => ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_mono
% 5.27/5.59 thf(fact_7772_floor__less__cancel,axiom,
% 5.27/5.59 ! [X4: real,Y: real] :
% 5.27/5.59 ( ( ord_less_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) )
% 5.27/5.59 => ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_cancel
% 5.27/5.59 thf(fact_7773_floor__less__cancel,axiom,
% 5.27/5.59 ! [X4: rat,Y: rat] :
% 5.27/5.59 ( ( ord_less_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) )
% 5.27/5.59 => ( ord_less_rat @ X4 @ Y ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_less_cancel
% 5.27/5.59 thf(fact_7774_floor__le__ceiling,axiom,
% 5.27/5.59 ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_ceiling
% 5.27/5.59 thf(fact_7775_floor__le__ceiling,axiom,
% 5.27/5.59 ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim2889992004027027881ng_rat @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_le_ceiling
% 5.27/5.59 thf(fact_7776_le__of__int__ceiling,axiom,
% 5.27/5.59 ! [X4: real] : ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_of_int_ceiling
% 5.27/5.59 thf(fact_7777_le__of__int__ceiling,axiom,
% 5.27/5.59 ! [X4: rat] : ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_of_int_ceiling
% 5.27/5.59 thf(fact_7778_floor__divide__lower,axiom,
% 5.27/5.59 ! [Q3: real,P2: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.27/5.59 => ( ord_less_eq_real @ ( times_times_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_lower
% 5.27/5.59 thf(fact_7779_floor__divide__lower,axiom,
% 5.27/5.59 ! [Q3: rat,P2: rat] :
% 5.27/5.59 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.27/5.59 => ( ord_less_eq_rat @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) @ P2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_lower
% 5.27/5.59 thf(fact_7780_take__bit__of__int,axiom,
% 5.27/5.59 ! [N2: nat,K: int] :
% 5.27/5.59 ( ( bit_se2923211474154528505it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 5.27/5.59 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N2 @ K ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % take_bit_of_int
% 5.27/5.59 thf(fact_7781_of__int__and__eq,axiom,
% 5.27/5.59 ! [K: int,L: int] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L ) )
% 5.27/5.59 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_and_eq
% 5.27/5.59 thf(fact_7782_of__int__not__eq,axiom,
% 5.27/5.59 ! [K: int] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.27/5.59 = ( bit_ri7919022796975470100ot_int @ ( ring_1_of_int_int @ K ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_not_eq
% 5.27/5.59 thf(fact_7783_of__int__xor__eq,axiom,
% 5.27/5.59 ! [K: int,L: int] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( bit_se6526347334894502574or_int @ K @ L ) )
% 5.27/5.59 = ( bit_se6526347334894502574or_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_xor_eq
% 5.27/5.59 thf(fact_7784_of__int__mask__eq,axiom,
% 5.27/5.59 ! [N2: nat] :
% 5.27/5.59 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.59 = ( bit_se2000444600071755411sk_int @ N2 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_int_mask_eq
% 5.27/5.59 thf(fact_7785_floor__divide__upper,axiom,
% 5.27/5.59 ! [Q3: real,P2: real] :
% 5.27/5.59 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.27/5.59 => ( ord_less_real @ P2 @ ( times_times_real @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_upper
% 5.27/5.59 thf(fact_7786_floor__divide__upper,axiom,
% 5.27/5.59 ! [Q3: rat,P2: rat] :
% 5.27/5.59 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.27/5.59 => ( ord_less_rat @ P2 @ ( times_times_rat @ ( plus_plus_rat @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % floor_divide_upper
% 5.27/5.59 thf(fact_7787_le__floor__add,axiom,
% 5.27/5.59 ! [X4: real,Y: real] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_floor_add
% 5.27/5.59 thf(fact_7788_le__floor__add,axiom,
% 5.27/5.59 ! [X4: rat,Y: rat] : ( ord_less_eq_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % le_floor_add
% 5.27/5.59 thf(fact_7789_ceiling__le,axiom,
% 5.27/5.59 ! [X4: real,A: int] :
% 5.27/5.59 ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) )
% 5.27/5.59 => ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_le
% 5.27/5.59 thf(fact_7790_ceiling__le,axiom,
% 5.27/5.59 ! [X4: rat,A: int] :
% 5.27/5.59 ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) )
% 5.27/5.59 => ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ A ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_le
% 5.27/5.59 thf(fact_7791_ceiling__le__iff,axiom,
% 5.27/5.59 ! [X4: real,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_le_iff
% 5.27/5.59 thf(fact_7792_ceiling__le__iff,axiom,
% 5.27/5.59 ! [X4: rat,Z: int] :
% 5.27/5.59 ( ( ord_less_eq_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 5.27/5.59 = ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % ceiling_le_iff
% 5.27/5.59 thf(fact_7793_less__ceiling__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: rat] :
% 5.27/5.59 ( ( ord_less_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.59 = ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_ceiling_iff
% 5.27/5.59 thf(fact_7794_less__ceiling__iff,axiom,
% 5.27/5.59 ! [Z: int,X4: real] :
% 5.27/5.59 ( ( ord_less_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.59 = ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ X4 ) ) ).
% 5.27/5.59
% 5.27/5.59 % less_ceiling_iff
% 5.27/5.59 thf(fact_7795_real__of__int__div4,axiom,
% 5.27/5.59 ! [N2: int,X4: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_div4
% 5.27/5.59 thf(fact_7796_real__of__int__div,axiom,
% 5.27/5.59 ! [D: int,N2: int] :
% 5.27/5.59 ( ( dvd_dvd_int @ D @ N2 )
% 5.27/5.59 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ D ) )
% 5.27/5.59 = ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.27/5.59
% 5.27/5.59 % real_of_int_div
% 5.27/5.59 thf(fact_7797_of__nat__floor,axiom,
% 5.27/5.59 ! [R3: real] :
% 5.27/5.59 ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 5.27/5.59 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim6058952711729229775r_real @ R3 ) ) ) @ R3 ) ) ).
% 5.27/5.59
% 5.27/5.59 % of_nat_floor
% 5.27/5.59 thf(fact_7798_of__nat__floor,axiom,
% 5.27/5.59 ! [R3: rat] :
% 5.27/5.59 ( ( ord_less_eq_rat @ zero_zero_rat @ R3 )
% 5.27/5.59 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( archim3151403230148437115or_rat @ R3 ) ) ) @ R3 ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_floor
% 5.27/5.60 thf(fact_7799_one__add__floor,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ one_one_int )
% 5.27/5.60 = ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_add_floor
% 5.27/5.60 thf(fact_7800_one__add__floor,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ one_one_int )
% 5.27/5.60 = ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_add_floor
% 5.27/5.60 thf(fact_7801_le__mult__nat__floor,axiom,
% 5.27/5.60 ! [A: real,B: real] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ B ) ) ) @ ( nat2 @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_nat_floor
% 5.27/5.60 thf(fact_7802_le__mult__nat__floor,axiom,
% 5.27/5.60 ! [A: rat,B: rat] : ( ord_less_eq_nat @ ( times_times_nat @ ( nat2 @ ( archim3151403230148437115or_rat @ A ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( nat2 @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_nat_floor
% 5.27/5.60 thf(fact_7803_floor__divide__of__nat__eq,axiom,
% 5.27/5.60 ! [M: nat,N2: nat] :
% 5.27/5.60 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.60 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_divide_of_nat_eq
% 5.27/5.60 thf(fact_7804_floor__divide__of__nat__eq,axiom,
% 5.27/5.60 ! [M: nat,N2: nat] :
% 5.27/5.60 ( ( archim3151403230148437115or_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.27/5.60 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_divide_of_nat_eq
% 5.27/5.60 thf(fact_7805_nat__floor__neg,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.60 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.60 = zero_zero_nat ) ) ).
% 5.27/5.60
% 5.27/5.60 % nat_floor_neg
% 5.27/5.60 thf(fact_7806_floor__log__eq__powr__iff,axiom,
% 5.27/5.60 ! [X4: real,B: real,K: int] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.60 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X4 ) )
% 5.27/5.60 = K )
% 5.27/5.60 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_log_eq_powr_iff
% 5.27/5.60 thf(fact_7807_of__int__nonneg,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_nonneg
% 5.27/5.60 thf(fact_7808_of__int__nonneg,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_nonneg
% 5.27/5.60 thf(fact_7809_of__int__nonneg,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_nonneg
% 5.27/5.60 thf(fact_7810_of__int__leD,axiom,
% 5.27/5.60 ! [N2: int,X4: code_integer] :
% 5.27/5.60 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_leD
% 5.27/5.60 thf(fact_7811_of__int__leD,axiom,
% 5.27/5.60 ! [N2: int,X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_leD
% 5.27/5.60 thf(fact_7812_of__int__leD,axiom,
% 5.27/5.60 ! [N2: int,X4: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_leD
% 5.27/5.60 thf(fact_7813_of__int__leD,axiom,
% 5.27/5.60 ! [N2: int,X4: int] :
% 5.27/5.60 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_eq_int @ one_one_int @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_leD
% 5.27/5.60 thf(fact_7814_of__int__pos,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_pos
% 5.27/5.60 thf(fact_7815_of__int__pos,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_pos
% 5.27/5.60 thf(fact_7816_of__int__pos,axiom,
% 5.27/5.60 ! [Z: int] :
% 5.27/5.60 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.27/5.60 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_pos
% 5.27/5.60 thf(fact_7817_of__int__lessD,axiom,
% 5.27/5.60 ! [N2: int,X4: code_integer] :
% 5.27/5.60 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_lessD
% 5.27/5.60 thf(fact_7818_of__int__lessD,axiom,
% 5.27/5.60 ! [N2: int,X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_lessD
% 5.27/5.60 thf(fact_7819_of__int__lessD,axiom,
% 5.27/5.60 ! [N2: int,X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_lessD
% 5.27/5.60 thf(fact_7820_of__int__lessD,axiom,
% 5.27/5.60 ! [N2: int,X4: int] :
% 5.27/5.60 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N2 ) ) @ X4 )
% 5.27/5.60 => ( ( N2 = zero_zero_int )
% 5.27/5.60 | ( ord_less_int @ one_one_int @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_lessD
% 5.27/5.60 thf(fact_7821_floor__eq3,axiom,
% 5.27/5.60 ! [N2: nat,X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 5.27/5.60 => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.27/5.60 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.60 = N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_eq3
% 5.27/5.60 thf(fact_7822_le__nat__floor,axiom,
% 5.27/5.60 ! [X4: nat,A: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X4 ) @ A )
% 5.27/5.60 => ( ord_less_eq_nat @ X4 @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_nat_floor
% 5.27/5.60 thf(fact_7823_floor__exists1,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ? [X5: int] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X5 ) @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.27/5.60 & ! [Y4: int] :
% 5.27/5.60 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y4 ) @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.27/5.60 => ( Y4 = X5 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_exists1
% 5.27/5.60 thf(fact_7824_floor__exists1,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ? [X5: int] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X5 ) @ X4 )
% 5.27/5.60 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ X5 @ one_one_int ) ) )
% 5.27/5.60 & ! [Y4: int] :
% 5.27/5.60 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y4 ) @ X4 )
% 5.27/5.60 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y4 @ one_one_int ) ) ) )
% 5.27/5.60 => ( Y4 = X5 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_exists1
% 5.27/5.60 thf(fact_7825_floor__exists,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ? [Z2: int] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z2 ) @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_exists
% 5.27/5.60 thf(fact_7826_floor__exists,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ? [Z2: int] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z2 ) @ X4 )
% 5.27/5.60 & ( ord_less_rat @ X4 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z2 @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_exists
% 5.27/5.60 thf(fact_7827_of__int__ceiling__le__add__one,axiom,
% 5.27/5.60 ! [R3: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ ( plus_plus_real @ R3 @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_ceiling_le_add_one
% 5.27/5.60 thf(fact_7828_of__int__ceiling__le__add__one,axiom,
% 5.27/5.60 ! [R3: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ ( plus_plus_rat @ R3 @ one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_ceiling_le_add_one
% 5.27/5.60 thf(fact_7829_of__int__neg__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_neg_numeral
% 5.27/5.60 thf(fact_7830_of__int__neg__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_neg_numeral
% 5.27/5.60 thf(fact_7831_of__int__neg__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_neg_numeral
% 5.27/5.60 thf(fact_7832_of__int__neg__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_neg_numeral
% 5.27/5.60 thf(fact_7833_of__int__neg__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_neg_numeral
% 5.27/5.60 thf(fact_7834_of__int__ceiling__diff__one__le,axiom,
% 5.27/5.60 ! [R3: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ R3 ) ) @ one_one_real ) @ R3 ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_ceiling_diff_one_le
% 5.27/5.60 thf(fact_7835_of__int__ceiling__diff__one__le,axiom,
% 5.27/5.60 ! [R3: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ R3 ) ) @ one_one_rat ) @ R3 ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_ceiling_diff_one_le
% 5.27/5.60 thf(fact_7836_ceiling__diff__floor__le__1,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim7802044766580827645g_real @ X4 ) @ ( archim6058952711729229775r_real @ X4 ) ) @ one_one_int ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_diff_floor_le_1
% 5.27/5.60 thf(fact_7837_ceiling__diff__floor__le__1,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_int @ ( minus_minus_int @ ( archim2889992004027027881ng_rat @ X4 ) @ ( archim3151403230148437115or_rat @ X4 ) ) @ one_one_int ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_diff_floor_le_1
% 5.27/5.60 thf(fact_7838_of__nat__less__of__int__iff,axiom,
% 5.27/5.60 ! [N2: nat,X4: int] :
% 5.27/5.60 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( ring_1_of_int_rat @ X4 ) )
% 5.27/5.60 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_less_of_int_iff
% 5.27/5.60 thf(fact_7839_of__nat__less__of__int__iff,axiom,
% 5.27/5.60 ! [N2: nat,X4: int] :
% 5.27/5.60 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) )
% 5.27/5.60 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_less_of_int_iff
% 5.27/5.60 thf(fact_7840_of__nat__less__of__int__iff,axiom,
% 5.27/5.60 ! [N2: nat,X4: int] :
% 5.27/5.60 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( ring_1_of_int_int @ X4 ) )
% 5.27/5.60 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N2 ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_less_of_int_iff
% 5.27/5.60 thf(fact_7841_int__le__real__less,axiom,
% 5.27/5.60 ( ord_less_eq_int
% 5.27/5.60 = ( ^ [N: int,M6: int] : ( ord_less_real @ ( ring_1_of_int_real @ N ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M6 ) @ one_one_real ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % int_le_real_less
% 5.27/5.60 thf(fact_7842_int__less__real__le,axiom,
% 5.27/5.60 ( ord_less_int
% 5.27/5.60 = ( ^ [N: int,M6: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) @ ( ring_1_of_int_real @ M6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % int_less_real_le
% 5.27/5.60 thf(fact_7843_of__int__not__numeral,axiom,
% 5.27/5.60 ! [K: num] :
% 5.27/5.60 ( ( ring_1_of_int_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_not_numeral
% 5.27/5.60 thf(fact_7844_ceiling__divide__eq__div,axiom,
% 5.27/5.60 ! [A: int,B: int] :
% 5.27/5.60 ( ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_eq_div
% 5.27/5.60 thf(fact_7845_ceiling__divide__eq__div,axiom,
% 5.27/5.60 ! [A: int,B: int] :
% 5.27/5.60 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_eq_div
% 5.27/5.60 thf(fact_7846_real__of__int__div__aux,axiom,
% 5.27/5.60 ! [X4: int,D: int] :
% 5.27/5.60 ( ( divide_divide_real @ ( ring_1_of_int_real @ X4 ) @ ( ring_1_of_int_real @ D ) )
% 5.27/5.60 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X4 @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X4 @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_of_int_div_aux
% 5.27/5.60 thf(fact_7847_le__mult__floor,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.27/5.60 => ( ord_less_eq_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor
% 5.27/5.60 thf(fact_7848_le__mult__floor,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.27/5.60 => ( ord_less_eq_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor
% 5.27/5.60 thf(fact_7849_floor__eq4,axiom,
% 5.27/5.60 ! [N2: nat,X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N2 ) @ X4 )
% 5.27/5.60 => ( ( ord_less_real @ X4 @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.27/5.60 => ( ( nat2 @ ( archim6058952711729229775r_real @ X4 ) )
% 5.27/5.60 = N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_eq4
% 5.27/5.60 thf(fact_7850_ceiling__split,axiom,
% 5.27/5.60 ! [P: int > $o,T2: real] :
% 5.27/5.60 ( ( P @ ( archim7802044766580827645g_real @ T2 ) )
% 5.27/5.60 = ( ! [I3: int] :
% 5.27/5.60 ( ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ I3 ) @ one_one_real ) @ T2 )
% 5.27/5.60 & ( ord_less_eq_real @ T2 @ ( ring_1_of_int_real @ I3 ) ) )
% 5.27/5.60 => ( P @ I3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_split
% 5.27/5.60 thf(fact_7851_ceiling__split,axiom,
% 5.27/5.60 ! [P: int > $o,T2: rat] :
% 5.27/5.60 ( ( P @ ( archim2889992004027027881ng_rat @ T2 ) )
% 5.27/5.60 = ( ! [I3: int] :
% 5.27/5.60 ( ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ I3 ) @ one_one_rat ) @ T2 )
% 5.27/5.60 & ( ord_less_eq_rat @ T2 @ ( ring_1_of_int_rat @ I3 ) ) )
% 5.27/5.60 => ( P @ I3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_split
% 5.27/5.60 thf(fact_7852_ceiling__eq__iff,axiom,
% 5.27/5.60 ! [X4: real,A: int] :
% 5.27/5.60 ( ( ( archim7802044766580827645g_real @ X4 )
% 5.27/5.60 = A )
% 5.27/5.60 = ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ A ) @ one_one_real ) @ X4 )
% 5.27/5.60 & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_eq_iff
% 5.27/5.60 thf(fact_7853_ceiling__eq__iff,axiom,
% 5.27/5.60 ! [X4: rat,A: int] :
% 5.27/5.60 ( ( ( archim2889992004027027881ng_rat @ X4 )
% 5.27/5.60 = A )
% 5.27/5.60 = ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ A ) @ one_one_rat ) @ X4 )
% 5.27/5.60 & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_eq_iff
% 5.27/5.60 thf(fact_7854_ceiling__unique,axiom,
% 5.27/5.60 ! [Z: int,X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ Z ) )
% 5.27/5.60 => ( ( archim7802044766580827645g_real @ X4 )
% 5.27/5.60 = Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_unique
% 5.27/5.60 thf(fact_7855_ceiling__unique,axiom,
% 5.27/5.60 ! [Z: int,X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ Z ) )
% 5.27/5.60 => ( ( archim2889992004027027881ng_rat @ X4 )
% 5.27/5.60 = Z ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_unique
% 5.27/5.60 thf(fact_7856_ceiling__correct,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) @ one_one_real ) @ X4 )
% 5.27/5.60 & ( ord_less_eq_real @ X4 @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_correct
% 5.27/5.60 thf(fact_7857_ceiling__correct,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) @ one_one_rat ) @ X4 )
% 5.27/5.60 & ( ord_less_eq_rat @ X4 @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_correct
% 5.27/5.60 thf(fact_7858_cot__def,axiom,
% 5.27/5.60 ( cot_real
% 5.27/5.60 = ( ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cot_def
% 5.27/5.60 thf(fact_7859_cot__def,axiom,
% 5.27/5.60 ( cot_complex
% 5.27/5.60 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( cos_complex @ X ) @ ( sin_complex @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cot_def
% 5.27/5.60 thf(fact_7860_ceiling__less__iff,axiom,
% 5.27/5.60 ! [X4: real,Z: int] :
% 5.27/5.60 ( ( ord_less_int @ ( archim7802044766580827645g_real @ X4 ) @ Z )
% 5.27/5.60 = ( ord_less_eq_real @ X4 @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_less_iff
% 5.27/5.60 thf(fact_7861_ceiling__less__iff,axiom,
% 5.27/5.60 ! [X4: rat,Z: int] :
% 5.27/5.60 ( ( ord_less_int @ ( archim2889992004027027881ng_rat @ X4 ) @ Z )
% 5.27/5.60 = ( ord_less_eq_rat @ X4 @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_less_iff
% 5.27/5.60 thf(fact_7862_le__ceiling__iff,axiom,
% 5.27/5.60 ! [Z: int,X4: rat] :
% 5.27/5.60 ( ( ord_less_eq_int @ Z @ ( archim2889992004027027881ng_rat @ X4 ) )
% 5.27/5.60 = ( ord_less_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_ceiling_iff
% 5.27/5.60 thf(fact_7863_le__ceiling__iff,axiom,
% 5.27/5.60 ! [Z: int,X4: real] :
% 5.27/5.60 ( ( ord_less_eq_int @ Z @ ( archim7802044766580827645g_real @ X4 ) )
% 5.27/5.60 = ( ord_less_real @ ( minus_minus_real @ ( ring_1_of_int_real @ Z ) @ one_one_real ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_ceiling_iff
% 5.27/5.60 thf(fact_7864_real__of__int__div2,axiom,
% 5.27/5.60 ! [N2: int,X4: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_of_int_div2
% 5.27/5.60 thf(fact_7865_real__of__int__div3,axiom,
% 5.27/5.60 ! [N2: int,X4: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N2 ) @ ( ring_1_of_int_real @ X4 ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N2 @ X4 ) ) ) @ one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % real_of_int_div3
% 5.27/5.60 thf(fact_7866_ceiling__divide__upper,axiom,
% 5.27/5.60 ! [Q3: real,P2: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.27/5.60 => ( ord_less_eq_real @ P2 @ ( times_times_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_upper
% 5.27/5.60 thf(fact_7867_ceiling__divide__upper,axiom,
% 5.27/5.60 ! [Q3: rat,P2: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.27/5.60 => ( ord_less_eq_rat @ P2 @ ( times_times_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ Q3 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_upper
% 5.27/5.60 thf(fact_7868_even__of__int__iff,axiom,
% 5.27/5.60 ! [K: int] :
% 5.27/5.60 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.27/5.60 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.27/5.60
% 5.27/5.60 % even_of_int_iff
% 5.27/5.60 thf(fact_7869_even__of__int__iff,axiom,
% 5.27/5.60 ! [K: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.27/5.60 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.27/5.60
% 5.27/5.60 % even_of_int_iff
% 5.27/5.60 thf(fact_7870_of__int__of__nat,axiom,
% 5.27/5.60 ( ring_17405671764205052669omplex
% 5.27/5.60 = ( ^ [K3: int] : ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri8010041392384452111omplex @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_of_nat
% 5.27/5.60 thf(fact_7871_of__int__of__nat,axiom,
% 5.27/5.60 ( ring_18347121197199848620nteger
% 5.27/5.60 = ( ^ [K3: int] : ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( semiri4939895301339042750nteger @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri4939895301339042750nteger @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_of_nat
% 5.27/5.60 thf(fact_7872_of__int__of__nat,axiom,
% 5.27/5.60 ( ring_1_of_int_rat
% 5.27/5.60 = ( ^ [K3: int] : ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri681578069525770553at_rat @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_of_nat
% 5.27/5.60 thf(fact_7873_of__int__of__nat,axiom,
% 5.27/5.60 ( ring_1_of_int_real
% 5.27/5.60 = ( ^ [K3: int] : ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri5074537144036343181t_real @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_of_nat
% 5.27/5.60 thf(fact_7874_of__int__of__nat,axiom,
% 5.27/5.60 ( ring_1_of_int_int
% 5.27/5.60 = ( ^ [K3: int] : ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( nat2 @ ( uminus_uminus_int @ K3 ) ) ) ) @ ( semiri1314217659103216013at_int @ ( nat2 @ K3 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_of_nat
% 5.27/5.60 thf(fact_7875_ceiling__divide__lower,axiom,
% 5.27/5.60 ! [Q3: rat,P2: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ Q3 )
% 5.27/5.60 => ( ord_less_rat @ ( times_times_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( divide_divide_rat @ P2 @ Q3 ) ) ) @ one_one_rat ) @ Q3 ) @ P2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_lower
% 5.27/5.60 thf(fact_7876_ceiling__divide__lower,axiom,
% 5.27/5.60 ! [Q3: real,P2: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ Q3 )
% 5.27/5.60 => ( ord_less_real @ ( times_times_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( divide_divide_real @ P2 @ Q3 ) ) ) @ one_one_real ) @ Q3 ) @ P2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_divide_lower
% 5.27/5.60 thf(fact_7877_ceiling__eq,axiom,
% 5.27/5.60 ! [N2: int,X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_real @ X4 @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) )
% 5.27/5.60 => ( ( archim7802044766580827645g_real @ X4 )
% 5.27/5.60 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_eq
% 5.27/5.60 thf(fact_7878_ceiling__eq,axiom,
% 5.27/5.60 ! [N2: int,X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( ring_1_of_int_rat @ N2 ) @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_rat @ X4 @ ( plus_plus_rat @ ( ring_1_of_int_rat @ N2 ) @ one_one_rat ) )
% 5.27/5.60 => ( ( archim2889992004027027881ng_rat @ X4 )
% 5.27/5.60 = ( plus_plus_int @ N2 @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_eq
% 5.27/5.60 thf(fact_7879_cos__one__2pi__int,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( cos_real @ X4 )
% 5.27/5.60 = one_one_real )
% 5.27/5.60 = ( ? [X: int] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cos_one_2pi_int
% 5.27/5.60 thf(fact_7880_arccos__cos__eq__abs__2pi,axiom,
% 5.27/5.60 ! [Theta: real] :
% 5.27/5.60 ~ ! [K2: int] :
% 5.27/5.60 ( ( arccos @ ( cos_real @ Theta ) )
% 5.27/5.60 != ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % arccos_cos_eq_abs_2pi
% 5.27/5.60 thf(fact_7881_cot__gt__zero,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ord_less_real @ X4 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.60 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cot_gt_zero
% 5.27/5.60 thf(fact_7882_floor__log2__div2,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.60 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.60 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_log2_div2
% 5.27/5.60 thf(fact_7883_tan__cot_H,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 5.27/5.60 = ( cot_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % tan_cot'
% 5.27/5.60 thf(fact_7884_cos__zero__iff__int,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( cos_real @ X4 )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 = ( ? [I3: int] :
% 5.27/5.60 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.60 & ( X4
% 5.27/5.60 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cos_zero_iff_int
% 5.27/5.60 thf(fact_7885_sin__zero__iff__int,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( sin_real @ X4 )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 = ( ? [I3: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.60 & ( X4
% 5.27/5.60 = ( times_times_real @ ( ring_1_of_int_real @ I3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sin_zero_iff_int
% 5.27/5.60 thf(fact_7886_powr__int,axiom,
% 5.27/5.60 ! [X4: real,I2: int] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.27/5.60 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 5.27/5.60 = ( power_power_real @ X4 @ ( nat2 @ I2 ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I2 )
% 5.27/5.60 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ I2 ) )
% 5.27/5.60 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ I2 ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % powr_int
% 5.27/5.60 thf(fact_7887_round__unique,axiom,
% 5.27/5.60 ! [X4: real,Y: int] :
% 5.27/5.60 ( ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.27/5.60 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.60 => ( ( archim8280529875227126926d_real @ X4 )
% 5.27/5.60 = Y ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_unique
% 5.27/5.60 thf(fact_7888_round__unique,axiom,
% 5.27/5.60 ! [X4: rat,Y: int] :
% 5.27/5.60 ( ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.27/5.60 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.60 => ( ( archim7778729529865785530nd_rat @ X4 )
% 5.27/5.60 = Y ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_unique
% 5.27/5.60 thf(fact_7889_round__unique_H,axiom,
% 5.27/5.60 ! [X4: rat,N2: int] :
% 5.27/5.60 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ ( ring_1_of_int_rat @ N2 ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 => ( ( archim7778729529865785530nd_rat @ X4 )
% 5.27/5.60 = N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_unique'
% 5.27/5.60 thf(fact_7890_round__unique_H,axiom,
% 5.27/5.60 ! [X4: real,N2: int] :
% 5.27/5.60 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ ( ring_1_of_int_real @ N2 ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.60 => ( ( archim8280529875227126926d_real @ X4 )
% 5.27/5.60 = N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_unique'
% 5.27/5.60 thf(fact_7891_of__int__round__abs__le,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ X4 ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_abs_le
% 5.27/5.60 thf(fact_7892_of__int__round__abs__le,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ X4 ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_abs_le
% 5.27/5.60 thf(fact_7893_of__int__round__gt,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_gt
% 5.27/5.60 thf(fact_7894_of__int__round__gt,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_gt
% 5.27/5.60 thf(fact_7895_of__int__round__ge,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( minus_minus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_ge
% 5.27/5.60 thf(fact_7896_of__int__round__ge,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_ge
% 5.27/5.60 thf(fact_7897_round__numeral,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N2 ) )
% 5.27/5.60 = ( numeral_numeral_int @ N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_numeral
% 5.27/5.60 thf(fact_7898_round__1,axiom,
% 5.27/5.60 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.27/5.60 = one_one_int ) ).
% 5.27/5.60
% 5.27/5.60 % round_1
% 5.27/5.60 thf(fact_7899_round__1,axiom,
% 5.27/5.60 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.27/5.60 = one_one_int ) ).
% 5.27/5.60
% 5.27/5.60 % round_1
% 5.27/5.60 thf(fact_7900_round__neg__numeral,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N2 ) ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_neg_numeral
% 5.27/5.60 thf(fact_7901_round__neg__numeral,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N2 ) ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_neg_numeral
% 5.27/5.60 thf(fact_7902_round__mono,axiom,
% 5.27/5.60 ! [X4: rat,Y: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ X4 @ Y )
% 5.27/5.60 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_mono
% 5.27/5.60 thf(fact_7903_floor__le__round,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim8280529875227126926d_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_le_round
% 5.27/5.60 thf(fact_7904_floor__le__round,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim7778729529865785530nd_rat @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_le_round
% 5.27/5.60 thf(fact_7905_ceiling__ge__round,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_int @ ( archim8280529875227126926d_real @ X4 ) @ ( archim7802044766580827645g_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % ceiling_ge_round
% 5.27/5.60 thf(fact_7906_round__diff__minimal,axiom,
% 5.27/5.60 ! [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_diff_minimal
% 5.27/5.60 thf(fact_7907_round__diff__minimal,axiom,
% 5.27/5.60 ! [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_diff_minimal
% 5.27/5.60 thf(fact_7908_round__def,axiom,
% 5.27/5.60 ( archim8280529875227126926d_real
% 5.27/5.60 = ( ^ [X: real] : ( archim6058952711729229775r_real @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_def
% 5.27/5.60 thf(fact_7909_round__def,axiom,
% 5.27/5.60 ( archim7778729529865785530nd_rat
% 5.27/5.60 = ( ^ [X: rat] : ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_def
% 5.27/5.60 thf(fact_7910_of__int__round__le,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X4 ) ) @ ( plus_plus_real @ X4 @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_le
% 5.27/5.60 thf(fact_7911_of__int__round__le,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X4 ) ) @ ( plus_plus_rat @ X4 @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_round_le
% 5.27/5.60 thf(fact_7912_round__altdef,axiom,
% 5.27/5.60 ( archim8280529875227126926d_real
% 5.27/5.60 = ( ^ [X: real] : ( if_int @ ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( archim2898591450579166408c_real @ X ) ) @ ( archim7802044766580827645g_real @ X ) @ ( archim6058952711729229775r_real @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_altdef
% 5.27/5.60 thf(fact_7913_round__altdef,axiom,
% 5.27/5.60 ( archim7778729529865785530nd_rat
% 5.27/5.60 = ( ^ [X: rat] : ( if_int @ ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( archimedean_frac_rat @ X ) ) @ ( archim2889992004027027881ng_rat @ X ) @ ( archim3151403230148437115or_rat @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % round_altdef
% 5.27/5.60 thf(fact_7914_powr__real__of__int,axiom,
% 5.27/5.60 ! [X4: real,N2: int] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.27/5.60 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 5.27/5.60 = ( power_power_real @ X4 @ ( nat2 @ N2 ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N2 )
% 5.27/5.60 => ( ( powr_real @ X4 @ ( ring_1_of_int_real @ N2 ) )
% 5.27/5.60 = ( inverse_inverse_real @ ( power_power_real @ X4 @ ( nat2 @ ( uminus_uminus_int @ N2 ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % powr_real_of_int
% 5.27/5.60 thf(fact_7915_cis__2pi,axiom,
% 5.27/5.60 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % cis_2pi
% 5.27/5.60 thf(fact_7916_i__even__power,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % i_even_power
% 5.27/5.60 thf(fact_7917_gbinomial__absorption_H,axiom,
% 5.27/5.60 ! [K: nat,A: rat] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_rat @ A @ K )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption'
% 5.27/5.60 thf(fact_7918_gbinomial__absorption_H,axiom,
% 5.27/5.60 ! [K: nat,A: complex] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_complex @ A @ K )
% 5.27/5.60 = ( times_times_complex @ ( divide1717551699836669952omplex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption'
% 5.27/5.60 thf(fact_7919_gbinomial__absorption_H,axiom,
% 5.27/5.60 ! [K: nat,A: real] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_real @ A @ K )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption'
% 5.27/5.60 thf(fact_7920_inverse__inverse__eq,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = A ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_inverse_eq
% 5.27/5.60 thf(fact_7921_inverse__inverse__eq,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.27/5.60 = A ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_inverse_eq
% 5.27/5.60 thf(fact_7922_inverse__eq__iff__eq,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ A )
% 5.27/5.60 = ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( A = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_iff_eq
% 5.27/5.60 thf(fact_7923_inverse__eq__iff__eq,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 = ( A = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_iff_eq
% 5.27/5.60 thf(fact_7924_inverse__nonzero__iff__nonzero,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ( inverse_inverse_rat @ A )
% 5.27/5.60 = zero_zero_rat )
% 5.27/5.60 = ( A = zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonzero_iff_nonzero
% 5.27/5.60 thf(fact_7925_inverse__nonzero__iff__nonzero,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ A )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 = ( A = zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonzero_iff_nonzero
% 5.27/5.60 thf(fact_7926_inverse__nonzero__iff__nonzero,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = zero_zero_complex )
% 5.27/5.60 = ( A = zero_zero_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonzero_iff_nonzero
% 5.27/5.60 thf(fact_7927_inverse__zero,axiom,
% 5.27/5.60 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.27/5.60 = zero_zero_rat ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero
% 5.27/5.60 thf(fact_7928_inverse__zero,axiom,
% 5.27/5.60 ( ( inverse_inverse_real @ zero_zero_real )
% 5.27/5.60 = zero_zero_real ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero
% 5.27/5.60 thf(fact_7929_inverse__zero,axiom,
% 5.27/5.60 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.27/5.60 = zero_zero_complex ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero
% 5.27/5.60 thf(fact_7930_inverse__mult__distrib,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.27/5.60 = ( times_times_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_mult_distrib
% 5.27/5.60 thf(fact_7931_inverse__mult__distrib,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.27/5.60 = ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_mult_distrib
% 5.27/5.60 thf(fact_7932_inverse__eq__1__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ( inverse_inverse_rat @ X4 )
% 5.27/5.60 = one_one_rat )
% 5.27/5.60 = ( X4 = one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_1_iff
% 5.27/5.60 thf(fact_7933_inverse__eq__1__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ X4 )
% 5.27/5.60 = one_one_real )
% 5.27/5.60 = ( X4 = one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_1_iff
% 5.27/5.60 thf(fact_7934_inverse__eq__1__iff,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ X4 )
% 5.27/5.60 = one_one_complex )
% 5.27/5.60 = ( X4 = one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_1_iff
% 5.27/5.60 thf(fact_7935_inverse__1,axiom,
% 5.27/5.60 ( ( inverse_inverse_rat @ one_one_rat )
% 5.27/5.60 = one_one_rat ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_1
% 5.27/5.60 thf(fact_7936_inverse__1,axiom,
% 5.27/5.60 ( ( inverse_inverse_real @ one_one_real )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_1
% 5.27/5.60 thf(fact_7937_inverse__1,axiom,
% 5.27/5.60 ( ( invers8013647133539491842omplex @ one_one_complex )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_1
% 5.27/5.60 thf(fact_7938_inverse__divide,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( divide_divide_real @ A @ B ) )
% 5.27/5.60 = ( divide_divide_real @ B @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_divide
% 5.27/5.60 thf(fact_7939_inverse__divide,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.27/5.60 = ( divide1717551699836669952omplex @ B @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_divide
% 5.27/5.60 thf(fact_7940_inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.60 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_minus_eq
% 5.27/5.60 thf(fact_7941_inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_minus_eq
% 5.27/5.60 thf(fact_7942_inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_minus_eq
% 5.27/5.60 thf(fact_7943_abs__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % abs_inverse
% 5.27/5.60 thf(fact_7944_abs__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % abs_inverse
% 5.27/5.60 thf(fact_7945_abs__inverse,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( abs_abs_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.27/5.60 = ( invers8013647133539491842omplex @ ( abs_abs_complex @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % abs_inverse
% 5.27/5.60 thf(fact_7946_inverse__sgn,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) )
% 5.27/5.60 = ( sgn_sgn_rat @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_sgn
% 5.27/5.60 thf(fact_7947_inverse__sgn,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( sgn_sgn_real @ A ) )
% 5.27/5.60 = ( sgn_sgn_real @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_sgn
% 5.27/5.60 thf(fact_7948_sgn__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( sgn_sgn_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = ( inverse_inverse_rat @ ( sgn_sgn_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sgn_inverse
% 5.27/5.60 thf(fact_7949_sgn__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( sgn_sgn_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = ( inverse_inverse_real @ ( sgn_sgn_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sgn_inverse
% 5.27/5.60 thf(fact_7950_sgn__inverse,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( sgn_sgn_complex @ ( invers8013647133539491842omplex @ A ) )
% 5.27/5.60 = ( invers8013647133539491842omplex @ ( sgn_sgn_complex @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sgn_inverse
% 5.27/5.60 thf(fact_7951_inverse__nonnegative__iff__nonnegative,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonnegative_iff_nonnegative
% 5.27/5.60 thf(fact_7952_inverse__nonnegative__iff__nonnegative,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonnegative_iff_nonnegative
% 5.27/5.60 thf(fact_7953_inverse__nonpositive__iff__nonpositive,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.27/5.60 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonpositive_iff_nonpositive
% 5.27/5.60 thf(fact_7954_inverse__nonpositive__iff__nonpositive,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.27/5.60 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_nonpositive_iff_nonpositive
% 5.27/5.60 thf(fact_7955_inverse__positive__iff__positive,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_positive_iff_positive
% 5.27/5.60 thf(fact_7956_inverse__positive__iff__positive,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_positive_iff_positive
% 5.27/5.60 thf(fact_7957_inverse__negative__iff__negative,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.27/5.60 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_negative_iff_negative
% 5.27/5.60 thf(fact_7958_inverse__negative__iff__negative,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.27/5.60 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_negative_iff_negative
% 5.27/5.60 thf(fact_7959_inverse__less__iff__less__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff_less_neg
% 5.27/5.60 thf(fact_7960_inverse__less__iff__less__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff_less_neg
% 5.27/5.60 thf(fact_7961_inverse__less__iff__less,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.27/5.60 => ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff_less
% 5.27/5.60 thf(fact_7962_inverse__less__iff__less,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.60 => ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ord_less_real @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff_less
% 5.27/5.60 thf(fact_7963_gbinomial__0_I2_J,axiom,
% 5.27/5.60 ! [K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ zero_zero_complex @ ( suc @ K ) )
% 5.27/5.60 = zero_zero_complex ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(2)
% 5.27/5.60 thf(fact_7964_gbinomial__0_I2_J,axiom,
% 5.27/5.60 ! [K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ zero_zero_real @ ( suc @ K ) )
% 5.27/5.60 = zero_zero_real ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(2)
% 5.27/5.60 thf(fact_7965_gbinomial__0_I2_J,axiom,
% 5.27/5.60 ! [K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ zero_zero_rat @ ( suc @ K ) )
% 5.27/5.60 = zero_zero_rat ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(2)
% 5.27/5.60 thf(fact_7966_gbinomial__0_I2_J,axiom,
% 5.27/5.60 ! [K: nat] :
% 5.27/5.60 ( ( gbinomial_nat @ zero_zero_nat @ ( suc @ K ) )
% 5.27/5.60 = zero_zero_nat ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(2)
% 5.27/5.60 thf(fact_7967_gbinomial__0_I2_J,axiom,
% 5.27/5.60 ! [K: nat] :
% 5.27/5.60 ( ( gbinomial_int @ zero_zero_int @ ( suc @ K ) )
% 5.27/5.60 = zero_zero_int ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(2)
% 5.27/5.60 thf(fact_7968_gbinomial__0_I1_J,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( gbinomial_complex @ A @ zero_zero_nat )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(1)
% 5.27/5.60 thf(fact_7969_gbinomial__0_I1_J,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( gbinomial_real @ A @ zero_zero_nat )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(1)
% 5.27/5.60 thf(fact_7970_gbinomial__0_I1_J,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( gbinomial_rat @ A @ zero_zero_nat )
% 5.27/5.60 = one_one_rat ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(1)
% 5.27/5.60 thf(fact_7971_gbinomial__0_I1_J,axiom,
% 5.27/5.60 ! [A: nat] :
% 5.27/5.60 ( ( gbinomial_nat @ A @ zero_zero_nat )
% 5.27/5.60 = one_one_nat ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(1)
% 5.27/5.60 thf(fact_7972_gbinomial__0_I1_J,axiom,
% 5.27/5.60 ! [A: int] :
% 5.27/5.60 ( ( gbinomial_int @ A @ zero_zero_nat )
% 5.27/5.60 = one_one_int ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_0(1)
% 5.27/5.60 thf(fact_7973_norm__ii,axiom,
% 5.27/5.60 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % norm_ii
% 5.27/5.60 thf(fact_7974_norm__cis,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % norm_cis
% 5.27/5.60 thf(fact_7975_inverse__le__iff__le__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff_le_neg
% 5.27/5.60 thf(fact_7976_inverse__le__iff__le__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff_le_neg
% 5.27/5.60 thf(fact_7977_inverse__le__iff__le,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.27/5.60 => ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff_le
% 5.27/5.60 thf(fact_7978_inverse__le__iff__le,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.60 => ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff_le
% 5.27/5.60 thf(fact_7979_right__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( times_times_rat @ A @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % right_inverse
% 5.27/5.60 thf(fact_7980_right__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( times_times_real @ A @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % right_inverse
% 5.27/5.60 thf(fact_7981_right__inverse,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( times_times_complex @ A @ ( invers8013647133539491842omplex @ A ) )
% 5.27/5.60 = one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % right_inverse
% 5.27/5.60 thf(fact_7982_left__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.27/5.60 = one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % left_inverse
% 5.27/5.60 thf(fact_7983_left__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.27/5.60 = one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % left_inverse
% 5.27/5.60 thf(fact_7984_left__inverse,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.27/5.60 = one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % left_inverse
% 5.27/5.60 thf(fact_7985_inverse__eq__divide__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( inverse_inverse_rat @ ( numeral_numeral_rat @ W ) )
% 5.27/5.60 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_numeral
% 5.27/5.60 thf(fact_7986_inverse__eq__divide__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( numeral_numeral_real @ W ) )
% 5.27/5.60 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_numeral
% 5.27/5.60 thf(fact_7987_inverse__eq__divide__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.27/5.60 = ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_numeral
% 5.27/5.60 thf(fact_7988_inverse__eq__divide__neg__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.27/5.60 = ( divide_divide_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_neg_numeral
% 5.27/5.60 thf(fact_7989_inverse__eq__divide__neg__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( inverse_inverse_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.27/5.60 = ( divide_divide_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_neg_numeral
% 5.27/5.60 thf(fact_7990_inverse__eq__divide__neg__numeral,axiom,
% 5.27/5.60 ! [W: num] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.60 = ( divide1717551699836669952omplex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide_neg_numeral
% 5.27/5.60 thf(fact_7991_exp__two__pi__i_H,axiom,
% 5.27/5.60 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % exp_two_pi_i'
% 5.27/5.60 thf(fact_7992_exp__two__pi__i,axiom,
% 5.27/5.60 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % exp_two_pi_i
% 5.27/5.60 thf(fact_7993_cis__pi__half,axiom,
% 5.27/5.60 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = imaginary_unit ) ).
% 5.27/5.60
% 5.27/5.60 % cis_pi_half
% 5.27/5.60 thf(fact_7994_power2__i,axiom,
% 5.27/5.60 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % power2_i
% 5.27/5.60 thf(fact_7995_cis__minus__pi__half,axiom,
% 5.27/5.60 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.27/5.60
% 5.27/5.60 % cis_minus_pi_half
% 5.27/5.60 thf(fact_7996_mult__commute__imp__mult__inverse__commute,axiom,
% 5.27/5.60 ! [Y: real,X4: real] :
% 5.27/5.60 ( ( ( times_times_real @ Y @ X4 )
% 5.27/5.60 = ( times_times_real @ X4 @ Y ) )
% 5.27/5.60 => ( ( times_times_real @ ( inverse_inverse_real @ Y ) @ X4 )
% 5.27/5.60 = ( times_times_real @ X4 @ ( inverse_inverse_real @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_commute_imp_mult_inverse_commute
% 5.27/5.60 thf(fact_7997_mult__commute__imp__mult__inverse__commute,axiom,
% 5.27/5.60 ! [Y: complex,X4: complex] :
% 5.27/5.60 ( ( ( times_times_complex @ Y @ X4 )
% 5.27/5.60 = ( times_times_complex @ X4 @ Y ) )
% 5.27/5.60 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ Y ) @ X4 )
% 5.27/5.60 = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_commute_imp_mult_inverse_commute
% 5.27/5.60 thf(fact_7998_power__inverse,axiom,
% 5.27/5.60 ! [A: real,N2: nat] :
% 5.27/5.60 ( ( power_power_real @ ( inverse_inverse_real @ A ) @ N2 )
% 5.27/5.60 = ( inverse_inverse_real @ ( power_power_real @ A @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_inverse
% 5.27/5.60 thf(fact_7999_power__inverse,axiom,
% 5.27/5.60 ! [A: complex,N2: nat] :
% 5.27/5.60 ( ( power_power_complex @ ( invers8013647133539491842omplex @ A ) @ N2 )
% 5.27/5.60 = ( invers8013647133539491842omplex @ ( power_power_complex @ A @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_inverse
% 5.27/5.60 thf(fact_8000_inverse__eq__imp__eq,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ A )
% 5.27/5.60 = ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( A = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_imp_eq
% 5.27/5.60 thf(fact_8001_inverse__eq__imp__eq,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 => ( A = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_imp_eq
% 5.27/5.60 thf(fact_8002_field__class_Ofield__inverse__zero,axiom,
% 5.27/5.60 ( ( inverse_inverse_rat @ zero_zero_rat )
% 5.27/5.60 = zero_zero_rat ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse_zero
% 5.27/5.60 thf(fact_8003_field__class_Ofield__inverse__zero,axiom,
% 5.27/5.60 ( ( inverse_inverse_real @ zero_zero_real )
% 5.27/5.60 = zero_zero_real ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse_zero
% 5.27/5.60 thf(fact_8004_field__class_Ofield__inverse__zero,axiom,
% 5.27/5.60 ( ( invers8013647133539491842omplex @ zero_zero_complex )
% 5.27/5.60 = zero_zero_complex ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse_zero
% 5.27/5.60 thf(fact_8005_inverse__zero__imp__zero,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ( inverse_inverse_rat @ A )
% 5.27/5.60 = zero_zero_rat )
% 5.27/5.60 => ( A = zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero_imp_zero
% 5.27/5.60 thf(fact_8006_inverse__zero__imp__zero,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ A )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 => ( A = zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero_imp_zero
% 5.27/5.60 thf(fact_8007_inverse__zero__imp__zero,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = zero_zero_complex )
% 5.27/5.60 => ( A = zero_zero_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_zero_imp_zero
% 5.27/5.60 thf(fact_8008_nonzero__inverse__eq__imp__eq,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ( inverse_inverse_rat @ A )
% 5.27/5.60 = ( inverse_inverse_rat @ B ) )
% 5.27/5.60 => ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( A = B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_imp_eq
% 5.27/5.60 thf(fact_8009_nonzero__inverse__eq__imp__eq,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ( inverse_inverse_real @ A )
% 5.27/5.60 = ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( A = B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_imp_eq
% 5.27/5.60 thf(fact_8010_nonzero__inverse__eq__imp__eq,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 => ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( A = B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_imp_eq
% 5.27/5.60 thf(fact_8011_nonzero__inverse__inverse__eq,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = A ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_inverse_eq
% 5.27/5.60 thf(fact_8012_nonzero__inverse__inverse__eq,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = A ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_inverse_eq
% 5.27/5.60 thf(fact_8013_nonzero__inverse__inverse__eq,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ ( invers8013647133539491842omplex @ A ) )
% 5.27/5.60 = A ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_inverse_eq
% 5.27/5.60 thf(fact_8014_nonzero__imp__inverse__nonzero,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ A )
% 5.27/5.60 != zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_imp_inverse_nonzero
% 5.27/5.60 thf(fact_8015_nonzero__imp__inverse__nonzero,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ A )
% 5.27/5.60 != zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_imp_inverse_nonzero
% 5.27/5.60 thf(fact_8016_nonzero__imp__inverse__nonzero,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 != zero_zero_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_imp_inverse_nonzero
% 5.27/5.60 thf(fact_8017_norm__inverse__le__norm,axiom,
% 5.27/5.60 ! [R3: real,X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ R3 @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.27/5.60 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( inverse_inverse_real @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % norm_inverse_le_norm
% 5.27/5.60 thf(fact_8018_norm__inverse__le__norm,axiom,
% 5.27/5.60 ! [R3: real,X4: complex] :
% 5.27/5.60 ( ( ord_less_eq_real @ R3 @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.27/5.60 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( invers8013647133539491842omplex @ X4 ) ) @ ( inverse_inverse_real @ R3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % norm_inverse_le_norm
% 5.27/5.60 thf(fact_8019_positive__imp__inverse__positive,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % positive_imp_inverse_positive
% 5.27/5.60 thf(fact_8020_positive__imp__inverse__positive,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % positive_imp_inverse_positive
% 5.27/5.60 thf(fact_8021_negative__imp__inverse__negative,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % negative_imp_inverse_negative
% 5.27/5.60 thf(fact_8022_negative__imp__inverse__negative,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % negative_imp_inverse_negative
% 5.27/5.60 thf(fact_8023_inverse__positive__imp__positive,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 => ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_positive_imp_positive
% 5.27/5.60 thf(fact_8024_inverse__positive__imp__positive,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 => ( ( A != zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ zero_zero_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_positive_imp_positive
% 5.27/5.60 thf(fact_8025_inverse__negative__imp__negative,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ zero_zero_rat )
% 5.27/5.60 => ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_negative_imp_negative
% 5.27/5.60 thf(fact_8026_inverse__negative__imp__negative,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ zero_zero_real )
% 5.27/5.60 => ( ( A != zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_negative_imp_negative
% 5.27/5.60 thf(fact_8027_less__imp__inverse__less__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ A @ B )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_imp_inverse_less_neg
% 5.27/5.60 thf(fact_8028_less__imp__inverse__less__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ A @ B )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_imp_inverse_less_neg
% 5.27/5.60 thf(fact_8029_inverse__less__imp__less__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_imp_less_neg
% 5.27/5.60 thf(fact_8030_inverse__less__imp__less__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_imp_less_neg
% 5.27/5.60 thf(fact_8031_less__imp__inverse__less,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ A @ B )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ord_less_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_imp_inverse_less
% 5.27/5.60 thf(fact_8032_less__imp__inverse__less,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ A @ B )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ord_less_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_imp_inverse_less
% 5.27/5.60 thf(fact_8033_inverse__less__imp__less,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ord_less_rat @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_imp_less
% 5.27/5.60 thf(fact_8034_inverse__less__imp__less,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ord_less_real @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_imp_less
% 5.27/5.60 thf(fact_8035_nonzero__inverse__mult__distrib,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.60 = ( times_times_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_mult_distrib
% 5.27/5.60 thf(fact_8036_nonzero__inverse__mult__distrib,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ ( times_times_real @ A @ B ) )
% 5.27/5.60 = ( times_times_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_mult_distrib
% 5.27/5.60 thf(fact_8037_nonzero__inverse__mult__distrib,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ ( times_times_complex @ A @ B ) )
% 5.27/5.60 = ( times_times_complex @ ( invers8013647133539491842omplex @ B ) @ ( invers8013647133539491842omplex @ A ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_mult_distrib
% 5.27/5.60 thf(fact_8038_nonzero__inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ ( uminus_uminus_rat @ A ) )
% 5.27/5.60 = ( uminus_uminus_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_minus_eq
% 5.27/5.60 thf(fact_8039_nonzero__inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ ( uminus_uminus_real @ A ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_minus_eq
% 5.27/5.60 thf(fact_8040_nonzero__inverse__minus__eq,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ ( invers8013647133539491842omplex @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_minus_eq
% 5.27/5.60 thf(fact_8041_inverse__unique,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ( times_times_rat @ A @ B )
% 5.27/5.60 = one_one_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ A )
% 5.27/5.60 = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_unique
% 5.27/5.60 thf(fact_8042_inverse__unique,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ( times_times_real @ A @ B )
% 5.27/5.60 = one_one_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ A )
% 5.27/5.60 = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_unique
% 5.27/5.60 thf(fact_8043_inverse__unique,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ( times_times_complex @ A @ B )
% 5.27/5.60 = one_one_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = B ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_unique
% 5.27/5.60 thf(fact_8044_inverse__numeral__1,axiom,
% 5.27/5.60 ( ( inverse_inverse_real @ ( numeral_numeral_real @ one ) )
% 5.27/5.60 = ( numeral_numeral_real @ one ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_numeral_1
% 5.27/5.60 thf(fact_8045_inverse__numeral__1,axiom,
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.27/5.60 = ( numera6690914467698888265omplex @ one ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_numeral_1
% 5.27/5.60 thf(fact_8046_divide__inverse__commute,axiom,
% 5.27/5.60 ( divide_divide_real
% 5.27/5.60 = ( ^ [A3: real,B2: real] : ( times_times_real @ ( inverse_inverse_real @ B2 ) @ A3 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % divide_inverse_commute
% 5.27/5.60 thf(fact_8047_divide__inverse__commute,axiom,
% 5.27/5.60 ( divide1717551699836669952omplex
% 5.27/5.60 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ ( invers8013647133539491842omplex @ B2 ) @ A3 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % divide_inverse_commute
% 5.27/5.60 thf(fact_8048_divide__inverse,axiom,
% 5.27/5.60 ( divide_divide_real
% 5.27/5.60 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % divide_inverse
% 5.27/5.60 thf(fact_8049_divide__inverse,axiom,
% 5.27/5.60 ( divide1717551699836669952omplex
% 5.27/5.60 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % divide_inverse
% 5.27/5.60 thf(fact_8050_field__class_Ofield__divide__inverse,axiom,
% 5.27/5.60 ( divide_divide_real
% 5.27/5.60 = ( ^ [A3: real,B2: real] : ( times_times_real @ A3 @ ( inverse_inverse_real @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_divide_inverse
% 5.27/5.60 thf(fact_8051_field__class_Ofield__divide__inverse,axiom,
% 5.27/5.60 ( divide1717551699836669952omplex
% 5.27/5.60 = ( ^ [A3: complex,B2: complex] : ( times_times_complex @ A3 @ ( invers8013647133539491842omplex @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_divide_inverse
% 5.27/5.60 thf(fact_8052_inverse__eq__divide,axiom,
% 5.27/5.60 ( inverse_inverse_rat
% 5.27/5.60 = ( divide_divide_rat @ one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide
% 5.27/5.60 thf(fact_8053_inverse__eq__divide,axiom,
% 5.27/5.60 ( inverse_inverse_real
% 5.27/5.60 = ( divide_divide_real @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide
% 5.27/5.60 thf(fact_8054_inverse__eq__divide,axiom,
% 5.27/5.60 ( invers8013647133539491842omplex
% 5.27/5.60 = ( divide1717551699836669952omplex @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_eq_divide
% 5.27/5.60 thf(fact_8055_power__mult__inverse__distrib,axiom,
% 5.27/5.60 ! [X4: real,M: nat] :
% 5.27/5.60 ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( inverse_inverse_real @ X4 ) )
% 5.27/5.60 = ( times_times_real @ ( inverse_inverse_real @ X4 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_mult_inverse_distrib
% 5.27/5.60 thf(fact_8056_power__mult__inverse__distrib,axiom,
% 5.27/5.60 ! [X4: complex,M: nat] :
% 5.27/5.60 ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( invers8013647133539491842omplex @ X4 ) )
% 5.27/5.60 = ( times_times_complex @ ( invers8013647133539491842omplex @ X4 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_mult_inverse_distrib
% 5.27/5.60 thf(fact_8057_power__mult__power__inverse__commute,axiom,
% 5.27/5.60 ! [X4: real,M: nat,N2: nat] :
% 5.27/5.60 ( ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) )
% 5.27/5.60 = ( times_times_real @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ N2 ) @ ( power_power_real @ X4 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_mult_power_inverse_commute
% 5.27/5.60 thf(fact_8058_power__mult__power__inverse__commute,axiom,
% 5.27/5.60 ! [X4: complex,M: nat,N2: nat] :
% 5.27/5.60 ( ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) )
% 5.27/5.60 = ( times_times_complex @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ N2 ) @ ( power_power_complex @ X4 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_mult_power_inverse_commute
% 5.27/5.60 thf(fact_8059_mult__inverse__of__nat__commute,axiom,
% 5.27/5.60 ! [Xa: nat,X4: real] :
% 5.27/5.60 ( ( times_times_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) @ X4 )
% 5.27/5.60 = ( times_times_real @ X4 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ Xa ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_inverse_of_nat_commute
% 5.27/5.60 thf(fact_8060_mult__inverse__of__nat__commute,axiom,
% 5.27/5.60 ! [Xa: nat,X4: complex] :
% 5.27/5.60 ( ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) @ X4 )
% 5.27/5.60 = ( times_times_complex @ X4 @ ( invers8013647133539491842omplex @ ( semiri8010041392384452111omplex @ Xa ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_inverse_of_nat_commute
% 5.27/5.60 thf(fact_8061_nonzero__abs__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( abs_abs_rat @ ( inverse_inverse_rat @ A ) )
% 5.27/5.60 = ( inverse_inverse_rat @ ( abs_abs_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_abs_inverse
% 5.27/5.60 thf(fact_8062_nonzero__abs__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( abs_abs_real @ ( inverse_inverse_real @ A ) )
% 5.27/5.60 = ( inverse_inverse_real @ ( abs_abs_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_abs_inverse
% 5.27/5.60 thf(fact_8063_divide__real__def,axiom,
% 5.27/5.60 ( divide_divide_real
% 5.27/5.60 = ( ^ [X: real,Y5: real] : ( times_times_real @ X @ ( inverse_inverse_real @ Y5 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % divide_real_def
% 5.27/5.60 thf(fact_8064_frac__ge__0,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_ge_0
% 5.27/5.60 thf(fact_8065_frac__ge__0,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_ge_0
% 5.27/5.60 thf(fact_8066_frac__lt__1,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_real @ ( archim2898591450579166408c_real @ X4 ) @ one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % frac_lt_1
% 5.27/5.60 thf(fact_8067_frac__lt__1,axiom,
% 5.27/5.60 ! [X4: rat] : ( ord_less_rat @ ( archimedean_frac_rat @ X4 ) @ one_one_rat ) ).
% 5.27/5.60
% 5.27/5.60 % frac_lt_1
% 5.27/5.60 thf(fact_8068_frac__1__eq,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ one_one_real ) )
% 5.27/5.60 = ( archim2898591450579166408c_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_1_eq
% 5.27/5.60 thf(fact_8069_frac__1__eq,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ one_one_rat ) )
% 5.27/5.60 = ( archimedean_frac_rat @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_1_eq
% 5.27/5.60 thf(fact_8070_le__imp__inverse__le__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_imp_inverse_le_neg
% 5.27/5.60 thf(fact_8071_le__imp__inverse__le__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_imp_inverse_le_neg
% 5.27/5.60 thf(fact_8072_inverse__le__imp__le__neg,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_imp_le_neg
% 5.27/5.60 thf(fact_8073_inverse__le__imp__le__neg,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.27/5.60 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_imp_le_neg
% 5.27/5.60 thf(fact_8074_le__imp__inverse__le,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ A @ B )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ord_less_eq_rat @ ( inverse_inverse_rat @ B ) @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_imp_inverse_le
% 5.27/5.60 thf(fact_8075_le__imp__inverse__le,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ord_less_eq_real @ ( inverse_inverse_real @ B ) @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_imp_inverse_le
% 5.27/5.60 thf(fact_8076_inverse__le__imp__le,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_imp_le
% 5.27/5.60 thf(fact_8077_inverse__le__imp__le,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_imp_le
% 5.27/5.60 thf(fact_8078_inverse__le__1__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 5.27/5.60 = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.27/5.60 | ( ord_less_eq_rat @ one_one_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_1_iff
% 5.27/5.60 thf(fact_8079_inverse__le__1__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 5.27/5.60 = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.60 | ( ord_less_eq_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_1_iff
% 5.27/5.60 thf(fact_8080_one__less__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.27/5.60 => ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_less_inverse
% 5.27/5.60 thf(fact_8081_one__less__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( ord_less_real @ A @ one_one_real )
% 5.27/5.60 => ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_less_inverse
% 5.27/5.60 thf(fact_8082_one__less__inverse__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 5.27/5.60 = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.60 & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_less_inverse_iff
% 5.27/5.60 thf(fact_8083_one__less__inverse__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 5.27/5.60 = ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_less_inverse_iff
% 5.27/5.60 thf(fact_8084_field__class_Ofield__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( times_times_rat @ ( inverse_inverse_rat @ A ) @ A )
% 5.27/5.60 = one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse
% 5.27/5.60 thf(fact_8085_field__class_Ofield__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( times_times_real @ ( inverse_inverse_real @ A ) @ A )
% 5.27/5.60 = one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse
% 5.27/5.60 thf(fact_8086_field__class_Ofield__inverse,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ A )
% 5.27/5.60 = one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % field_class.field_inverse
% 5.27/5.60 thf(fact_8087_division__ring__inverse__add,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( plus_plus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_add
% 5.27/5.60 thf(fact_8088_division__ring__inverse__add,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( plus_plus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_add
% 5.27/5.60 thf(fact_8089_division__ring__inverse__add,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( plus_plus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_add
% 5.27/5.60 thf(fact_8090_inverse__add,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( ( plus_plus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( times_times_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( inverse_inverse_rat @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_add
% 5.27/5.60 thf(fact_8091_inverse__add,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( ( plus_plus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( times_times_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( inverse_inverse_real @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_add
% 5.27/5.60 thf(fact_8092_inverse__add,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( ( plus_plus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 = ( times_times_complex @ ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( invers8013647133539491842omplex @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_add
% 5.27/5.60 thf(fact_8093_division__ring__inverse__diff,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ B @ A ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_diff
% 5.27/5.60 thf(fact_8094_division__ring__inverse__diff,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ B @ A ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_diff
% 5.27/5.60 thf(fact_8095_division__ring__inverse__diff,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 = ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ B @ A ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % division_ring_inverse_diff
% 5.27/5.60 thf(fact_8096_nonzero__inverse__eq__divide,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( inverse_inverse_rat @ A )
% 5.27/5.60 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_divide
% 5.27/5.60 thf(fact_8097_nonzero__inverse__eq__divide,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( inverse_inverse_real @ A )
% 5.27/5.60 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_divide
% 5.27/5.60 thf(fact_8098_nonzero__inverse__eq__divide,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( invers8013647133539491842omplex @ A )
% 5.27/5.60 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nonzero_inverse_eq_divide
% 5.27/5.60 thf(fact_8099_gbinomial__Suc__Suc,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_Suc_Suc
% 5.27/5.60 thf(fact_8100_gbinomial__Suc__Suc,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ A @ ( suc @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_Suc_Suc
% 5.27/5.60 thf(fact_8101_gbinomial__Suc__Suc,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_Suc_Suc
% 5.27/5.60 thf(fact_8102_gbinomial__of__nat__symmetric,axiom,
% 5.27/5.60 ! [K: nat,N2: nat] :
% 5.27/5.60 ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.60 => ( ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ K )
% 5.27/5.60 = ( gbinomial_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( minus_minus_nat @ N2 @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_of_nat_symmetric
% 5.27/5.60 thf(fact_8103_inverse__powr,axiom,
% 5.27/5.60 ! [Y: real,A: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.60 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.27/5.60 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_powr
% 5.27/5.60 thf(fact_8104_Complex__eq__i,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ( complex2 @ X4 @ Y )
% 5.27/5.60 = imaginary_unit )
% 5.27/5.60 = ( ( X4 = zero_zero_real )
% 5.27/5.60 & ( Y = one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Complex_eq_i
% 5.27/5.60 thf(fact_8105_imaginary__unit_Ocode,axiom,
% 5.27/5.60 ( imaginary_unit
% 5.27/5.60 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % imaginary_unit.code
% 5.27/5.60 thf(fact_8106_inverse__le__iff,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.60 => ( ord_less_eq_rat @ B @ A ) )
% 5.27/5.60 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff
% 5.27/5.60 thf(fact_8107_inverse__le__iff,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.27/5.60 => ( ord_less_eq_real @ B @ A ) )
% 5.27/5.60 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.27/5.60 => ( ord_less_eq_real @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_le_iff
% 5.27/5.60 thf(fact_8108_inverse__less__iff,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.27/5.60 => ( ord_less_rat @ B @ A ) )
% 5.27/5.60 & ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.27/5.60 => ( ord_less_rat @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff
% 5.27/5.60 thf(fact_8109_inverse__less__iff,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.27/5.60 => ( ord_less_real @ B @ A ) )
% 5.27/5.60 & ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.27/5.60 => ( ord_less_real @ A @ B ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_iff
% 5.27/5.60 thf(fact_8110_one__le__inverse,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_le_inverse
% 5.27/5.60 thf(fact_8111_one__le__inverse,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.27/5.60 => ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ A ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_le_inverse
% 5.27/5.60 thf(fact_8112_inverse__less__1__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ ( inverse_inverse_rat @ X4 ) @ one_one_rat )
% 5.27/5.60 = ( ( ord_less_eq_rat @ X4 @ zero_zero_rat )
% 5.27/5.60 | ( ord_less_rat @ one_one_rat @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_1_iff
% 5.27/5.60 thf(fact_8113_inverse__less__1__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( inverse_inverse_real @ X4 ) @ one_one_real )
% 5.27/5.60 = ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.60 | ( ord_less_real @ one_one_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_less_1_iff
% 5.27/5.60 thf(fact_8114_one__le__inverse__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ one_one_rat @ ( inverse_inverse_rat @ X4 ) )
% 5.27/5.60 = ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.60 & ( ord_less_eq_rat @ X4 @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_le_inverse_iff
% 5.27/5.60 thf(fact_8115_one__le__inverse__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ one_one_real @ ( inverse_inverse_real @ X4 ) )
% 5.27/5.60 = ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 & ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % one_le_inverse_iff
% 5.27/5.60 thf(fact_8116_inverse__diff__inverse,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( A != zero_zero_rat )
% 5.27/5.60 => ( ( B != zero_zero_rat )
% 5.27/5.60 => ( ( minus_minus_rat @ ( inverse_inverse_rat @ A ) @ ( inverse_inverse_rat @ B ) )
% 5.27/5.60 = ( uminus_uminus_rat @ ( times_times_rat @ ( times_times_rat @ ( inverse_inverse_rat @ A ) @ ( minus_minus_rat @ A @ B ) ) @ ( inverse_inverse_rat @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_diff_inverse
% 5.27/5.60 thf(fact_8117_inverse__diff__inverse,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( A != zero_zero_real )
% 5.27/5.60 => ( ( B != zero_zero_real )
% 5.27/5.60 => ( ( minus_minus_real @ ( inverse_inverse_real @ A ) @ ( inverse_inverse_real @ B ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( inverse_inverse_real @ A ) @ ( minus_minus_real @ A @ B ) ) @ ( inverse_inverse_real @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_diff_inverse
% 5.27/5.60 thf(fact_8118_inverse__diff__inverse,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( A != zero_zero_complex )
% 5.27/5.60 => ( ( B != zero_zero_complex )
% 5.27/5.60 => ( ( minus_minus_complex @ ( invers8013647133539491842omplex @ A ) @ ( invers8013647133539491842omplex @ B ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ ( times_times_complex @ ( times_times_complex @ ( invers8013647133539491842omplex @ A ) @ ( minus_minus_complex @ A @ B ) ) @ ( invers8013647133539491842omplex @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % inverse_diff_inverse
% 5.27/5.60 thf(fact_8119_reals__Archimedean,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.60 => ? [N3: nat] : ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % reals_Archimedean
% 5.27/5.60 thf(fact_8120_reals__Archimedean,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ? [N3: nat] : ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % reals_Archimedean
% 5.27/5.60 thf(fact_8121_gbinomial__addition__formula,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ A @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_complex @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_addition_formula
% 5.27/5.60 thf(fact_8122_gbinomial__addition__formula,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ A @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_real @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ ( suc @ K ) ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_addition_formula
% 5.27/5.60 thf(fact_8123_gbinomial__addition__formula,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ A @ ( suc @ K ) )
% 5.27/5.60 = ( plus_plus_rat @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_addition_formula
% 5.27/5.60 thf(fact_8124_gbinomial__absorb__comp,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( times_times_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( gbinomial_rat @ A @ K ) )
% 5.27/5.60 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorb_comp
% 5.27/5.60 thf(fact_8125_gbinomial__absorb__comp,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( times_times_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( gbinomial_complex @ A @ K ) )
% 5.27/5.60 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorb_comp
% 5.27/5.60 thf(fact_8126_gbinomial__absorb__comp,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( times_times_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( gbinomial_real @ A @ K ) )
% 5.27/5.60 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorb_comp
% 5.27/5.60 thf(fact_8127_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.27/5.60 ! [K: nat,A: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ K ) @ A )
% 5.27/5.60 => ( ord_less_eq_real @ ( power_power_real @ ( divide_divide_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ K ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_ge_n_over_k_pow_k
% 5.27/5.60 thf(fact_8128_gbinomial__ge__n__over__k__pow__k,axiom,
% 5.27/5.60 ! [K: nat,A: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ K ) @ A )
% 5.27/5.60 => ( ord_less_eq_rat @ ( power_power_rat @ ( divide_divide_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ K ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_ge_n_over_k_pow_k
% 5.27/5.60 thf(fact_8129_gbinomial__mult__1,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( times_times_rat @ A @ ( gbinomial_rat @ A @ K ) )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1
% 5.27/5.60 thf(fact_8130_gbinomial__mult__1,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( times_times_complex @ A @ ( gbinomial_complex @ A @ K ) )
% 5.27/5.60 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1
% 5.27/5.60 thf(fact_8131_gbinomial__mult__1,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( times_times_real @ A @ ( gbinomial_real @ A @ K ) )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1
% 5.27/5.60 thf(fact_8132_gbinomial__mult__1_H,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ A )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1'
% 5.27/5.60 thf(fact_8133_gbinomial__mult__1_H,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ A )
% 5.27/5.60 = ( plus_plus_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ K ) @ ( gbinomial_complex @ A @ K ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1'
% 5.27/5.60 thf(fact_8134_gbinomial__mult__1_H,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( times_times_real @ ( gbinomial_real @ A @ K ) @ A )
% 5.27/5.60 = ( 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 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_mult_1'
% 5.27/5.60 thf(fact_8135_forall__pos__mono__1,axiom,
% 5.27/5.60 ! [P: real > $o,E2: real] :
% 5.27/5.60 ( ! [D3: real,E: real] :
% 5.27/5.60 ( ( ord_less_real @ D3 @ E )
% 5.27/5.60 => ( ( P @ D3 )
% 5.27/5.60 => ( P @ E ) ) )
% 5.27/5.60 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.60 => ( P @ E2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % forall_pos_mono_1
% 5.27/5.60 thf(fact_8136_forall__pos__mono,axiom,
% 5.27/5.60 ! [P: real > $o,E2: real] :
% 5.27/5.60 ( ! [D3: real,E: real] :
% 5.27/5.60 ( ( ord_less_real @ D3 @ E )
% 5.27/5.60 => ( ( P @ D3 )
% 5.27/5.60 => ( P @ E ) ) )
% 5.27/5.60 => ( ! [N3: nat] :
% 5.27/5.60 ( ( N3 != zero_zero_nat )
% 5.27/5.60 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.60 => ( P @ E2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % forall_pos_mono
% 5.27/5.60 thf(fact_8137_real__arch__inverse,axiom,
% 5.27/5.60 ! [E2: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.60 = ( ? [N: nat] :
% 5.27/5.60 ( ( N != zero_zero_nat )
% 5.27/5.60 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.27/5.60 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N ) ) @ E2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_arch_inverse
% 5.27/5.60 thf(fact_8138_sqrt__divide__self__eq,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( divide_divide_real @ ( sqrt @ X4 ) @ X4 )
% 5.27/5.60 = ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sqrt_divide_self_eq
% 5.27/5.60 thf(fact_8139_ln__inverse,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ln_ln_real @ ( inverse_inverse_real @ X4 ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( ln_ln_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ln_inverse
% 5.27/5.60 thf(fact_8140_ex__inverse__of__nat__less,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ X4 )
% 5.27/5.60 => ? [N3: nat] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.60 & ( ord_less_rat @ ( inverse_inverse_rat @ ( semiri681578069525770553at_rat @ N3 ) ) @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ex_inverse_of_nat_less
% 5.27/5.60 thf(fact_8141_ex__inverse__of__nat__less,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ? [N3: nat] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.27/5.60 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % ex_inverse_of_nat_less
% 5.27/5.60 thf(fact_8142_power__diff__conv__inverse,axiom,
% 5.27/5.60 ! [X4: rat,M: nat,N2: nat] :
% 5.27/5.60 ( ( X4 != zero_zero_rat )
% 5.27/5.60 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.60 => ( ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.60 = ( times_times_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ ( inverse_inverse_rat @ X4 ) @ M ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_diff_conv_inverse
% 5.27/5.60 thf(fact_8143_power__diff__conv__inverse,axiom,
% 5.27/5.60 ! [X4: real,M: nat,N2: nat] :
% 5.27/5.60 ( ( X4 != zero_zero_real )
% 5.27/5.60 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.60 => ( ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.60 = ( times_times_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ ( inverse_inverse_real @ X4 ) @ M ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_diff_conv_inverse
% 5.27/5.60 thf(fact_8144_power__diff__conv__inverse,axiom,
% 5.27/5.60 ! [X4: complex,M: nat,N2: nat] :
% 5.27/5.60 ( ( X4 != zero_zero_complex )
% 5.27/5.60 => ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.60 => ( ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ M ) )
% 5.27/5.60 = ( times_times_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ ( invers8013647133539491842omplex @ X4 ) @ M ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_diff_conv_inverse
% 5.27/5.60 thf(fact_8145_Suc__times__gbinomial,axiom,
% 5.27/5.60 ! [K: nat,A: rat] :
% 5.27/5.60 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Suc_times_gbinomial
% 5.27/5.60 thf(fact_8146_Suc__times__gbinomial,axiom,
% 5.27/5.60 ! [K: nat,A: complex] :
% 5.27/5.60 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Suc_times_gbinomial
% 5.27/5.60 thf(fact_8147_Suc__times__gbinomial,axiom,
% 5.27/5.60 ! [K: nat,A: real] :
% 5.27/5.60 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_real @ ( plus_plus_real @ A @ one_one_real ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Suc_times_gbinomial
% 5.27/5.60 thf(fact_8148_gbinomial__absorption,axiom,
% 5.27/5.60 ! [K: nat,A: rat] :
% 5.27/5.60 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) @ ( gbinomial_rat @ A @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_rat @ A @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption
% 5.27/5.60 thf(fact_8149_gbinomial__absorption,axiom,
% 5.27/5.60 ! [K: nat,A: complex] :
% 5.27/5.60 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) @ ( gbinomial_complex @ A @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_complex @ A @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption
% 5.27/5.60 thf(fact_8150_gbinomial__absorption,axiom,
% 5.27/5.60 ! [K: nat,A: real] :
% 5.27/5.60 ( ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) @ ( gbinomial_real @ A @ ( suc @ K ) ) )
% 5.27/5.60 = ( times_times_real @ A @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_absorption
% 5.27/5.60 thf(fact_8151_gbinomial__trinomial__revision,axiom,
% 5.27/5.60 ! [K: nat,M: nat,A: rat] :
% 5.27/5.60 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.60 => ( ( times_times_rat @ ( gbinomial_rat @ A @ M ) @ ( gbinomial_rat @ ( semiri681578069525770553at_rat @ M ) @ K ) )
% 5.27/5.60 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ ( semiri681578069525770553at_rat @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_trinomial_revision
% 5.27/5.60 thf(fact_8152_gbinomial__trinomial__revision,axiom,
% 5.27/5.60 ! [K: nat,M: nat,A: complex] :
% 5.27/5.60 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.60 => ( ( times_times_complex @ ( gbinomial_complex @ A @ M ) @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ M ) @ K ) )
% 5.27/5.60 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ ( semiri8010041392384452111omplex @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_trinomial_revision
% 5.27/5.60 thf(fact_8153_gbinomial__trinomial__revision,axiom,
% 5.27/5.60 ! [K: nat,M: nat,A: real] :
% 5.27/5.60 ( ( ord_less_eq_nat @ K @ M )
% 5.27/5.60 => ( ( times_times_real @ ( gbinomial_real @ A @ M ) @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ M ) @ K ) )
% 5.27/5.60 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( gbinomial_real @ ( minus_minus_real @ A @ ( semiri5074537144036343181t_real @ K ) ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_trinomial_revision
% 5.27/5.60 thf(fact_8154_log__inverse,axiom,
% 5.27/5.60 ! [A: real,X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( A != one_one_real )
% 5.27/5.60 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( log @ A @ ( inverse_inverse_real @ X4 ) )
% 5.27/5.60 = ( uminus_uminus_real @ ( log @ A @ X4 ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % log_inverse
% 5.27/5.60 thf(fact_8155_frac__eq,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( archim2898591450579166408c_real @ X4 )
% 5.27/5.60 = X4 )
% 5.27/5.60 = ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 & ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_eq
% 5.27/5.60 thf(fact_8156_frac__eq,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ( archimedean_frac_rat @ X4 )
% 5.27/5.60 = X4 )
% 5.27/5.60 = ( ( ord_less_eq_rat @ zero_zero_rat @ X4 )
% 5.27/5.60 & ( ord_less_rat @ X4 @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_eq
% 5.27/5.60 thf(fact_8157_frac__add,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.27/5.60 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.27/5.60 => ( ( archim2898591450579166408c_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( minus_minus_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_add
% 5.27/5.60 thf(fact_8158_frac__add,axiom,
% 5.27/5.60 ! [X4: rat,Y: rat] :
% 5.27/5.60 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.27/5.60 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.27/5.60 => ( ( archimedean_frac_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 5.27/5.60 = ( minus_minus_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_add
% 5.27/5.60 thf(fact_8159_gbinomial__rec,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_rat @ ( gbinomial_rat @ A @ K ) @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_rec
% 5.27/5.60 thf(fact_8160_gbinomial__rec,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_complex @ ( gbinomial_complex @ A @ K ) @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_rec
% 5.27/5.60 thf(fact_8161_gbinomial__rec,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_real @ ( gbinomial_real @ A @ K ) @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_rec
% 5.27/5.60 thf(fact_8162_gbinomial__factors,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( semiri681578069525770553at_rat @ ( suc @ K ) ) ) @ ( gbinomial_rat @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_factors
% 5.27/5.60 thf(fact_8163_gbinomial__factors,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ one_one_complex ) @ ( semiri8010041392384452111omplex @ ( suc @ K ) ) ) @ ( gbinomial_complex @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_factors
% 5.27/5.60 thf(fact_8164_gbinomial__factors,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ ( plus_plus_real @ A @ one_one_real ) @ ( suc @ K ) )
% 5.27/5.60 = ( times_times_real @ ( divide_divide_real @ ( plus_plus_real @ A @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( suc @ K ) ) ) @ ( gbinomial_real @ A @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_factors
% 5.27/5.60 thf(fact_8165_gbinomial__negated__upper,axiom,
% 5.27/5.60 ( gbinomial_complex
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_negated_upper
% 5.27/5.60 thf(fact_8166_gbinomial__negated__upper,axiom,
% 5.27/5.60 ( gbinomial_rat
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_negated_upper
% 5.27/5.60 thf(fact_8167_gbinomial__negated__upper,axiom,
% 5.27/5.60 ( gbinomial_real
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_negated_upper
% 5.27/5.60 thf(fact_8168_gbinomial__index__swap,axiom,
% 5.27/5.60 ! [K: nat,N2: nat] :
% 5.27/5.60 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ K ) )
% 5.27/5.60 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N2 ) @ ( gbinomial_complex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( semiri8010041392384452111omplex @ K ) ) @ one_one_complex ) @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_index_swap
% 5.27/5.60 thf(fact_8169_gbinomial__index__swap,axiom,
% 5.27/5.60 ! [K: nat,N2: nat] :
% 5.27/5.60 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ K ) )
% 5.27/5.60 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N2 ) @ ( gbinomial_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ ( semiri681578069525770553at_rat @ K ) ) @ one_one_rat ) @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_index_swap
% 5.27/5.60 thf(fact_8170_gbinomial__index__swap,axiom,
% 5.27/5.60 ! [K: nat,N2: nat] :
% 5.27/5.60 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ K ) )
% 5.27/5.60 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( gbinomial_real @ ( minus_minus_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ K ) ) @ one_one_real ) @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_index_swap
% 5.27/5.60 thf(fact_8171_exp__plus__inverse__exp,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % exp_plus_inverse_exp
% 5.27/5.60 thf(fact_8172_cmod__unit__one,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % cmod_unit_one
% 5.27/5.60 thf(fact_8173_gbinomial__minus,axiom,
% 5.27/5.60 ! [A: complex,K: nat] :
% 5.27/5.60 ( ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K )
% 5.27/5.60 = ( 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 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_minus
% 5.27/5.60 thf(fact_8174_gbinomial__minus,axiom,
% 5.27/5.60 ! [A: rat,K: nat] :
% 5.27/5.60 ( ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K )
% 5.27/5.60 = ( 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 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_minus
% 5.27/5.60 thf(fact_8175_gbinomial__minus,axiom,
% 5.27/5.60 ! [A: real,K: nat] :
% 5.27/5.60 ( ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K )
% 5.27/5.60 = ( 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 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_minus
% 5.27/5.60 thf(fact_8176_plus__inverse__ge__2,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % plus_inverse_ge_2
% 5.27/5.60 thf(fact_8177_real__inv__sqrt__pow2,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( inverse_inverse_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_inv_sqrt_pow2
% 5.27/5.60 thf(fact_8178_gbinomial__reduce__nat,axiom,
% 5.27/5.60 ! [K: nat,A: complex] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_complex @ A @ K )
% 5.27/5.60 = ( 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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_reduce_nat
% 5.27/5.60 thf(fact_8179_gbinomial__reduce__nat,axiom,
% 5.27/5.60 ! [K: nat,A: real] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_real @ A @ K )
% 5.27/5.60 = ( 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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_reduce_nat
% 5.27/5.60 thf(fact_8180_gbinomial__reduce__nat,axiom,
% 5.27/5.60 ! [K: nat,A: rat] :
% 5.27/5.60 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.27/5.60 => ( ( gbinomial_rat @ A @ K )
% 5.27/5.60 = ( 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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_reduce_nat
% 5.27/5.60 thf(fact_8181_gbinomial__pochhammer,axiom,
% 5.27/5.60 ( gbinomial_complex
% 5.27/5.60 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) @ ( comm_s2602460028002588243omplex @ ( uminus1482373934393186551omplex @ A3 ) @ K3 ) ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer
% 5.27/5.60 thf(fact_8182_gbinomial__pochhammer,axiom,
% 5.27/5.60 ( gbinomial_rat
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer
% 5.27/5.60 thf(fact_8183_gbinomial__pochhammer,axiom,
% 5.27/5.60 ( gbinomial_real
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer
% 5.27/5.60 thf(fact_8184_gbinomial__pochhammer_H,axiom,
% 5.27/5.60 ( gbinomial_rat
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer'
% 5.27/5.60 thf(fact_8185_gbinomial__pochhammer_H,axiom,
% 5.27/5.60 ( gbinomial_complex
% 5.27/5.60 = ( ^ [A3: complex,K3: nat] : ( divide1717551699836669952omplex @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ K3 ) ) @ one_one_complex ) @ K3 ) @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer'
% 5.27/5.60 thf(fact_8186_gbinomial__pochhammer_H,axiom,
% 5.27/5.60 ( gbinomial_real
% 5.27/5.60 = ( ^ [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 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % gbinomial_pochhammer'
% 5.27/5.60 thf(fact_8187_tan__cot,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X4 ) )
% 5.27/5.60 = ( inverse_inverse_real @ ( tan_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tan_cot
% 5.27/5.60 thf(fact_8188_floor__add,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.27/5.60 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_real @ ( plus_plus_real @ ( archim2898591450579166408c_real @ X4 ) @ ( archim2898591450579166408c_real @ Y ) ) @ one_one_real )
% 5.27/5.60 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_add
% 5.27/5.60 thf(fact_8189_floor__add,axiom,
% 5.27/5.60 ! [X4: rat,Y: rat] :
% 5.27/5.60 ( ( ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.27/5.60 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) )
% 5.27/5.60 & ( ~ ( ord_less_rat @ ( plus_plus_rat @ ( archimedean_frac_rat @ X4 ) @ ( archimedean_frac_rat @ Y ) ) @ one_one_rat )
% 5.27/5.60 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_add
% 5.27/5.60 thf(fact_8190_real__le__x__sinh,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ord_less_eq_real @ X4 @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_le_x_sinh
% 5.27/5.60 thf(fact_8191_real__le__abs__sinh,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X4 ) @ ( inverse_inverse_real @ ( exp_real @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % real_le_abs_sinh
% 5.27/5.60 thf(fact_8192_tan__sec,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( cos_real @ X4 )
% 5.27/5.60 != zero_zero_real )
% 5.27/5.60 => ( ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = ( power_power_real @ ( inverse_inverse_real @ ( cos_real @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tan_sec
% 5.27/5.60 thf(fact_8193_tan__sec,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( ( cos_complex @ X4 )
% 5.27/5.60 != zero_zero_complex )
% 5.27/5.60 => ( ( plus_plus_complex @ one_one_complex @ ( power_power_complex @ ( tan_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = ( power_power_complex @ ( invers8013647133539491842omplex @ ( cos_complex @ X4 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tan_sec
% 5.27/5.60 thf(fact_8194_Arg__minus__ii,axiom,
% 5.27/5.60 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.27/5.60 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Arg_minus_ii
% 5.27/5.60 thf(fact_8195_csqrt__ii,axiom,
% 5.27/5.60 ( ( csqrt @ imaginary_unit )
% 5.27/5.60 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % csqrt_ii
% 5.27/5.60 thf(fact_8196_Arg__ii,axiom,
% 5.27/5.60 ( ( arg @ imaginary_unit )
% 5.27/5.60 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Arg_ii
% 5.27/5.60 thf(fact_8197_sinh__ln__real,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( sinh_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.60 = ( divide_divide_real @ ( minus_minus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_ln_real
% 5.27/5.60 thf(fact_8198_cis__multiple__2pi,axiom,
% 5.27/5.60 ! [N2: real] :
% 5.27/5.60 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.27/5.60 = one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % cis_multiple_2pi
% 5.27/5.60 thf(fact_8199_sinh__real__less__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 5.27/5.60 = ( ord_less_real @ X4 @ Y ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_less_iff
% 5.27/5.60 thf(fact_8200_sinh__real__le__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) )
% 5.27/5.60 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_le_iff
% 5.27/5.60 thf(fact_8201_sinh__real__neg__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 5.27/5.60 = ( ord_less_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_neg_iff
% 5.27/5.60 thf(fact_8202_sinh__real__pos__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 5.27/5.60 = ( ord_less_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_pos_iff
% 5.27/5.60 thf(fact_8203_sinh__real__nonneg__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X4 ) )
% 5.27/5.60 = ( ord_less_eq_real @ zero_zero_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_nonneg_iff
% 5.27/5.60 thf(fact_8204_sinh__real__nonpos__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ ( sinh_real @ X4 ) @ zero_zero_real )
% 5.27/5.60 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_real_nonpos_iff
% 5.27/5.60 thf(fact_8205_floor__add2,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 | ( member_real @ Y @ ring_1_Ints_real ) )
% 5.27/5.60 => ( ( archim6058952711729229775r_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( archim6058952711729229775r_real @ X4 ) @ ( archim6058952711729229775r_real @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_add2
% 5.27/5.60 thf(fact_8206_floor__add2,axiom,
% 5.27/5.60 ! [X4: rat,Y: rat] :
% 5.27/5.60 ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 | ( member_rat @ Y @ ring_1_Ints_rat ) )
% 5.27/5.60 => ( ( archim3151403230148437115or_rat @ ( plus_plus_rat @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_int @ ( archim3151403230148437115or_rat @ X4 ) @ ( archim3151403230148437115or_rat @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % floor_add2
% 5.27/5.60 thf(fact_8207_frac__gt__0__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ ( archim2898591450579166408c_real @ X4 ) )
% 5.27/5.60 = ( ~ ( member_real @ X4 @ ring_1_Ints_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_gt_0_iff
% 5.27/5.60 thf(fact_8208_frac__gt__0__iff,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ord_less_rat @ zero_zero_rat @ ( archimedean_frac_rat @ X4 ) )
% 5.27/5.60 = ( ~ ( member_rat @ X4 @ ring_1_Ints_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_gt_0_iff
% 5.27/5.60 thf(fact_8209_power2__csqrt,axiom,
% 5.27/5.60 ! [Z: complex] :
% 5.27/5.60 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = Z ) ).
% 5.27/5.60
% 5.27/5.60 % power2_csqrt
% 5.27/5.60 thf(fact_8210_Ints__power,axiom,
% 5.27/5.60 ! [A: real,N2: nat] :
% 5.27/5.60 ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( member_real @ ( power_power_real @ A @ N2 ) @ ring_1_Ints_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_power
% 5.27/5.60 thf(fact_8211_Ints__power,axiom,
% 5.27/5.60 ! [A: int,N2: nat] :
% 5.27/5.60 ( ( member_int @ A @ ring_1_Ints_int )
% 5.27/5.60 => ( member_int @ ( power_power_int @ A @ N2 ) @ ring_1_Ints_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_power
% 5.27/5.60 thf(fact_8212_Ints__power,axiom,
% 5.27/5.60 ! [A: complex,N2: nat] :
% 5.27/5.60 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.27/5.60 => ( member_complex @ ( power_power_complex @ A @ N2 ) @ ring_1_Ints_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_power
% 5.27/5.60 thf(fact_8213_Ints__numeral,axiom,
% 5.27/5.60 ! [N2: num] : ( member_complex @ ( numera6690914467698888265omplex @ N2 ) @ ring_1_Ints_complex ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_numeral
% 5.27/5.60 thf(fact_8214_Ints__numeral,axiom,
% 5.27/5.60 ! [N2: num] : ( member_real @ ( numeral_numeral_real @ N2 ) @ ring_1_Ints_real ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_numeral
% 5.27/5.60 thf(fact_8215_Ints__numeral,axiom,
% 5.27/5.60 ! [N2: num] : ( member_int @ ( numeral_numeral_int @ N2 ) @ ring_1_Ints_int ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_numeral
% 5.27/5.60 thf(fact_8216_Ints__1,axiom,
% 5.27/5.60 member_complex @ one_one_complex @ ring_1_Ints_complex ).
% 5.27/5.60
% 5.27/5.60 % Ints_1
% 5.27/5.60 thf(fact_8217_Ints__1,axiom,
% 5.27/5.60 member_rat @ one_one_rat @ ring_1_Ints_rat ).
% 5.27/5.60
% 5.27/5.60 % Ints_1
% 5.27/5.60 thf(fact_8218_Ints__1,axiom,
% 5.27/5.60 member_int @ one_one_int @ ring_1_Ints_int ).
% 5.27/5.60
% 5.27/5.60 % Ints_1
% 5.27/5.60 thf(fact_8219_Ints__1,axiom,
% 5.27/5.60 member_real @ one_one_real @ ring_1_Ints_real ).
% 5.27/5.60
% 5.27/5.60 % Ints_1
% 5.27/5.60 thf(fact_8220_Ints__add,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.27/5.60 => ( ( member_complex @ B @ ring_1_Ints_complex )
% 5.27/5.60 => ( member_complex @ ( plus_plus_complex @ A @ B ) @ ring_1_Ints_complex ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_add
% 5.27/5.60 thf(fact_8221_Ints__add,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ( member_real @ B @ ring_1_Ints_real )
% 5.27/5.60 => ( member_real @ ( plus_plus_real @ A @ B ) @ ring_1_Ints_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_add
% 5.27/5.60 thf(fact_8222_Ints__add,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( member_rat @ B @ ring_1_Ints_rat )
% 5.27/5.60 => ( member_rat @ ( plus_plus_rat @ A @ B ) @ ring_1_Ints_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_add
% 5.27/5.60 thf(fact_8223_Ints__add,axiom,
% 5.27/5.60 ! [A: int,B: int] :
% 5.27/5.60 ( ( member_int @ A @ ring_1_Ints_int )
% 5.27/5.60 => ( ( member_int @ B @ ring_1_Ints_int )
% 5.27/5.60 => ( member_int @ ( plus_plus_int @ A @ B ) @ ring_1_Ints_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_add
% 5.27/5.60 thf(fact_8224_Ints__double__eq__0__iff,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.27/5.60 => ( ( ( plus_plus_complex @ A @ A )
% 5.27/5.60 = zero_zero_complex )
% 5.27/5.60 = ( A = zero_zero_complex ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_double_eq_0_iff
% 5.27/5.60 thf(fact_8225_Ints__double__eq__0__iff,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ( ( plus_plus_real @ A @ A )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 = ( A = zero_zero_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_double_eq_0_iff
% 5.27/5.60 thf(fact_8226_Ints__double__eq__0__iff,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( ( plus_plus_rat @ A @ A )
% 5.27/5.60 = zero_zero_rat )
% 5.27/5.60 = ( A = zero_zero_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_double_eq_0_iff
% 5.27/5.60 thf(fact_8227_Ints__double__eq__0__iff,axiom,
% 5.27/5.60 ! [A: int] :
% 5.27/5.60 ( ( member_int @ A @ ring_1_Ints_int )
% 5.27/5.60 => ( ( ( plus_plus_int @ A @ A )
% 5.27/5.60 = zero_zero_int )
% 5.27/5.60 = ( A = zero_zero_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_double_eq_0_iff
% 5.27/5.60 thf(fact_8228_Ints__odd__nonzero,axiom,
% 5.27/5.60 ! [A: complex] :
% 5.27/5.60 ( ( member_complex @ A @ ring_1_Ints_complex )
% 5.27/5.60 => ( ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ A ) @ A )
% 5.27/5.60 != zero_zero_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_nonzero
% 5.27/5.60 thf(fact_8229_Ints__odd__nonzero,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A )
% 5.27/5.60 != zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_nonzero
% 5.27/5.60 thf(fact_8230_Ints__odd__nonzero,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A )
% 5.27/5.60 != zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_nonzero
% 5.27/5.60 thf(fact_8231_Ints__odd__nonzero,axiom,
% 5.27/5.60 ! [A: int] :
% 5.27/5.60 ( ( member_int @ A @ ring_1_Ints_int )
% 5.27/5.60 => ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A )
% 5.27/5.60 != zero_zero_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_nonzero
% 5.27/5.60 thf(fact_8232_of__int__divide__in__Ints,axiom,
% 5.27/5.60 ! [B: int,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.60 => ( member_rat @ ( divide_divide_rat @ ( ring_1_of_int_rat @ A ) @ ( ring_1_of_int_rat @ B ) ) @ ring_1_Ints_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_divide_in_Ints
% 5.27/5.60 thf(fact_8233_of__int__divide__in__Ints,axiom,
% 5.27/5.60 ! [B: int,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.60 => ( member_int @ ( divide_divide_int @ ( ring_1_of_int_int @ A ) @ ( ring_1_of_int_int @ B ) ) @ ring_1_Ints_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_divide_in_Ints
% 5.27/5.60 thf(fact_8234_of__int__divide__in__Ints,axiom,
% 5.27/5.60 ! [B: int,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.60 => ( member_real @ ( divide_divide_real @ ( ring_1_of_int_real @ A ) @ ( ring_1_of_int_real @ B ) ) @ ring_1_Ints_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_divide_in_Ints
% 5.27/5.60 thf(fact_8235_of__int__divide__in__Ints,axiom,
% 5.27/5.60 ! [B: int,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.60 => ( member_complex @ ( divide1717551699836669952omplex @ ( ring_17405671764205052669omplex @ A ) @ ( ring_17405671764205052669omplex @ B ) ) @ ring_1_Ints_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_divide_in_Ints
% 5.27/5.60 thf(fact_8236_of__int__divide__in__Ints,axiom,
% 5.27/5.60 ! [B: int,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ B @ A )
% 5.27/5.60 => ( member_Code_integer @ ( divide6298287555418463151nteger @ ( ring_18347121197199848620nteger @ A ) @ ( ring_18347121197199848620nteger @ B ) ) @ ring_11222124179247155820nteger ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_int_divide_in_Ints
% 5.27/5.60 thf(fact_8237_Ints__odd__less__0,axiom,
% 5.27/5.60 ! [A: real] :
% 5.27/5.60 ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ( ord_less_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ A ) @ A ) @ zero_zero_real )
% 5.27/5.60 = ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_less_0
% 5.27/5.60 thf(fact_8238_Ints__odd__less__0,axiom,
% 5.27/5.60 ! [A: rat] :
% 5.27/5.60 ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( ord_less_rat @ ( plus_plus_rat @ ( plus_plus_rat @ one_one_rat @ A ) @ A ) @ zero_zero_rat )
% 5.27/5.60 = ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_less_0
% 5.27/5.60 thf(fact_8239_Ints__odd__less__0,axiom,
% 5.27/5.60 ! [A: int] :
% 5.27/5.60 ( ( member_int @ A @ ring_1_Ints_int )
% 5.27/5.60 => ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ A ) @ A ) @ zero_zero_int )
% 5.27/5.60 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_odd_less_0
% 5.27/5.60 thf(fact_8240_Ints__nonzero__abs__ge1,axiom,
% 5.27/5.60 ! [X4: code_integer] :
% 5.27/5.60 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.27/5.60 => ( ( X4 != zero_z3403309356797280102nteger )
% 5.27/5.60 => ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_ge1
% 5.27/5.60 thf(fact_8241_Ints__nonzero__abs__ge1,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( X4 != zero_zero_real )
% 5.27/5.60 => ( ord_less_eq_real @ one_one_real @ ( abs_abs_real @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_ge1
% 5.27/5.60 thf(fact_8242_Ints__nonzero__abs__ge1,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( X4 != zero_zero_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ one_one_rat @ ( abs_abs_rat @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_ge1
% 5.27/5.60 thf(fact_8243_Ints__nonzero__abs__ge1,axiom,
% 5.27/5.60 ! [X4: int] :
% 5.27/5.60 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.27/5.60 => ( ( X4 != zero_zero_int )
% 5.27/5.60 => ( ord_less_eq_int @ one_one_int @ ( abs_abs_int @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_ge1
% 5.27/5.60 thf(fact_8244_Ints__nonzero__abs__less1,axiom,
% 5.27/5.60 ! [X4: code_integer] :
% 5.27/5.60 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.27/5.60 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X4 ) @ one_one_Code_integer )
% 5.27/5.60 => ( X4 = zero_z3403309356797280102nteger ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_less1
% 5.27/5.60 thf(fact_8245_Ints__nonzero__abs__less1,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.60 => ( X4 = zero_zero_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_less1
% 5.27/5.60 thf(fact_8246_Ints__nonzero__abs__less1,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( ord_less_rat @ ( abs_abs_rat @ X4 ) @ one_one_rat )
% 5.27/5.60 => ( X4 = zero_zero_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_less1
% 5.27/5.60 thf(fact_8247_Ints__nonzero__abs__less1,axiom,
% 5.27/5.60 ! [X4: int] :
% 5.27/5.60 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.27/5.60 => ( ( ord_less_int @ ( abs_abs_int @ X4 ) @ one_one_int )
% 5.27/5.60 => ( X4 = zero_zero_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_nonzero_abs_less1
% 5.27/5.60 thf(fact_8248_Ints__eq__abs__less1,axiom,
% 5.27/5.60 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.60 ( ( member_Code_integer @ X4 @ ring_11222124179247155820nteger )
% 5.27/5.60 => ( ( member_Code_integer @ Y @ ring_11222124179247155820nteger )
% 5.27/5.60 => ( ( X4 = Y )
% 5.27/5.60 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X4 @ Y ) ) @ one_one_Code_integer ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_eq_abs_less1
% 5.27/5.60 thf(fact_8249_Ints__eq__abs__less1,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( member_real @ Y @ ring_1_Ints_real )
% 5.27/5.60 => ( ( X4 = Y )
% 5.27/5.60 = ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y ) ) @ one_one_real ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_eq_abs_less1
% 5.27/5.60 thf(fact_8250_Ints__eq__abs__less1,axiom,
% 5.27/5.60 ! [X4: rat,Y: rat] :
% 5.27/5.60 ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( member_rat @ Y @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( X4 = Y )
% 5.27/5.60 = ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X4 @ Y ) ) @ one_one_rat ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_eq_abs_less1
% 5.27/5.60 thf(fact_8251_Ints__eq__abs__less1,axiom,
% 5.27/5.60 ! [X4: int,Y: int] :
% 5.27/5.60 ( ( member_int @ X4 @ ring_1_Ints_int )
% 5.27/5.60 => ( ( member_int @ Y @ ring_1_Ints_int )
% 5.27/5.60 => ( ( X4 = Y )
% 5.27/5.60 = ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X4 @ Y ) ) @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Ints_eq_abs_less1
% 5.27/5.60 thf(fact_8252_of__real__sqrt,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X4 ) )
% 5.27/5.60 = ( csqrt @ ( real_V4546457046886955230omplex @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_real_sqrt
% 5.27/5.60 thf(fact_8253_frac__neg,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.60 = zero_zero_real ) )
% 5.27/5.60 & ( ~ ( member_real @ X4 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( archim2898591450579166408c_real @ ( uminus_uminus_real @ X4 ) )
% 5.27/5.60 = ( minus_minus_real @ one_one_real @ ( archim2898591450579166408c_real @ X4 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_neg
% 5.27/5.60 thf(fact_8254_frac__neg,axiom,
% 5.27/5.60 ! [X4: rat] :
% 5.27/5.60 ( ( ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 5.27/5.60 = zero_zero_rat ) )
% 5.27/5.60 & ( ~ ( member_rat @ X4 @ ring_1_Ints_rat )
% 5.27/5.60 => ( ( archimedean_frac_rat @ ( uminus_uminus_rat @ X4 ) )
% 5.27/5.60 = ( minus_minus_rat @ one_one_rat @ ( archimedean_frac_rat @ X4 ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_neg
% 5.27/5.60 thf(fact_8255_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8256_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8257_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim6058952711729229775r_real @ A ) @ ( archim6058952711729229775r_real @ B ) ) ) @ ( ring_1_of_int_int @ ( archim6058952711729229775r_real @ ( times_times_real @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8258_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_real @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8259_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_rat @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8260_le__mult__floor__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( times_times_int @ ( archim3151403230148437115or_rat @ A ) @ ( archim3151403230148437115or_rat @ B ) ) ) @ ( ring_1_of_int_int @ ( archim3151403230148437115or_rat @ ( times_times_rat @ A @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % le_mult_floor_Ints
% 5.27/5.60 thf(fact_8261_frac__unique__iff,axiom,
% 5.27/5.60 ! [X4: real,A: real] :
% 5.27/5.60 ( ( ( archim2898591450579166408c_real @ X4 )
% 5.27/5.60 = A )
% 5.27/5.60 = ( ( member_real @ ( minus_minus_real @ X4 @ A ) @ ring_1_Ints_real )
% 5.27/5.60 & ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 & ( ord_less_real @ A @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_unique_iff
% 5.27/5.60 thf(fact_8262_frac__unique__iff,axiom,
% 5.27/5.60 ! [X4: rat,A: rat] :
% 5.27/5.60 ( ( ( archimedean_frac_rat @ X4 )
% 5.27/5.60 = A )
% 5.27/5.60 = ( ( member_rat @ ( minus_minus_rat @ X4 @ A ) @ ring_1_Ints_rat )
% 5.27/5.60 & ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 & ( ord_less_rat @ A @ one_one_rat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % frac_unique_iff
% 5.27/5.60 thf(fact_8263_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8264_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8265_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.60 => ( ( member_real @ A @ ring_1_Ints_real )
% 5.27/5.60 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim7802044766580827645g_real @ ( times_times_real @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim7802044766580827645g_real @ A ) @ ( archim7802044766580827645g_real @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8266_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_real @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8267_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_rat @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8268_mult__ceiling__le__Ints,axiom,
% 5.27/5.60 ! [A: rat,B: rat] :
% 5.27/5.60 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.27/5.60 => ( ( member_rat @ A @ ring_1_Ints_rat )
% 5.27/5.60 => ( ord_less_eq_int @ ( ring_1_of_int_int @ ( archim2889992004027027881ng_rat @ ( times_times_rat @ A @ B ) ) ) @ ( ring_1_of_int_int @ ( times_times_int @ ( archim2889992004027027881ng_rat @ A ) @ ( archim2889992004027027881ng_rat @ B ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % mult_ceiling_le_Ints
% 5.27/5.60 thf(fact_8269_Arg__bounded,axiom,
% 5.27/5.60 ! [Z: complex] :
% 5.27/5.60 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.27/5.60 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.27/5.60
% 5.27/5.60 % Arg_bounded
% 5.27/5.60 thf(fact_8270_sin__integer__2pi,axiom,
% 5.27/5.60 ! [N2: real] :
% 5.27/5.60 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.27/5.60 = zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % sin_integer_2pi
% 5.27/5.60 thf(fact_8271_cos__integer__2pi,axiom,
% 5.27/5.60 ! [N2: real] :
% 5.27/5.60 ( ( member_real @ N2 @ ring_1_Ints_real )
% 5.27/5.60 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N2 ) )
% 5.27/5.60 = one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % cos_integer_2pi
% 5.27/5.60 thf(fact_8272_complex__inverse,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.27/5.60 = ( 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 ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % complex_inverse
% 5.27/5.60 thf(fact_8273_sinh__field__def,axiom,
% 5.27/5.60 ( sinh_real
% 5.27/5.60 = ( ^ [Z5: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_field_def
% 5.27/5.60 thf(fact_8274_sinh__field__def,axiom,
% 5.27/5.60 ( sinh_complex
% 5.27/5.60 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_field_def
% 5.27/5.60 thf(fact_8275_cis__Arg__unique,axiom,
% 5.27/5.60 ! [Z: complex,X4: real] :
% 5.27/5.60 ( ( ( sgn_sgn_complex @ Z )
% 5.27/5.60 = ( cis @ X4 ) )
% 5.27/5.60 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_real @ X4 @ pi )
% 5.27/5.60 => ( ( arg @ Z )
% 5.27/5.60 = X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cis_Arg_unique
% 5.27/5.60 thf(fact_8276_Arg__correct,axiom,
% 5.27/5.60 ! [Z: complex] :
% 5.27/5.60 ( ( Z != zero_zero_complex )
% 5.27/5.60 => ( ( ( sgn_sgn_complex @ Z )
% 5.27/5.60 = ( cis @ ( arg @ Z ) ) )
% 5.27/5.60 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.27/5.60 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Arg_correct
% 5.27/5.60 thf(fact_8277_cosh__ln__real,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( cosh_real @ ( ln_ln_real @ X4 ) )
% 5.27/5.60 = ( divide_divide_real @ ( plus_plus_real @ X4 @ ( inverse_inverse_real @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_ln_real
% 5.27/5.60 thf(fact_8278_cosh__double,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( cosh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.60 = ( plus_plus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_double
% 5.27/5.60 thf(fact_8279_cosh__double,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( cosh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.60 = ( plus_plus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_double
% 5.27/5.60 thf(fact_8280_horner__sum__of__bool__2__less,axiom,
% 5.27/5.60 ! [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 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % horner_sum_of_bool_2_less
% 5.27/5.60 thf(fact_8281_cosh__zero__iff,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ( cosh_real @ X4 )
% 5.27/5.60 = zero_zero_real )
% 5.27/5.60 = ( ( power_power_real @ ( exp_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_zero_iff
% 5.27/5.60 thf(fact_8282_cosh__zero__iff,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( ( cosh_complex @ X4 )
% 5.27/5.60 = zero_zero_complex )
% 5.27/5.60 = ( ( power_power_complex @ ( exp_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_zero_iff
% 5.27/5.60 thf(fact_8283_push__bit__numeral__minus__1,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ N2 ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.60 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_numeral_minus_1
% 5.27/5.60 thf(fact_8284_push__bit__numeral__minus__1,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ N2 ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_numeral_minus_1
% 5.27/5.60 thf(fact_8285_push__bit__nonnegative__int__iff,axiom,
% 5.27/5.60 ! [N2: nat,K: int] :
% 5.27/5.60 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.27/5.60 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_nonnegative_int_iff
% 5.27/5.60 thf(fact_8286_push__bit__negative__int__iff,axiom,
% 5.27/5.60 ! [N2: nat,K: int] :
% 5.27/5.60 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.60 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_negative_int_iff
% 5.27/5.60 thf(fact_8287_push__bit__eq__0__iff,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( ( bit_se545348938243370406it_int @ N2 @ A )
% 5.27/5.60 = zero_zero_int )
% 5.27/5.60 = ( A = zero_zero_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_eq_0_iff
% 5.27/5.60 thf(fact_8288_push__bit__eq__0__iff,axiom,
% 5.27/5.60 ! [N2: nat,A: nat] :
% 5.27/5.60 ( ( ( bit_se547839408752420682it_nat @ N2 @ A )
% 5.27/5.60 = zero_zero_nat )
% 5.27/5.60 = ( A = zero_zero_nat ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_eq_0_iff
% 5.27/5.60 thf(fact_8289_push__bit__of__0,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ zero_zero_int )
% 5.27/5.60 = zero_zero_int ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_0
% 5.27/5.60 thf(fact_8290_push__bit__of__0,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ zero_zero_nat )
% 5.27/5.60 = zero_zero_nat ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_0
% 5.27/5.60 thf(fact_8291_push__bit__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_push_bit
% 5.27/5.60 thf(fact_8292_push__bit__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ ( plus_plus_nat @ M @ N2 ) @ A ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_push_bit
% 5.27/5.60 thf(fact_8293_push__bit__and,axiom,
% 5.27/5.60 ! [N2: nat,A: int,B: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.27/5.60 = ( bit_se725231765392027082nd_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_and
% 5.27/5.60 thf(fact_8294_push__bit__and,axiom,
% 5.27/5.60 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.27/5.60 = ( bit_se727722235901077358nd_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_and
% 5.27/5.60 thf(fact_8295_push__bit__xor,axiom,
% 5.27/5.60 ! [N2: nat,A: int,B: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( bit_se6526347334894502574or_int @ A @ B ) )
% 5.27/5.60 = ( bit_se6526347334894502574or_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_xor
% 5.27/5.60 thf(fact_8296_push__bit__xor,axiom,
% 5.27/5.60 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( bit_se6528837805403552850or_nat @ A @ B ) )
% 5.27/5.60 = ( bit_se6528837805403552850or_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_xor
% 5.27/5.60 thf(fact_8297_concat__bit__of__zero__1,axiom,
% 5.27/5.60 ! [N2: nat,L: int] :
% 5.27/5.60 ( ( bit_concat_bit @ N2 @ zero_zero_int @ L )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ N2 @ L ) ) ).
% 5.27/5.60
% 5.27/5.60 % concat_bit_of_zero_1
% 5.27/5.60 thf(fact_8298_cosh__0,axiom,
% 5.27/5.60 ( ( cosh_complex @ zero_zero_complex )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_0
% 5.27/5.60 thf(fact_8299_cosh__0,axiom,
% 5.27/5.60 ( ( cosh_real @ zero_zero_real )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_0
% 5.27/5.60 thf(fact_8300_push__bit__Suc__numeral,axiom,
% 5.27/5.60 ! [N2: nat,K: num] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( numeral_numeral_int @ K ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ N2 @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc_numeral
% 5.27/5.60 thf(fact_8301_push__bit__Suc__numeral,axiom,
% 5.27/5.60 ! [N2: nat,K: num] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc_numeral
% 5.27/5.60 thf(fact_8302_push__bit__Suc__minus__numeral,axiom,
% 5.27/5.60 ! [N2: nat,K: num] :
% 5.27/5.60 ( ( bit_se7788150548672797655nteger @ ( suc @ N2 ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.27/5.60 = ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc_minus_numeral
% 5.27/5.60 thf(fact_8303_push__bit__Suc__minus__numeral,axiom,
% 5.27/5.60 ! [N2: nat,K: num] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc_minus_numeral
% 5.27/5.60 thf(fact_8304_push__bit__numeral,axiom,
% 5.27/5.60 ! [L: num,K: num] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_int @ K ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_numeral
% 5.27/5.60 thf(fact_8305_push__bit__numeral,axiom,
% 5.27/5.60 ! [L: num,K: num] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ ( numeral_numeral_nat @ L ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ ( pred_numeral @ L ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_numeral
% 5.27/5.60 thf(fact_8306_push__bit__minus__one__eq__not__mask,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.27/5.60 = ( bit_ri7632146776885996613nteger @ ( bit_se2119862282449309892nteger @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus_one_eq_not_mask
% 5.27/5.60 thf(fact_8307_push__bit__minus__one__eq__not__mask,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.60 = ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus_one_eq_not_mask
% 5.27/5.60 thf(fact_8308_push__bit__Suc,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( suc @ N2 ) @ A )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc
% 5.27/5.60 thf(fact_8309_push__bit__Suc,axiom,
% 5.27/5.60 ! [N2: nat,A: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ ( suc @ N2 ) @ A )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_Suc
% 5.27/5.60 thf(fact_8310_push__bit__of__1,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ one_one_int )
% 5.27/5.60 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_1
% 5.27/5.60 thf(fact_8311_push__bit__of__1,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ one_one_nat )
% 5.27/5.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_1
% 5.27/5.60 thf(fact_8312_push__bit__of__Suc__0,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_Suc_0
% 5.27/5.60 thf(fact_8313_even__push__bit__iff,axiom,
% 5.27/5.60 ! [N2: nat,A: code_integer] :
% 5.27/5.60 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se7788150548672797655nteger @ N2 @ A ) )
% 5.27/5.60 = ( ( N2 != zero_zero_nat )
% 5.27/5.60 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % even_push_bit_iff
% 5.27/5.60 thf(fact_8314_even__push__bit__iff,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 5.27/5.60 = ( ( N2 != zero_zero_nat )
% 5.27/5.60 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % even_push_bit_iff
% 5.27/5.60 thf(fact_8315_even__push__bit__iff,axiom,
% 5.27/5.60 ! [N2: nat,A: nat] :
% 5.27/5.60 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 5.27/5.60 = ( ( N2 != zero_zero_nat )
% 5.27/5.60 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % even_push_bit_iff
% 5.27/5.60 thf(fact_8316_push__bit__minus__numeral,axiom,
% 5.27/5.60 ! [L: num,K: num] :
% 5.27/5.60 ( ( bit_se7788150548672797655nteger @ ( numeral_numeral_nat @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.27/5.60 = ( bit_se7788150548672797655nteger @ ( pred_numeral @ L ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus_numeral
% 5.27/5.60 thf(fact_8317_push__bit__minus__numeral,axiom,
% 5.27/5.60 ! [L: num,K: num] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus_numeral
% 5.27/5.60 thf(fact_8318_push__bit__of__int,axiom,
% 5.27/5.60 ! [N2: nat,K: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( ring_1_of_int_int @ K ) )
% 5.27/5.60 = ( ring_1_of_int_int @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_int
% 5.27/5.60 thf(fact_8319_of__nat__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat] :
% 5.27/5.60 ( ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ M @ ( semiri1314217659103216013at_int @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_push_bit
% 5.27/5.60 thf(fact_8320_of__nat__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat] :
% 5.27/5.60 ( ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ M @ N2 ) )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ M @ ( semiri1316708129612266289at_nat @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % of_nat_push_bit
% 5.27/5.60 thf(fact_8321_push__bit__of__nat,axiom,
% 5.27/5.60 ! [N2: nat,M: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( semiri1314217659103216013at_int @ M ) )
% 5.27/5.60 = ( semiri1314217659103216013at_int @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_nat
% 5.27/5.60 thf(fact_8322_push__bit__of__nat,axiom,
% 5.27/5.60 ! [N2: nat,M: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( semiri1316708129612266289at_nat @ M ) )
% 5.27/5.60 = ( semiri1316708129612266289at_nat @ ( bit_se547839408752420682it_nat @ N2 @ M ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_of_nat
% 5.27/5.60 thf(fact_8323_push__bit__nat__eq,axiom,
% 5.27/5.60 ! [N2: nat,K: int] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( nat2 @ K ) )
% 5.27/5.60 = ( nat2 @ ( bit_se545348938243370406it_int @ N2 @ K ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_nat_eq
% 5.27/5.60 thf(fact_8324_push__bit__minus,axiom,
% 5.27/5.60 ! [N2: nat,A: code_integer] :
% 5.27/5.60 ( ( bit_se7788150548672797655nteger @ N2 @ ( uminus1351360451143612070nteger @ A ) )
% 5.27/5.60 = ( uminus1351360451143612070nteger @ ( bit_se7788150548672797655nteger @ N2 @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus
% 5.27/5.60 thf(fact_8325_push__bit__minus,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ A ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus
% 5.27/5.60 thf(fact_8326_push__bit__add,axiom,
% 5.27/5.60 ! [N2: nat,A: int,B: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( plus_plus_int @ A @ B ) )
% 5.27/5.60 = ( plus_plus_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( bit_se545348938243370406it_int @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_add
% 5.27/5.60 thf(fact_8327_push__bit__add,axiom,
% 5.27/5.60 ! [N2: nat,A: nat,B: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( plus_plus_nat @ A @ B ) )
% 5.27/5.60 = ( plus_plus_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( bit_se547839408752420682it_nat @ N2 @ B ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_add
% 5.27/5.60 thf(fact_8328_cosh__real__pos,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_pos
% 5.27/5.60 thf(fact_8329_cosh__real__nonpos__le__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 5.27/5.60 = ( ord_less_eq_real @ Y @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_nonpos_le_iff
% 5.27/5.60 thf(fact_8330_cosh__real__nonneg__le__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.60 => ( ( ord_less_eq_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 5.27/5.60 = ( ord_less_eq_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_nonneg_le_iff
% 5.27/5.60 thf(fact_8331_cosh__real__nonneg,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_nonneg
% 5.27/5.60 thf(fact_8332_cosh__real__ge__1,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_ge_1
% 5.27/5.60 thf(fact_8333_push__bit__take__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2923211474154528505it_int @ N2 @ A ) )
% 5.27/5.60 = ( bit_se2923211474154528505it_int @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ M @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_take_bit
% 5.27/5.60 thf(fact_8334_push__bit__take__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ M @ ( bit_se2925701944663578781it_nat @ N2 @ A ) )
% 5.27/5.60 = ( bit_se2925701944663578781it_nat @ ( plus_plus_nat @ M @ N2 ) @ ( bit_se547839408752420682it_nat @ M @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_take_bit
% 5.27/5.60 thf(fact_8335_take__bit__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se2923211474154528505it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ A ) )
% 5.27/5.60 = ( bit_se545348938243370406it_int @ N2 @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % take_bit_push_bit
% 5.27/5.60 thf(fact_8336_take__bit__push__bit,axiom,
% 5.27/5.60 ! [M: nat,N2: nat,A: nat] :
% 5.27/5.60 ( ( bit_se2925701944663578781it_nat @ M @ ( bit_se547839408752420682it_nat @ N2 @ A ) )
% 5.27/5.60 = ( bit_se547839408752420682it_nat @ N2 @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ M @ N2 ) @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % take_bit_push_bit
% 5.27/5.60 thf(fact_8337_sinh__less__cosh__real,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_less_cosh_real
% 5.27/5.60 thf(fact_8338_sinh__le__cosh__real,axiom,
% 5.27/5.60 ! [X4: real] : ( ord_less_eq_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_le_cosh_real
% 5.27/5.60 thf(fact_8339_flip__bit__nat__def,axiom,
% 5.27/5.60 ( bit_se2161824704523386999it_nat
% 5.27/5.60 = ( ^ [M6: nat,N: nat] : ( bit_se6528837805403552850or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % flip_bit_nat_def
% 5.27/5.60 thf(fact_8340_cosh__real__strict__mono,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.60 => ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_strict_mono
% 5.27/5.60 thf(fact_8341_cosh__real__nonneg__less__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.60 => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 5.27/5.60 = ( ord_less_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_nonneg_less_iff
% 5.27/5.60 thf(fact_8342_cosh__real__nonpos__less__iff,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.27/5.60 => ( ( ord_less_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) )
% 5.27/5.60 = ( ord_less_real @ Y @ X4 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_real_nonpos_less_iff
% 5.27/5.60 thf(fact_8343_bit__push__bit__iff__int,axiom,
% 5.27/5.60 ! [M: nat,K: int,N2: nat] :
% 5.27/5.60 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N2 )
% 5.27/5.60 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.60 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_push_bit_iff_int
% 5.27/5.60 thf(fact_8344_bit__push__bit__iff__nat,axiom,
% 5.27/5.60 ! [M: nat,Q3: nat,N2: nat] :
% 5.27/5.60 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q3 ) @ N2 )
% 5.27/5.60 = ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.60 & ( bit_se1148574629649215175it_nat @ Q3 @ ( minus_minus_nat @ N2 @ M ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_push_bit_iff_nat
% 5.27/5.60 thf(fact_8345_concat__bit__eq,axiom,
% 5.27/5.60 ( bit_concat_bit
% 5.27/5.60 = ( ^ [N: nat,K3: int,L2: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % concat_bit_eq
% 5.27/5.60 thf(fact_8346_arcosh__cosh__real,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.60 => ( ( arcosh_real @ ( cosh_real @ X4 ) )
% 5.27/5.60 = X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % arcosh_cosh_real
% 5.27/5.60 thf(fact_8347_flip__bit__eq__xor,axiom,
% 5.27/5.60 ( bit_se2159334234014336723it_int
% 5.27/5.60 = ( ^ [N: nat,A3: int] : ( bit_se6526347334894502574or_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % flip_bit_eq_xor
% 5.27/5.60 thf(fact_8348_flip__bit__eq__xor,axiom,
% 5.27/5.60 ( bit_se2161824704523386999it_nat
% 5.27/5.60 = ( ^ [N: nat,A3: nat] : ( bit_se6528837805403552850or_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % flip_bit_eq_xor
% 5.27/5.60 thf(fact_8349_cosh__add,axiom,
% 5.27/5.60 ! [X4: complex,Y: complex] :
% 5.27/5.60 ( ( cosh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_complex @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_add
% 5.27/5.60 thf(fact_8350_cosh__add,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( cosh_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_real @ ( times_times_real @ ( cosh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( sinh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_add
% 5.27/5.60 thf(fact_8351_sinh__add,axiom,
% 5.27/5.60 ! [X4: complex,Y: complex] :
% 5.27/5.60 ( ( sinh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_complex @ ( times_times_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ Y ) ) @ ( times_times_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_add
% 5.27/5.60 thf(fact_8352_sinh__add,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( sinh_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( plus_plus_real @ ( times_times_real @ ( sinh_real @ X4 ) @ ( cosh_real @ Y ) ) @ ( times_times_real @ ( cosh_real @ X4 ) @ ( sinh_real @ Y ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_add
% 5.27/5.60 thf(fact_8353_cosh__plus__sinh,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( plus_plus_complex @ ( cosh_complex @ X4 ) @ ( sinh_complex @ X4 ) )
% 5.27/5.60 = ( exp_complex @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_plus_sinh
% 5.27/5.60 thf(fact_8354_cosh__plus__sinh,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( plus_plus_real @ ( cosh_real @ X4 ) @ ( sinh_real @ X4 ) )
% 5.27/5.60 = ( exp_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_plus_sinh
% 5.27/5.60 thf(fact_8355_sinh__plus__cosh,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( plus_plus_complex @ ( sinh_complex @ X4 ) @ ( cosh_complex @ X4 ) )
% 5.27/5.60 = ( exp_complex @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_plus_cosh
% 5.27/5.60 thf(fact_8356_sinh__plus__cosh,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( plus_plus_real @ ( sinh_real @ X4 ) @ ( cosh_real @ X4 ) )
% 5.27/5.60 = ( exp_real @ X4 ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_plus_cosh
% 5.27/5.60 thf(fact_8357_flip__bit__int__def,axiom,
% 5.27/5.60 ( bit_se2159334234014336723it_int
% 5.27/5.60 = ( ^ [N: nat,K3: int] : ( bit_se6526347334894502574or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % flip_bit_int_def
% 5.27/5.60 thf(fact_8358_tanh__def,axiom,
% 5.27/5.60 ( tanh_real
% 5.27/5.60 = ( ^ [X: real] : ( divide_divide_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tanh_def
% 5.27/5.60 thf(fact_8359_tanh__def,axiom,
% 5.27/5.60 ( tanh_complex
% 5.27/5.60 = ( ^ [X: complex] : ( divide1717551699836669952omplex @ ( sinh_complex @ X ) @ ( cosh_complex @ X ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tanh_def
% 5.27/5.60 thf(fact_8360_push__bit__double,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( times_times_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = ( times_times_int @ ( bit_se545348938243370406it_int @ N2 @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_double
% 5.27/5.60 thf(fact_8361_push__bit__double,axiom,
% 5.27/5.60 ! [N2: nat,A: nat] :
% 5.27/5.60 ( ( bit_se547839408752420682it_nat @ N2 @ ( times_times_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = ( times_times_nat @ ( bit_se547839408752420682it_nat @ N2 @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_double
% 5.27/5.60 thf(fact_8362_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.27/5.60 ( bit_se1146084159140164899it_int
% 5.27/5.60 = ( ^ [A3: int,N: nat] :
% 5.27/5.60 ( ( bit_se725231765392027082nd_int @ A3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) )
% 5.27/5.60 != zero_zero_int ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_iff_and_push_bit_not_eq_0
% 5.27/5.60 thf(fact_8363_bit__iff__and__push__bit__not__eq__0,axiom,
% 5.27/5.60 ( bit_se1148574629649215175it_nat
% 5.27/5.60 = ( ^ [A3: nat,N: nat] :
% 5.27/5.60 ( ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se547839408752420682it_nat @ N @ one_one_nat ) )
% 5.27/5.60 != zero_zero_nat ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_iff_and_push_bit_not_eq_0
% 5.27/5.60 thf(fact_8364_push__bit__mask__eq,axiom,
% 5.27/5.60 ! [M: nat,N2: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ M @ ( bit_se2000444600071755411sk_int @ N2 ) )
% 5.27/5.60 = ( bit_se725231765392027082nd_int @ ( bit_se2000444600071755411sk_int @ ( plus_plus_nat @ N2 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( bit_se2000444600071755411sk_int @ M ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_mask_eq
% 5.27/5.60 thf(fact_8365_unset__bit__eq__and__not,axiom,
% 5.27/5.60 ( bit_se4203085406695923979it_int
% 5.27/5.60 = ( ^ [N: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % unset_bit_eq_and_not
% 5.27/5.60 thf(fact_8366_unset__bit__int__def,axiom,
% 5.27/5.60 ( bit_se4203085406695923979it_int
% 5.27/5.60 = ( ^ [N: nat,K3: int] : ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % unset_bit_int_def
% 5.27/5.60 thf(fact_8367_push__bit__int__def,axiom,
% 5.27/5.60 ( bit_se545348938243370406it_int
% 5.27/5.60 = ( ^ [N: nat,K3: int] : ( times_times_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_int_def
% 5.27/5.60 thf(fact_8368_push__bit__nat__def,axiom,
% 5.27/5.60 ( bit_se547839408752420682it_nat
% 5.27/5.60 = ( ^ [N: nat,M6: nat] : ( times_times_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_nat_def
% 5.27/5.60 thf(fact_8369_push__bit__eq__mult,axiom,
% 5.27/5.60 ( bit_se545348938243370406it_int
% 5.27/5.60 = ( ^ [N: nat,A3: int] : ( times_times_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_eq_mult
% 5.27/5.60 thf(fact_8370_push__bit__eq__mult,axiom,
% 5.27/5.60 ( bit_se547839408752420682it_nat
% 5.27/5.60 = ( ^ [N: nat,A3: nat] : ( times_times_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_eq_mult
% 5.27/5.60 thf(fact_8371_exp__dvdE,axiom,
% 5.27/5.60 ! [N2: nat,A: code_integer] :
% 5.27/5.60 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) @ A )
% 5.27/5.60 => ~ ! [B5: code_integer] :
% 5.27/5.60 ( A
% 5.27/5.60 != ( bit_se7788150548672797655nteger @ N2 @ B5 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % exp_dvdE
% 5.27/5.60 thf(fact_8372_exp__dvdE,axiom,
% 5.27/5.60 ! [N2: nat,A: int] :
% 5.27/5.60 ( ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ A )
% 5.27/5.60 => ~ ! [B5: int] :
% 5.27/5.60 ( A
% 5.27/5.60 != ( bit_se545348938243370406it_int @ N2 @ B5 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % exp_dvdE
% 5.27/5.60 thf(fact_8373_exp__dvdE,axiom,
% 5.27/5.60 ! [N2: nat,A: nat] :
% 5.27/5.60 ( ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ A )
% 5.27/5.60 => ~ ! [B5: nat] :
% 5.27/5.60 ( A
% 5.27/5.60 != ( bit_se547839408752420682it_nat @ N2 @ B5 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % exp_dvdE
% 5.27/5.60 thf(fact_8374_sinh__double,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( sinh_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.60 = ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( sinh_complex @ X4 ) ) @ ( cosh_complex @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_double
% 5.27/5.60 thf(fact_8375_sinh__double,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( sinh_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 ) )
% 5.27/5.60 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( sinh_real @ X4 ) ) @ ( cosh_real @ X4 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_double
% 5.27/5.60 thf(fact_8376_push__bit__minus__one,axiom,
% 5.27/5.60 ! [N2: nat] :
% 5.27/5.60 ( ( bit_se545348938243370406it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.60 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % push_bit_minus_one
% 5.27/5.60 thf(fact_8377_tanh__add,axiom,
% 5.27/5.60 ! [X4: real,Y: real] :
% 5.27/5.60 ( ( ( cosh_real @ X4 )
% 5.27/5.60 != zero_zero_real )
% 5.27/5.60 => ( ( ( cosh_real @ Y )
% 5.27/5.60 != zero_zero_real )
% 5.27/5.60 => ( ( tanh_real @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.60 = ( divide_divide_real @ ( plus_plus_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( tanh_real @ X4 ) @ ( tanh_real @ Y ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tanh_add
% 5.27/5.60 thf(fact_8378_tanh__add,axiom,
% 5.27/5.60 ! [X4: complex,Y: complex] :
% 5.27/5.60 ( ( ( cosh_complex @ X4 )
% 5.27/5.60 != zero_zero_complex )
% 5.27/5.60 => ( ( ( cosh_complex @ Y )
% 5.27/5.60 != zero_zero_complex )
% 5.27/5.60 => ( ( tanh_complex @ ( plus_plus_complex @ X4 @ Y ) )
% 5.27/5.60 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) @ ( plus_plus_complex @ one_one_complex @ ( times_times_complex @ ( tanh_complex @ X4 ) @ ( tanh_complex @ Y ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % tanh_add
% 5.27/5.60 thf(fact_8379_cosh__field__def,axiom,
% 5.27/5.60 ( cosh_real
% 5.27/5.60 = ( ^ [Z5: real] : ( divide_divide_real @ ( plus_plus_real @ ( exp_real @ Z5 ) @ ( exp_real @ ( uminus_uminus_real @ Z5 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_field_def
% 5.27/5.60 thf(fact_8380_cosh__field__def,axiom,
% 5.27/5.60 ( cosh_complex
% 5.27/5.60 = ( ^ [Z5: complex] : ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( exp_complex @ Z5 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ Z5 ) ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_field_def
% 5.27/5.60 thf(fact_8381_cosh__square__eq,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( plus_plus_real @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_square_eq
% 5.27/5.60 thf(fact_8382_cosh__square__eq,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( plus_plus_complex @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % cosh_square_eq
% 5.27/5.60 thf(fact_8383_sinh__square__eq,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_square_eq
% 5.27/5.60 thf(fact_8384_sinh__square__eq,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.60 = ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % sinh_square_eq
% 5.27/5.60 thf(fact_8385_hyperbolic__pythagoras,axiom,
% 5.27/5.60 ! [X4: complex] :
% 5.27/5.60 ( ( minus_minus_complex @ ( power_power_complex @ ( cosh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ ( sinh_complex @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = one_one_complex ) ).
% 5.27/5.60
% 5.27/5.60 % hyperbolic_pythagoras
% 5.27/5.60 thf(fact_8386_hyperbolic__pythagoras,axiom,
% 5.27/5.60 ! [X4: real] :
% 5.27/5.60 ( ( minus_minus_real @ ( power_power_real @ ( cosh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( sinh_real @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.60 = one_one_real ) ).
% 5.27/5.60
% 5.27/5.60 % hyperbolic_pythagoras
% 5.27/5.60 thf(fact_8387_bit__horner__sum__bit__iff,axiom,
% 5.27/5.60 ! [Bs: list_o,N2: nat] :
% 5.27/5.60 ( ( bit_se9216721137139052372nteger @ ( groups3417619833198082522nteger @ zero_n356916108424825756nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 5.27/5.60 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 5.27/5.60 & ( nth_o @ Bs @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_horner_sum_bit_iff
% 5.27/5.60 thf(fact_8388_bit__horner__sum__bit__iff,axiom,
% 5.27/5.60 ! [Bs: list_o,N2: nat] :
% 5.27/5.60 ( ( bit_se1148574629649215175it_nat @ ( groups9119017779487936845_o_nat @ zero_n2687167440665602831ol_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 5.27/5.60 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 5.27/5.60 & ( nth_o @ Bs @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_horner_sum_bit_iff
% 5.27/5.60 thf(fact_8389_bit__horner__sum__bit__iff,axiom,
% 5.27/5.60 ! [Bs: list_o,N2: nat] :
% 5.27/5.60 ( ( bit_se1146084159140164899it_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ N2 )
% 5.27/5.60 = ( ( ord_less_nat @ N2 @ ( size_size_list_o @ Bs ) )
% 5.27/5.60 & ( nth_o @ Bs @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % bit_horner_sum_bit_iff
% 5.27/5.60 thf(fact_8390_Cauchy__iff2,axiom,
% 5.27/5.60 ( topolo4055970368930404560y_real
% 5.27/5.60 = ( ^ [X3: nat > real] :
% 5.27/5.60 ! [J3: nat] :
% 5.27/5.60 ? [M8: nat] :
% 5.27/5.60 ! [M6: nat] :
% 5.27/5.60 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.27/5.60 => ! [N: nat] :
% 5.27/5.60 ( ( ord_less_eq_nat @ M8 @ N )
% 5.27/5.60 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Cauchy_iff2
% 5.27/5.60 thf(fact_8391_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.27/5.60 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.60 ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.60 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.60 ( X4
% 5.27/5.60 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.60 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.27/5.60 => ( ! [Mi3: nat,Ma3: nat] :
% 5.27/5.60 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.60 => ( ( Xa = Mi3 )
% 5.27/5.60 | ( Xa = Ma3 ) ) )
% 5.27/5.60 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.60 ( ? [Vc: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.60 => ( ( Xa = Mi3 )
% 5.27/5.60 | ( Xa = Ma3 )
% 5.27/5.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.27/5.60 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.60 ( ? [Vd: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.60 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % VEBT_internal.membermima.elims(3)
% 5.27/5.60 thf(fact_8392_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.27/5.60 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.60 ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.60 = Y )
% 5.27/5.60 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.60 => Y )
% 5.27/5.60 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.27/5.60 => Y )
% 5.27/5.60 => ( ! [Mi3: nat,Ma3: nat] :
% 5.27/5.60 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.60 => ( Y
% 5.27/5.60 = ( ~ ( ( Xa = Mi3 )
% 5.27/5.60 | ( Xa = Ma3 ) ) ) ) )
% 5.27/5.60 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.60 ( ? [Vc: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.60 => ( Y
% 5.27/5.60 = ( ~ ( ( Xa = Mi3 )
% 5.27/5.60 | ( Xa = Ma3 )
% 5.27/5.60 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.27/5.60 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.60 ( ? [Vd: vEBT_VEBT] :
% 5.27/5.60 ( X4
% 5.27/5.60 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.60 => ( Y
% 5.27/5.60 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.60 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.60 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % VEBT_internal.membermima.elims(1)
% 5.27/5.60 thf(fact_8393_csqrt_Osimps_I1_J,axiom,
% 5.27/5.60 ! [Z: complex] :
% 5.27/5.60 ( ( re @ ( csqrt @ Z ) )
% 5.27/5.60 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % csqrt.simps(1)
% 5.27/5.60 thf(fact_8394_complex__Re__numeral,axiom,
% 5.27/5.60 ! [V: num] :
% 5.27/5.60 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.27/5.60 = ( numeral_numeral_real @ V ) ) ).
% 5.27/5.60
% 5.27/5.60 % complex_Re_numeral
% 5.27/5.60 thf(fact_8395_Re__divide__numeral,axiom,
% 5.27/5.60 ! [Z: complex,W: num] :
% 5.27/5.60 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.60 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % Re_divide_numeral
% 5.27/5.60 thf(fact_8396_lambda__zero,axiom,
% 5.27/5.60 ( ( ^ [H2: rat] : zero_zero_rat )
% 5.27/5.60 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_zero
% 5.27/5.60 thf(fact_8397_lambda__zero,axiom,
% 5.27/5.60 ( ( ^ [H2: complex] : zero_zero_complex )
% 5.27/5.60 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_zero
% 5.27/5.60 thf(fact_8398_lambda__zero,axiom,
% 5.27/5.60 ( ( ^ [H2: real] : zero_zero_real )
% 5.27/5.60 = ( times_times_real @ zero_zero_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_zero
% 5.27/5.60 thf(fact_8399_lambda__zero,axiom,
% 5.27/5.60 ( ( ^ [H2: nat] : zero_zero_nat )
% 5.27/5.60 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_zero
% 5.27/5.60 thf(fact_8400_lambda__zero,axiom,
% 5.27/5.60 ( ( ^ [H2: int] : zero_zero_int )
% 5.27/5.60 = ( times_times_int @ zero_zero_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_zero
% 5.27/5.60 thf(fact_8401_less__set__def,axiom,
% 5.27/5.60 ( ord_less_set_real
% 5.27/5.60 = ( ^ [A6: set_real,B6: set_real] :
% 5.27/5.60 ( ord_less_real_o
% 5.27/5.60 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.27/5.60 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_set_def
% 5.27/5.60 thf(fact_8402_less__set__def,axiom,
% 5.27/5.60 ( ord_less_set_nat
% 5.27/5.60 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.27/5.60 ( ord_less_nat_o
% 5.27/5.60 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.27/5.60 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_set_def
% 5.27/5.60 thf(fact_8403_less__set__def,axiom,
% 5.27/5.60 ( ord_less_set_complex
% 5.27/5.60 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.27/5.60 ( ord_less_complex_o
% 5.27/5.60 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.27/5.60 @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_set_def
% 5.27/5.60 thf(fact_8404_less__set__def,axiom,
% 5.27/5.60 ( ord_less_set_int
% 5.27/5.60 = ( ^ [A6: set_int,B6: set_int] :
% 5.27/5.60 ( ord_less_int_o
% 5.27/5.60 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.27/5.60 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_set_def
% 5.27/5.60 thf(fact_8405_less__set__def,axiom,
% 5.27/5.60 ( ord_le7866589430770878221at_nat
% 5.27/5.60 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.27/5.60 ( ord_le549003669493604880_nat_o
% 5.27/5.60 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.27/5.60 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_set_def
% 5.27/5.60 thf(fact_8406_less__eq__set__def,axiom,
% 5.27/5.60 ( ord_less_eq_set_real
% 5.27/5.60 = ( ^ [A6: set_real,B6: set_real] :
% 5.27/5.60 ( ord_less_eq_real_o
% 5.27/5.60 @ ^ [X: real] : ( member_real @ X @ A6 )
% 5.27/5.60 @ ^ [X: real] : ( member_real @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_eq_set_def
% 5.27/5.60 thf(fact_8407_less__eq__set__def,axiom,
% 5.27/5.60 ( ord_less_eq_set_nat
% 5.27/5.60 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.27/5.60 ( ord_less_eq_nat_o
% 5.27/5.60 @ ^ [X: nat] : ( member_nat @ X @ A6 )
% 5.27/5.60 @ ^ [X: nat] : ( member_nat @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_eq_set_def
% 5.27/5.60 thf(fact_8408_less__eq__set__def,axiom,
% 5.27/5.60 ( ord_le211207098394363844omplex
% 5.27/5.60 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.27/5.60 ( ord_le4573692005234683329plex_o
% 5.27/5.60 @ ^ [X: complex] : ( member_complex @ X @ A6 )
% 5.27/5.60 @ ^ [X: complex] : ( member_complex @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_eq_set_def
% 5.27/5.60 thf(fact_8409_less__eq__set__def,axiom,
% 5.27/5.60 ( ord_le3146513528884898305at_nat
% 5.27/5.60 = ( ^ [A6: set_Pr1261947904930325089at_nat,B6: set_Pr1261947904930325089at_nat] :
% 5.27/5.60 ( ord_le704812498762024988_nat_o
% 5.27/5.60 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ A6 )
% 5.27/5.60 @ ^ [X: product_prod_nat_nat] : ( member8440522571783428010at_nat @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_eq_set_def
% 5.27/5.60 thf(fact_8410_less__eq__set__def,axiom,
% 5.27/5.60 ( ord_less_eq_set_int
% 5.27/5.60 = ( ^ [A6: set_int,B6: set_int] :
% 5.27/5.60 ( ord_less_eq_int_o
% 5.27/5.60 @ ^ [X: int] : ( member_int @ X @ A6 )
% 5.27/5.60 @ ^ [X: int] : ( member_int @ X @ B6 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % less_eq_set_def
% 5.27/5.60 thf(fact_8411_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_Pr1261947904930325089at_nat,P: product_prod_nat_nat > $o] :
% 5.27/5.60 ( ord_le3146513528884898305at_nat
% 5.27/5.60 @ ( collec3392354462482085612at_nat
% 5.27/5.60 @ ^ [X: product_prod_nat_nat] :
% 5.27/5.60 ( ( member8440522571783428010at_nat @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8412_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_complex,P: complex > $o] :
% 5.27/5.60 ( ord_le211207098394363844omplex
% 5.27/5.60 @ ( collect_complex
% 5.27/5.60 @ ^ [X: complex] :
% 5.27/5.60 ( ( member_complex @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8413_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_real,P: real > $o] :
% 5.27/5.60 ( ord_less_eq_set_real
% 5.27/5.60 @ ( collect_real
% 5.27/5.60 @ ^ [X: real] :
% 5.27/5.60 ( ( member_real @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8414_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_list_nat,P: list_nat > $o] :
% 5.27/5.60 ( ord_le6045566169113846134st_nat
% 5.27/5.60 @ ( collect_list_nat
% 5.27/5.60 @ ^ [X: list_nat] :
% 5.27/5.60 ( ( member_list_nat @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8415_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_nat,P: nat > $o] :
% 5.27/5.60 ( ord_less_eq_set_nat
% 5.27/5.60 @ ( collect_nat
% 5.27/5.60 @ ^ [X: nat] :
% 5.27/5.60 ( ( member_nat @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8416_Collect__subset,axiom,
% 5.27/5.60 ! [A2: set_int,P: int > $o] :
% 5.27/5.60 ( ord_less_eq_set_int
% 5.27/5.60 @ ( collect_int
% 5.27/5.60 @ ^ [X: int] :
% 5.27/5.60 ( ( member_int @ X @ A2 )
% 5.27/5.60 & ( P @ X ) ) )
% 5.27/5.60 @ A2 ) ).
% 5.27/5.60
% 5.27/5.60 % Collect_subset
% 5.27/5.60 thf(fact_8417_subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ord_le211207098394363844omplex
% 5.27/5.60 @ ( collect_complex
% 5.27/5.60 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.27/5.60 @ ( collect_complex
% 5.27/5.60 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.27/5.60 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.27/5.60
% 5.27/5.60 % subset_divisors_dvd
% 5.27/5.60 thf(fact_8418_subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_eq_set_real
% 5.27/5.60 @ ( collect_real
% 5.27/5.60 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.27/5.60 @ ( collect_real
% 5.27/5.60 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.27/5.60 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.27/5.60
% 5.27/5.60 % subset_divisors_dvd
% 5.27/5.60 thf(fact_8419_subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: nat,B: nat] :
% 5.27/5.60 ( ( ord_less_eq_set_nat
% 5.27/5.60 @ ( collect_nat
% 5.27/5.60 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.27/5.60 @ ( collect_nat
% 5.27/5.60 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.27/5.60 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.27/5.60
% 5.27/5.60 % subset_divisors_dvd
% 5.27/5.60 thf(fact_8420_subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: code_integer,B: code_integer] :
% 5.27/5.60 ( ( ord_le7084787975880047091nteger
% 5.27/5.60 @ ( collect_Code_integer
% 5.27/5.60 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.27/5.60 @ ( collect_Code_integer
% 5.27/5.60 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.27/5.60 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.27/5.60
% 5.27/5.60 % subset_divisors_dvd
% 5.27/5.60 thf(fact_8421_subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: int,B: int] :
% 5.27/5.60 ( ( ord_less_eq_set_int
% 5.27/5.60 @ ( collect_int
% 5.27/5.60 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.27/5.60 @ ( collect_int
% 5.27/5.60 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.27/5.60 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.27/5.60
% 5.27/5.60 % subset_divisors_dvd
% 5.27/5.60 thf(fact_8422_strict__subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: complex,B: complex] :
% 5.27/5.60 ( ( ord_less_set_complex
% 5.27/5.60 @ ( collect_complex
% 5.27/5.60 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ A ) )
% 5.27/5.60 @ ( collect_complex
% 5.27/5.60 @ ^ [C2: complex] : ( dvd_dvd_complex @ C2 @ B ) ) )
% 5.27/5.60 = ( ( dvd_dvd_complex @ A @ B )
% 5.27/5.60 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % strict_subset_divisors_dvd
% 5.27/5.60 thf(fact_8423_strict__subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: real,B: real] :
% 5.27/5.60 ( ( ord_less_set_real
% 5.27/5.60 @ ( collect_real
% 5.27/5.60 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ A ) )
% 5.27/5.60 @ ( collect_real
% 5.27/5.60 @ ^ [C2: real] : ( dvd_dvd_real @ C2 @ B ) ) )
% 5.27/5.60 = ( ( dvd_dvd_real @ A @ B )
% 5.27/5.60 & ~ ( dvd_dvd_real @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % strict_subset_divisors_dvd
% 5.27/5.60 thf(fact_8424_strict__subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: nat,B: nat] :
% 5.27/5.60 ( ( ord_less_set_nat
% 5.27/5.60 @ ( collect_nat
% 5.27/5.60 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ A ) )
% 5.27/5.60 @ ( collect_nat
% 5.27/5.60 @ ^ [C2: nat] : ( dvd_dvd_nat @ C2 @ B ) ) )
% 5.27/5.60 = ( ( dvd_dvd_nat @ A @ B )
% 5.27/5.60 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % strict_subset_divisors_dvd
% 5.27/5.60 thf(fact_8425_strict__subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: int,B: int] :
% 5.27/5.60 ( ( ord_less_set_int
% 5.27/5.60 @ ( collect_int
% 5.27/5.60 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ A ) )
% 5.27/5.60 @ ( collect_int
% 5.27/5.60 @ ^ [C2: int] : ( dvd_dvd_int @ C2 @ B ) ) )
% 5.27/5.60 = ( ( dvd_dvd_int @ A @ B )
% 5.27/5.60 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % strict_subset_divisors_dvd
% 5.27/5.60 thf(fact_8426_strict__subset__divisors__dvd,axiom,
% 5.27/5.60 ! [A: code_integer,B: code_integer] :
% 5.27/5.60 ( ( ord_le1307284697595431911nteger
% 5.27/5.60 @ ( collect_Code_integer
% 5.27/5.60 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ A ) )
% 5.27/5.60 @ ( collect_Code_integer
% 5.27/5.60 @ ^ [C2: code_integer] : ( dvd_dvd_Code_integer @ C2 @ B ) ) )
% 5.27/5.60 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.27/5.60 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % strict_subset_divisors_dvd
% 5.27/5.60 thf(fact_8427_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_rat @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8428_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numera1916890842035813515d_enat @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8429_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numera6690914467698888265omplex @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8430_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_real @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8431_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_nat @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8432_numeral__code_I2_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_int @ ( bit0 @ N2 ) )
% 5.27/5.60 = ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(2)
% 5.27/5.60 thf(fact_8433_lambda__one,axiom,
% 5.27/5.60 ( ( ^ [X: rat] : X )
% 5.27/5.60 = ( times_times_rat @ one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_one
% 5.27/5.60 thf(fact_8434_lambda__one,axiom,
% 5.27/5.60 ( ( ^ [X: complex] : X )
% 5.27/5.60 = ( times_times_complex @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_one
% 5.27/5.60 thf(fact_8435_lambda__one,axiom,
% 5.27/5.60 ( ( ^ [X: real] : X )
% 5.27/5.60 = ( times_times_real @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_one
% 5.27/5.60 thf(fact_8436_lambda__one,axiom,
% 5.27/5.60 ( ( ^ [X: nat] : X )
% 5.27/5.60 = ( times_times_nat @ one_one_nat ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_one
% 5.27/5.60 thf(fact_8437_lambda__one,axiom,
% 5.27/5.60 ( ( ^ [X: int] : X )
% 5.27/5.60 = ( times_times_int @ one_one_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % lambda_one
% 5.27/5.60 thf(fact_8438_nat__less__as__int,axiom,
% 5.27/5.60 ( ord_less_nat
% 5.27/5.60 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nat_less_as_int
% 5.27/5.60 thf(fact_8439_nat__leq__as__int,axiom,
% 5.27/5.60 ( ord_less_eq_nat
% 5.27/5.60 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % nat_leq_as_int
% 5.27/5.60 thf(fact_8440_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_rat @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N2 ) @ ( numeral_numeral_rat @ N2 ) ) @ one_one_rat ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8441_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numera1916890842035813515d_enat @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_p3455044024723400733d_enat @ ( plus_p3455044024723400733d_enat @ ( numera1916890842035813515d_enat @ N2 ) @ ( numera1916890842035813515d_enat @ N2 ) ) @ one_on7984719198319812577d_enat ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8442_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numera6690914467698888265omplex @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N2 ) @ ( numera6690914467698888265omplex @ N2 ) ) @ one_one_complex ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8443_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_real @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N2 ) @ ( numeral_numeral_real @ N2 ) ) @ one_one_real ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8444_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_nat @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N2 ) @ ( numeral_numeral_nat @ N2 ) ) @ one_one_nat ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8445_numeral__code_I3_J,axiom,
% 5.27/5.60 ! [N2: num] :
% 5.27/5.60 ( ( numeral_numeral_int @ ( bit1 @ N2 ) )
% 5.27/5.60 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N2 ) @ ( numeral_numeral_int @ N2 ) ) @ one_one_int ) ) ).
% 5.27/5.60
% 5.27/5.60 % numeral_code(3)
% 5.27/5.60 thf(fact_8446_power__numeral__even,axiom,
% 5.27/5.60 ! [Z: complex,W: num] :
% 5.27/5.60 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.27/5.60 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.60
% 5.27/5.60 % power_numeral_even
% 5.27/5.60 thf(fact_8447_power__numeral__even,axiom,
% 5.27/5.60 ! [Z: real,W: num] :
% 5.27/5.60 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.27/5.61 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_even
% 5.27/5.61 thf(fact_8448_power__numeral__even,axiom,
% 5.27/5.61 ! [Z: nat,W: num] :
% 5.27/5.61 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.27/5.61 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_even
% 5.27/5.61 thf(fact_8449_power__numeral__even,axiom,
% 5.27/5.61 ! [Z: int,W: num] :
% 5.27/5.61 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.27/5.61 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_even
% 5.27/5.61 thf(fact_8450_power__numeral__odd,axiom,
% 5.27/5.61 ! [Z: complex,W: num] :
% 5.27/5.61 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.27/5.61 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_odd
% 5.27/5.61 thf(fact_8451_power__numeral__odd,axiom,
% 5.27/5.61 ! [Z: real,W: num] :
% 5.27/5.61 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.27/5.61 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_odd
% 5.27/5.61 thf(fact_8452_power__numeral__odd,axiom,
% 5.27/5.61 ! [Z: nat,W: num] :
% 5.27/5.61 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.27/5.61 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_odd
% 5.27/5.61 thf(fact_8453_power__numeral__odd,axiom,
% 5.27/5.61 ! [Z: int,W: num] :
% 5.27/5.61 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.27/5.61 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % power_numeral_odd
% 5.27/5.61 thf(fact_8454_nat__plus__as__int,axiom,
% 5.27/5.61 ( plus_plus_nat
% 5.27/5.61 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % nat_plus_as_int
% 5.27/5.61 thf(fact_8455_nat__div__as__int,axiom,
% 5.27/5.61 ( divide_divide_nat
% 5.27/5.61 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % nat_div_as_int
% 5.27/5.61 thf(fact_8456_nat__mod__as__int,axiom,
% 5.27/5.61 ( modulo_modulo_nat
% 5.27/5.61 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % nat_mod_as_int
% 5.27/5.61 thf(fact_8457_complex__Re__le__cmod,axiom,
% 5.27/5.61 ! [X4: complex] : ( ord_less_eq_real @ ( re @ X4 ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % complex_Re_le_cmod
% 5.27/5.61 thf(fact_8458_one__complex_Osimps_I1_J,axiom,
% 5.27/5.61 ( ( re @ one_one_complex )
% 5.27/5.61 = one_one_real ) ).
% 5.27/5.61
% 5.27/5.61 % one_complex.simps(1)
% 5.27/5.61 thf(fact_8459_set__conv__nth,axiom,
% 5.27/5.61 ( set_complex2
% 5.27/5.61 = ( ^ [Xs3: list_complex] :
% 5.27/5.61 ( collect_complex
% 5.27/5.61 @ ^ [Uu3: complex] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_complex @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_s3451745648224563538omplex @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8460_set__conv__nth,axiom,
% 5.27/5.61 ( set_real2
% 5.27/5.61 = ( ^ [Xs3: list_real] :
% 5.27/5.61 ( collect_real
% 5.27/5.61 @ ^ [Uu3: real] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_real @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_size_list_real @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8461_set__conv__nth,axiom,
% 5.27/5.61 ( set_list_nat2
% 5.27/5.61 = ( ^ [Xs3: list_list_nat] :
% 5.27/5.61 ( collect_list_nat
% 5.27/5.61 @ ^ [Uu3: list_nat] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_list_nat @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_s3023201423986296836st_nat @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8462_set__conv__nth,axiom,
% 5.27/5.61 ( set_VEBT_VEBT2
% 5.27/5.61 = ( ^ [Xs3: list_VEBT_VEBT] :
% 5.27/5.61 ( collect_VEBT_VEBT
% 5.27/5.61 @ ^ [Uu3: vEBT_VEBT] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_VEBT_VEBT @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_s6755466524823107622T_VEBT @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8463_set__conv__nth,axiom,
% 5.27/5.61 ( set_o2
% 5.27/5.61 = ( ^ [Xs3: list_o] :
% 5.27/5.61 ( collect_o
% 5.27/5.61 @ ^ [Uu3: $o] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_o @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_size_list_o @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8464_set__conv__nth,axiom,
% 5.27/5.61 ( set_nat2
% 5.27/5.61 = ( ^ [Xs3: list_nat] :
% 5.27/5.61 ( collect_nat
% 5.27/5.61 @ ^ [Uu3: nat] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_nat @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_size_list_nat @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8465_set__conv__nth,axiom,
% 5.27/5.61 ( set_int2
% 5.27/5.61 = ( ^ [Xs3: list_int] :
% 5.27/5.61 ( collect_int
% 5.27/5.61 @ ^ [Uu3: int] :
% 5.27/5.61 ? [I3: nat] :
% 5.27/5.61 ( ( Uu3
% 5.27/5.61 = ( nth_int @ Xs3 @ I3 ) )
% 5.27/5.61 & ( ord_less_nat @ I3 @ ( size_size_list_int @ Xs3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_conv_nth
% 5.27/5.61 thf(fact_8466_diff__nat__eq__if,axiom,
% 5.27/5.61 ! [Z6: int,Z: int] :
% 5.27/5.61 ( ( ( ord_less_int @ Z6 @ zero_zero_int )
% 5.27/5.61 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.27/5.61 = ( nat2 @ Z ) ) )
% 5.27/5.61 & ( ~ ( ord_less_int @ Z6 @ zero_zero_int )
% 5.27/5.61 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z6 ) )
% 5.27/5.61 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z6 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diff_nat_eq_if
% 5.27/5.61 thf(fact_8467_abs__Re__le__cmod,axiom,
% 5.27/5.61 ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % abs_Re_le_cmod
% 5.27/5.61 thf(fact_8468_Re__csqrt,axiom,
% 5.27/5.61 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Re_csqrt
% 5.27/5.61 thf(fact_8469_set__decode__def,axiom,
% 5.27/5.61 ( nat_set_decode
% 5.27/5.61 = ( ^ [X: nat] :
% 5.27/5.61 ( collect_nat
% 5.27/5.61 @ ^ [N: nat] :
% 5.27/5.61 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_decode_def
% 5.27/5.61 thf(fact_8470_signed__take__bit__code,axiom,
% 5.27/5.61 ( bit_ri6519982836138164636nteger
% 5.27/5.61 = ( ^ [N: nat,A3: code_integer] : ( if_Code_integer @ ( bit_se9216721137139052372nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_p5714425477246183910nteger @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) @ ( bit_se7788150548672797655nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) @ ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A3 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % signed_take_bit_code
% 5.27/5.61 thf(fact_8471_signed__take__bit__code,axiom,
% 5.27/5.61 ( bit_ri631733984087533419it_int
% 5.27/5.61 = ( ^ [N: nat,A3: int] : ( if_int @ ( bit_se1146084159140164899it_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ N ) @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) @ ( bit_se545348938243370406it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) ) ) @ ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A3 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % signed_take_bit_code
% 5.27/5.61 thf(fact_8472_pochhammer__code,axiom,
% 5.27/5.61 ( comm_s4028243227959126397er_rat
% 5.27/5.61 = ( ^ [A3: rat,N: nat] :
% 5.27/5.61 ( if_rat @ ( N = zero_zero_nat ) @ one_one_rat
% 5.27/5.61 @ ( set_fo1949268297981939178at_rat
% 5.27/5.61 @ ^ [O: nat] : ( times_times_rat @ ( plus_plus_rat @ A3 @ ( semiri681578069525770553at_rat @ O ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.27/5.61 @ one_one_rat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_code
% 5.27/5.61 thf(fact_8473_pochhammer__code,axiom,
% 5.27/5.61 ( comm_s2602460028002588243omplex
% 5.27/5.61 = ( ^ [A3: complex,N: nat] :
% 5.27/5.61 ( if_complex @ ( N = zero_zero_nat ) @ one_one_complex
% 5.27/5.61 @ ( set_fo1517530859248394432omplex
% 5.27/5.61 @ ^ [O: nat] : ( times_times_complex @ ( plus_plus_complex @ A3 @ ( semiri8010041392384452111omplex @ O ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.27/5.61 @ one_one_complex ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_code
% 5.27/5.61 thf(fact_8474_pochhammer__code,axiom,
% 5.27/5.61 ( comm_s7457072308508201937r_real
% 5.27/5.61 = ( ^ [A3: real,N: nat] :
% 5.27/5.61 ( if_real @ ( N = zero_zero_nat ) @ one_one_real
% 5.27/5.61 @ ( set_fo3111899725591712190t_real
% 5.27/5.61 @ ^ [O: nat] : ( times_times_real @ ( plus_plus_real @ A3 @ ( semiri5074537144036343181t_real @ O ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.27/5.61 @ one_one_real ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_code
% 5.27/5.61 thf(fact_8475_pochhammer__code,axiom,
% 5.27/5.61 ( comm_s4660882817536571857er_int
% 5.27/5.61 = ( ^ [A3: int,N: nat] :
% 5.27/5.61 ( if_int @ ( N = zero_zero_nat ) @ one_one_int
% 5.27/5.61 @ ( set_fo2581907887559384638at_int
% 5.27/5.61 @ ^ [O: nat] : ( times_times_int @ ( plus_plus_int @ A3 @ ( semiri1314217659103216013at_int @ O ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.27/5.61 @ one_one_int ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_code
% 5.27/5.61 thf(fact_8476_pochhammer__code,axiom,
% 5.27/5.61 ( comm_s4663373288045622133er_nat
% 5.27/5.61 = ( ^ [A3: nat,N: nat] :
% 5.27/5.61 ( if_nat @ ( N = zero_zero_nat ) @ one_one_nat
% 5.27/5.61 @ ( set_fo2584398358068434914at_nat
% 5.27/5.61 @ ^ [O: nat] : ( times_times_nat @ ( plus_plus_nat @ A3 @ ( semiri1316708129612266289at_nat @ O ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ N @ one_one_nat )
% 5.27/5.61 @ one_one_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_code
% 5.27/5.61 thf(fact_8477_cmod__plus__Re__le__0__iff,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.27/5.61 = ( ( re @ Z )
% 5.27/5.61 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cmod_plus_Re_le_0_iff
% 5.27/5.61 thf(fact_8478_gbinomial__code,axiom,
% 5.27/5.61 ( gbinomial_rat
% 5.27/5.61 = ( ^ [A3: rat,K3: nat] :
% 5.27/5.61 ( if_rat @ ( K3 = zero_zero_nat ) @ one_one_rat
% 5.27/5.61 @ ( divide_divide_rat
% 5.27/5.61 @ ( set_fo1949268297981939178at_rat
% 5.27/5.61 @ ^ [L2: nat] : ( times_times_rat @ ( minus_minus_rat @ A3 @ ( semiri681578069525770553at_rat @ L2 ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.27/5.61 @ one_one_rat )
% 5.27/5.61 @ ( semiri773545260158071498ct_rat @ K3 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_code
% 5.27/5.61 thf(fact_8479_gbinomial__code,axiom,
% 5.27/5.61 ( gbinomial_complex
% 5.27/5.61 = ( ^ [A3: complex,K3: nat] :
% 5.27/5.61 ( if_complex @ ( K3 = zero_zero_nat ) @ one_one_complex
% 5.27/5.61 @ ( divide1717551699836669952omplex
% 5.27/5.61 @ ( set_fo1517530859248394432omplex
% 5.27/5.61 @ ^ [L2: nat] : ( times_times_complex @ ( minus_minus_complex @ A3 @ ( semiri8010041392384452111omplex @ L2 ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.27/5.61 @ one_one_complex )
% 5.27/5.61 @ ( semiri5044797733671781792omplex @ K3 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_code
% 5.27/5.61 thf(fact_8480_gbinomial__code,axiom,
% 5.27/5.61 ( gbinomial_real
% 5.27/5.61 = ( ^ [A3: real,K3: nat] :
% 5.27/5.61 ( if_real @ ( K3 = zero_zero_nat ) @ one_one_real
% 5.27/5.61 @ ( divide_divide_real
% 5.27/5.61 @ ( set_fo3111899725591712190t_real
% 5.27/5.61 @ ^ [L2: nat] : ( times_times_real @ ( minus_minus_real @ A3 @ ( semiri5074537144036343181t_real @ L2 ) ) )
% 5.27/5.61 @ zero_zero_nat
% 5.27/5.61 @ ( minus_minus_nat @ K3 @ one_one_nat )
% 5.27/5.61 @ one_one_real )
% 5.27/5.61 @ ( semiri2265585572941072030t_real @ K3 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_code
% 5.27/5.61 thf(fact_8481_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.27/5.61 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X4: nat] :
% 5.27/5.61 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X4 )
% 5.27/5.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.simps(3)
% 5.27/5.61 thf(fact_8482_CauchyD,axiom,
% 5.27/5.61 ! [X8: nat > complex,E2: real] :
% 5.27/5.61 ( ( topolo6517432010174082258omplex @ X8 )
% 5.27/5.61 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.61 => ? [M9: nat] :
% 5.27/5.61 ! [M2: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M9 @ M2 )
% 5.27/5.61 => ! [N6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.27/5.61 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % CauchyD
% 5.27/5.61 thf(fact_8483_CauchyD,axiom,
% 5.27/5.61 ! [X8: nat > real,E2: real] :
% 5.27/5.61 ( ( topolo4055970368930404560y_real @ X8 )
% 5.27/5.61 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.61 => ? [M9: nat] :
% 5.27/5.61 ! [M2: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M9 @ M2 )
% 5.27/5.61 => ! [N6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M9 @ N6 )
% 5.27/5.61 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M2 ) @ ( X8 @ N6 ) ) ) @ E2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % CauchyD
% 5.27/5.61 thf(fact_8484_CauchyI,axiom,
% 5.27/5.61 ! [X8: nat > complex] :
% 5.27/5.61 ( ! [E: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E )
% 5.27/5.61 => ? [M10: nat] :
% 5.27/5.61 ! [M5: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M10 @ M5 )
% 5.27/5.61 => ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M10 @ N3 )
% 5.27/5.61 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 5.27/5.61 => ( topolo6517432010174082258omplex @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % CauchyI
% 5.27/5.61 thf(fact_8485_CauchyI,axiom,
% 5.27/5.61 ! [X8: nat > real] :
% 5.27/5.61 ( ! [E: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E )
% 5.27/5.61 => ? [M10: nat] :
% 5.27/5.61 ! [M5: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M10 @ M5 )
% 5.27/5.61 => ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M10 @ N3 )
% 5.27/5.61 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) ) @ E ) ) ) )
% 5.27/5.61 => ( topolo4055970368930404560y_real @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % CauchyI
% 5.27/5.61 thf(fact_8486_Cauchy__iff,axiom,
% 5.27/5.61 ( topolo6517432010174082258omplex
% 5.27/5.61 = ( ^ [X3: nat > complex] :
% 5.27/5.61 ! [E3: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.27/5.61 => ? [M8: nat] :
% 5.27/5.61 ! [M6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.27/5.61 => ! [N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M8 @ N )
% 5.27/5.61 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Cauchy_iff
% 5.27/5.61 thf(fact_8487_Cauchy__iff,axiom,
% 5.27/5.61 ( topolo4055970368930404560y_real
% 5.27/5.61 = ( ^ [X3: nat > real] :
% 5.27/5.61 ! [E3: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E3 )
% 5.27/5.61 => ? [M8: nat] :
% 5.27/5.61 ! [M6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M8 @ M6 )
% 5.27/5.61 => ! [N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M8 @ N )
% 5.27/5.61 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) ) @ E3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Cauchy_iff
% 5.27/5.61 thf(fact_8488_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.27/5.61 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd2: vEBT_VEBT,X4: nat] :
% 5.27/5.61 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd2 ) @ X4 )
% 5.27/5.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.simps(5)
% 5.27/5.61 thf(fact_8489_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.27/5.61 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X4: nat] :
% 5.27/5.61 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc2 ) @ X4 )
% 5.27/5.61 = ( ( X4 = Mi )
% 5.27/5.61 | ( X4 = Ma )
% 5.27/5.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ X4 @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.simps(4)
% 5.27/5.61 thf(fact_8490_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.61 ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 = Y )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ( Y
% 5.27/5.61 = ( ~ ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) ) ) )
% 5.27/5.61 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.27/5.61 => Y )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.61 ( ? [S3: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ( Y
% 5.27/5.61 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.elims(1)
% 5.27/5.61 thf(fact_8491_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ~ ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.61 ( ? [S3: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.elims(2)
% 5.27/5.61 thf(fact_8492_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) )
% 5.27/5.61 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.61 ( ? [S3: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.elims(3)
% 5.27/5.61 thf(fact_8493_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat] :
% 5.27/5.61 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.61 => ~ ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.61 ( ? [Vc: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.61 => ~ ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 )
% 5.27/5.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.27/5.61 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.27/5.61 ( ? [Vd: vEBT_VEBT] :
% 5.27/5.61 ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.elims(2)
% 5.27/5.61 thf(fact_8494_of__int__code__if,axiom,
% 5.27/5.61 ( ring_1_of_int_real
% 5.27/5.61 = ( ^ [K3: int] :
% 5.27/5.61 ( if_real @ ( K3 = zero_zero_int ) @ zero_zero_real
% 5.27/5.61 @ ( if_real @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.61 @ ( if_real
% 5.27/5.61 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_int_code_if
% 5.27/5.61 thf(fact_8495_of__int__code__if,axiom,
% 5.27/5.61 ( ring_1_of_int_int
% 5.27/5.61 = ( ^ [K3: int] :
% 5.27/5.61 ( if_int @ ( K3 = zero_zero_int ) @ zero_zero_int
% 5.27/5.61 @ ( if_int @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.61 @ ( if_int
% 5.27/5.61 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_int_code_if
% 5.27/5.61 thf(fact_8496_of__int__code__if,axiom,
% 5.27/5.61 ( ring_17405671764205052669omplex
% 5.27/5.61 = ( ^ [K3: int] :
% 5.27/5.61 ( if_complex @ ( K3 = zero_zero_int ) @ zero_zero_complex
% 5.27/5.61 @ ( if_complex @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.61 @ ( if_complex
% 5.27/5.61 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_int_code_if
% 5.27/5.61 thf(fact_8497_of__int__code__if,axiom,
% 5.27/5.61 ( ring_18347121197199848620nteger
% 5.27/5.61 = ( ^ [K3: int] :
% 5.27/5.61 ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.27/5.61 @ ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.61 @ ( if_Code_integer
% 5.27/5.61 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_int_code_if
% 5.27/5.61 thf(fact_8498_of__int__code__if,axiom,
% 5.27/5.61 ( ring_1_of_int_rat
% 5.27/5.61 = ( ^ [K3: int] :
% 5.27/5.61 ( if_rat @ ( K3 = zero_zero_int ) @ zero_zero_rat
% 5.27/5.61 @ ( if_rat @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.61 @ ( if_rat
% 5.27/5.61 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_int_code_if
% 5.27/5.61 thf(fact_8499_monoseq__arctan__series,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.61 => ( topolo6980174941875973593q_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_arctan_series
% 5.27/5.61 thf(fact_8500_csqrt_Ocode,axiom,
% 5.27/5.61 ( csqrt
% 5.27/5.61 = ( ^ [Z5: complex] :
% 5.27/5.61 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.61 @ ( times_times_real
% 5.27/5.61 @ ( if_real
% 5.27/5.61 @ ( ( im @ Z5 )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 @ one_one_real
% 5.27/5.61 @ ( sgn_sgn_real @ ( im @ Z5 ) ) )
% 5.27/5.61 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z5 ) @ ( re @ Z5 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt.code
% 5.27/5.61 thf(fact_8501_ln__series,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ( ord_less_real @ X4 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.61 => ( ( ln_ln_real @ X4 )
% 5.27/5.61 = ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % ln_series
% 5.27/5.61 thf(fact_8502_powser__zero,axiom,
% 5.27/5.61 ! [F: nat > complex] :
% 5.27/5.61 ( ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) )
% 5.27/5.61 = ( F @ zero_zero_nat ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_zero
% 5.27/5.61 thf(fact_8503_powser__zero,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) )
% 5.27/5.61 = ( F @ zero_zero_nat ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_zero
% 5.27/5.61 thf(fact_8504_Re__power__real,axiom,
% 5.27/5.61 ! [X4: complex,N2: nat] :
% 5.27/5.61 ( ( ( im @ X4 )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 => ( ( re @ ( power_power_complex @ X4 @ N2 ) )
% 5.27/5.61 = ( power_power_real @ ( re @ X4 ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Re_power_real
% 5.27/5.61 thf(fact_8505_Im__divide__numeral,axiom,
% 5.27/5.61 ! [Z: complex,W: num] :
% 5.27/5.61 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.27/5.61 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Im_divide_numeral
% 5.27/5.61 thf(fact_8506_csqrt__of__real__nonneg,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( ( im @ X4 )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) )
% 5.27/5.61 => ( ( csqrt @ X4 )
% 5.27/5.61 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X4 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_of_real_nonneg
% 5.27/5.61 thf(fact_8507_csqrt__minus,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( ( ord_less_real @ ( im @ X4 ) @ zero_zero_real )
% 5.27/5.61 | ( ( ( im @ X4 )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X4 ) ) ) )
% 5.27/5.61 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X4 ) )
% 5.27/5.61 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_minus
% 5.27/5.61 thf(fact_8508_csqrt__of__real__nonpos,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( ( im @ X4 )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ ( re @ X4 ) @ zero_zero_real )
% 5.27/5.61 => ( ( csqrt @ X4 )
% 5.27/5.61 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X4 ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_of_real_nonpos
% 5.27/5.61 thf(fact_8509_imaginary__unit_Osimps_I2_J,axiom,
% 5.27/5.61 ( ( im @ imaginary_unit )
% 5.27/5.61 = one_one_real ) ).
% 5.27/5.61
% 5.27/5.61 % imaginary_unit.simps(2)
% 5.27/5.61 thf(fact_8510_abs__Im__le__cmod,axiom,
% 5.27/5.61 ! [X4: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( real_V1022390504157884413omplex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % abs_Im_le_cmod
% 5.27/5.61 thf(fact_8511_cmod__Im__le__iff,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( ( ( re @ X4 )
% 5.27/5.61 = ( re @ Y ) )
% 5.27/5.61 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.27/5.61 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X4 ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cmod_Im_le_iff
% 5.27/5.61 thf(fact_8512_cmod__Re__le__iff,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( ( ( im @ X4 )
% 5.27/5.61 = ( im @ Y ) )
% 5.27/5.61 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X4 ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.27/5.61 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X4 ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cmod_Re_le_iff
% 5.27/5.61 thf(fact_8513_csqrt__principal,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.27/5.61 | ( ( ( re @ ( csqrt @ Z ) )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_principal
% 5.27/5.61 thf(fact_8514_cmod__le,axiom,
% 5.27/5.61 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cmod_le
% 5.27/5.61 thf(fact_8515_monoseq__realpow,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.61 => ( topolo6980174941875973593q_real @ ( power_power_real @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_realpow
% 5.27/5.61 thf(fact_8516_cmod__power2,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.61 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cmod_power2
% 5.27/5.61 thf(fact_8517_Im__power2,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( im @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.61 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X4 ) ) @ ( im @ X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Im_power2
% 5.27/5.61 thf(fact_8518_Re__power2,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( re @ ( power_power_complex @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.61 = ( minus_minus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Re_power2
% 5.27/5.61 thf(fact_8519_complex__eq__0,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( Z = zero_zero_complex )
% 5.27/5.61 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.61 = zero_zero_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % complex_eq_0
% 5.27/5.61 thf(fact_8520_norm__complex__def,axiom,
% 5.27/5.61 ( real_V1022390504157884413omplex
% 5.27/5.61 = ( ^ [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 ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % norm_complex_def
% 5.27/5.61 thf(fact_8521_inverse__complex_Osimps_I1_J,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( re @ ( invers8013647133539491842omplex @ X4 ) )
% 5.27/5.61 = ( divide_divide_real @ ( re @ X4 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % inverse_complex.simps(1)
% 5.27/5.61 thf(fact_8522_complex__neq__0,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( Z != zero_zero_complex )
% 5.27/5.61 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % complex_neq_0
% 5.27/5.61 thf(fact_8523_Re__divide,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( ( re @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 5.27/5.61 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Re_divide
% 5.27/5.61 thf(fact_8524_csqrt__unique,axiom,
% 5.27/5.61 ! [W: complex,Z: complex] :
% 5.27/5.61 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.61 = Z )
% 5.27/5.61 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.27/5.61 | ( ( ( re @ W )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.27/5.61 => ( ( csqrt @ Z )
% 5.27/5.61 = W ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_unique
% 5.27/5.61 thf(fact_8525_csqrt__square,axiom,
% 5.27/5.61 ! [B: complex] :
% 5.27/5.61 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.27/5.61 | ( ( ( re @ B )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.27/5.61 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.61 = B ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt_square
% 5.27/5.61 thf(fact_8526_inverse__complex_Osimps_I2_J,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( im @ ( invers8013647133539491842omplex @ X4 ) )
% 5.27/5.61 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X4 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X4 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % inverse_complex.simps(2)
% 5.27/5.61 thf(fact_8527_Im__divide,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( ( im @ ( divide1717551699836669952omplex @ X4 @ Y ) )
% 5.27/5.61 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X4 ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X4 ) @ ( 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 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Im_divide
% 5.27/5.61 thf(fact_8528_complex__abs__le__norm,axiom,
% 5.27/5.61 ! [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 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % complex_abs_le_norm
% 5.27/5.61 thf(fact_8529_complex__unit__circle,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( Z != zero_zero_complex )
% 5.27/5.61 => ( ( 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 ) ) ) )
% 5.27/5.61 = one_one_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % complex_unit_circle
% 5.27/5.61 thf(fact_8530_inverse__complex_Ocode,axiom,
% 5.27/5.61 ( invers8013647133539491842omplex
% 5.27/5.61 = ( ^ [X: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % inverse_complex.code
% 5.27/5.61 thf(fact_8531_Complex__divide,axiom,
% 5.27/5.61 ( divide1717551699836669952omplex
% 5.27/5.61 = ( ^ [X: complex,Y5: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y5 ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y5 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y5 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Complex_divide
% 5.27/5.61 thf(fact_8532_pi__series,axiom,
% 5.27/5.61 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.27/5.61 = ( suminf_real
% 5.27/5.61 @ ^ [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 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pi_series
% 5.27/5.61 thf(fact_8533_csqrt_Osimps_I2_J,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( im @ ( csqrt @ Z ) )
% 5.27/5.61 = ( times_times_real
% 5.27/5.61 @ ( if_real
% 5.27/5.61 @ ( ( im @ Z )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 @ one_one_real
% 5.27/5.61 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.27/5.61 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % csqrt.simps(2)
% 5.27/5.61 thf(fact_8534_arctan__series,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.61 => ( ( arctan @ X4 )
% 5.27/5.61 = ( suminf_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % arctan_series
% 5.27/5.61 thf(fact_8535_suminf__geometric,axiom,
% 5.27/5.61 ! [C: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.27/5.61 => ( ( suminf_real @ ( power_power_real @ C ) )
% 5.27/5.61 = ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_geometric
% 5.27/5.61 thf(fact_8536_suminf__geometric,axiom,
% 5.27/5.61 ! [C: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.27/5.61 => ( ( suminf_complex @ ( power_power_complex @ C ) )
% 5.27/5.61 = ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_geometric
% 5.27/5.61 thf(fact_8537_summable__arctan__series,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_arctan_series
% 5.27/5.61 thf(fact_8538_vebt__buildup_Oelims,axiom,
% 5.27/5.61 ! [X4: nat,Y: vEBT_VEBT] :
% 5.27/5.61 ( ( ( vEBT_vebt_buildup @ X4 )
% 5.27/5.61 = Y )
% 5.27/5.61 => ( ( ( X4 = zero_zero_nat )
% 5.27/5.61 => ( Y
% 5.27/5.61 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.27/5.61 => ( ( ( X4
% 5.27/5.61 = ( suc @ zero_zero_nat ) )
% 5.27/5.61 => ( Y
% 5.27/5.61 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.27/5.61 => ~ ! [Va2: nat] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.61 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.61 => ( Y
% 5.27/5.61 = ( 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 ) ) ) ) ) ) )
% 5.27/5.61 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.61 => ( Y
% 5.27/5.61 = ( 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 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % vebt_buildup.elims
% 5.27/5.61 thf(fact_8539_Im__Reals__divide,axiom,
% 5.27/5.61 ! [R3: complex,Z: complex] :
% 5.27/5.61 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( im @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 5.27/5.61 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R3 ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Im_Reals_divide
% 5.27/5.61 thf(fact_8540_intind,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,P: nat > $o,X4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( P @ X4 )
% 5.27/5.61 => ( P @ ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % intind
% 5.27/5.61 thf(fact_8541_intind,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,P: int > $o,X4: int] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( P @ X4 )
% 5.27/5.61 => ( P @ ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % intind
% 5.27/5.61 thf(fact_8542_intind,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,P: vEBT_VEBT > $o,X4: vEBT_VEBT] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( P @ X4 )
% 5.27/5.61 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % intind
% 5.27/5.61 thf(fact_8543_replicate__eq__replicate,axiom,
% 5.27/5.61 ! [M: nat,X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.27/5.61 ( ( ( replicate_VEBT_VEBT @ M @ X4 )
% 5.27/5.61 = ( replicate_VEBT_VEBT @ N2 @ Y ) )
% 5.27/5.61 = ( ( M = N2 )
% 5.27/5.61 & ( ( M != zero_zero_nat )
% 5.27/5.61 => ( X4 = Y ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eq_replicate
% 5.27/5.61 thf(fact_8544_length__replicate,axiom,
% 5.27/5.61 ! [N2: nat,X4: vEBT_VEBT] :
% 5.27/5.61 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) )
% 5.27/5.61 = N2 ) ).
% 5.27/5.61
% 5.27/5.61 % length_replicate
% 5.27/5.61 thf(fact_8545_length__replicate,axiom,
% 5.27/5.61 ! [N2: nat,X4: $o] :
% 5.27/5.61 ( ( size_size_list_o @ ( replicate_o @ N2 @ X4 ) )
% 5.27/5.61 = N2 ) ).
% 5.27/5.61
% 5.27/5.61 % length_replicate
% 5.27/5.61 thf(fact_8546_length__replicate,axiom,
% 5.27/5.61 ! [N2: nat,X4: nat] :
% 5.27/5.61 ( ( size_size_list_nat @ ( replicate_nat @ N2 @ X4 ) )
% 5.27/5.61 = N2 ) ).
% 5.27/5.61
% 5.27/5.61 % length_replicate
% 5.27/5.61 thf(fact_8547_length__replicate,axiom,
% 5.27/5.61 ! [N2: nat,X4: int] :
% 5.27/5.61 ( ( size_size_list_int @ ( replicate_int @ N2 @ X4 ) )
% 5.27/5.61 = N2 ) ).
% 5.27/5.61
% 5.27/5.61 % length_replicate
% 5.27/5.61 thf(fact_8548_summable__iff__shift,axiom,
% 5.27/5.61 ! [F: nat > real,K: nat] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.27/5.61 = ( summable_real @ F ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_iff_shift
% 5.27/5.61 thf(fact_8549_Ball__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: int,P: int > $o] :
% 5.27/5.61 ( ( ! [X: int] :
% 5.27/5.61 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.27/5.61 => ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Ball_set_replicate
% 5.27/5.61 thf(fact_8550_Ball__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: nat,P: nat > $o] :
% 5.27/5.61 ( ( ! [X: nat] :
% 5.27/5.61 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.27/5.61 => ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Ball_set_replicate
% 5.27/5.61 thf(fact_8551_Ball__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.27/5.61 ( ( ! [X: vEBT_VEBT] :
% 5.27/5.61 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.27/5.61 => ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 | ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Ball_set_replicate
% 5.27/5.61 thf(fact_8552_Bex__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: int,P: int > $o] :
% 5.27/5.61 ( ( ? [X: int] :
% 5.27/5.61 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N2 @ A ) ) )
% 5.27/5.61 & ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Bex_set_replicate
% 5.27/5.61 thf(fact_8553_Bex__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: nat,P: nat > $o] :
% 5.27/5.61 ( ( ? [X: nat] :
% 5.27/5.61 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N2 @ A ) ) )
% 5.27/5.61 & ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Bex_set_replicate
% 5.27/5.61 thf(fact_8554_Bex__set__replicate,axiom,
% 5.27/5.61 ! [N2: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.27/5.61 ( ( ? [X: vEBT_VEBT] :
% 5.27/5.61 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ A ) ) )
% 5.27/5.61 & ( P @ X ) ) )
% 5.27/5.61 = ( ( P @ A )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Bex_set_replicate
% 5.27/5.61 thf(fact_8555_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: real,N2: nat,Y: real] :
% 5.27/5.61 ( ( member_real @ X4 @ ( set_real2 @ ( replicate_real @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8556_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: complex,N2: nat,Y: complex] :
% 5.27/5.61 ( ( member_complex @ X4 @ ( set_complex2 @ ( replicate_complex @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8557_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: product_prod_nat_nat,N2: nat,Y: product_prod_nat_nat] :
% 5.27/5.61 ( ( member8440522571783428010at_nat @ X4 @ ( set_Pr5648618587558075414at_nat @ ( replic4235873036481779905at_nat @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8558_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: int,N2: nat,Y: int] :
% 5.27/5.61 ( ( member_int @ X4 @ ( set_int2 @ ( replicate_int @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8559_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: nat,N2: nat,Y: nat] :
% 5.27/5.61 ( ( member_nat @ X4 @ ( set_nat2 @ ( replicate_nat @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8560_in__set__replicate,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,N2: nat,Y: vEBT_VEBT] :
% 5.27/5.61 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N2 @ Y ) ) )
% 5.27/5.61 = ( ( X4 = Y )
% 5.27/5.61 & ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % in_set_replicate
% 5.27/5.61 thf(fact_8561_nth__replicate,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,X4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( nth_nat @ ( replicate_nat @ N2 @ X4 ) @ I2 )
% 5.27/5.61 = X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % nth_replicate
% 5.27/5.61 thf(fact_8562_nth__replicate,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,X4: int] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( nth_int @ ( replicate_int @ N2 @ X4 ) @ I2 )
% 5.27/5.61 = X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % nth_replicate
% 5.27/5.61 thf(fact_8563_nth__replicate,axiom,
% 5.27/5.61 ! [I2: nat,N2: nat,X4: vEBT_VEBT] :
% 5.27/5.61 ( ( ord_less_nat @ I2 @ N2 )
% 5.27/5.61 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N2 @ X4 ) @ I2 )
% 5.27/5.61 = X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % nth_replicate
% 5.27/5.61 thf(fact_8564_summable__divide__iff,axiom,
% 5.27/5.61 ! [F: nat > real,C: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.27/5.61 = ( ( C = zero_zero_real )
% 5.27/5.61 | ( summable_real @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_divide_iff
% 5.27/5.61 thf(fact_8565_summable__divide__iff,axiom,
% 5.27/5.61 ! [F: nat > complex,C: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.27/5.61 = ( ( C = zero_zero_complex )
% 5.27/5.61 | ( summable_complex @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_divide_iff
% 5.27/5.61 thf(fact_8566_summable__geometric__iff,axiom,
% 5.27/5.61 ! [C: real] :
% 5.27/5.61 ( ( summable_real @ ( power_power_real @ C ) )
% 5.27/5.61 = ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_geometric_iff
% 5.27/5.61 thf(fact_8567_summable__geometric__iff,axiom,
% 5.27/5.61 ! [C: complex] :
% 5.27/5.61 ( ( summable_complex @ ( power_power_complex @ C ) )
% 5.27/5.61 = ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_geometric_iff
% 5.27/5.61 thf(fact_8568_summable__comparison__test,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real] :
% 5.27/5.61 ( ? [N7: nat] :
% 5.27/5.61 ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( summable_real @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_comparison_test
% 5.27/5.61 thf(fact_8569_summable__comparison__test,axiom,
% 5.27/5.61 ! [F: nat > complex,G: nat > real] :
% 5.27/5.61 ( ? [N7: nat] :
% 5.27/5.61 ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( summable_complex @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_comparison_test
% 5.27/5.61 thf(fact_8570_summable__comparison__test_H,axiom,
% 5.27/5.61 ! [G: nat > real,N4: nat,F: nat > real] :
% 5.27/5.61 ( ( summable_real @ G )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( summable_real @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_comparison_test'
% 5.27/5.61 thf(fact_8571_summable__comparison__test_H,axiom,
% 5.27/5.61 ! [G: nat > real,N4: nat,F: nat > complex] :
% 5.27/5.61 ( ( summable_real @ G )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( summable_complex @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_comparison_test'
% 5.27/5.61 thf(fact_8572_suminf__le,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( summable_real @ F )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( ord_less_eq_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_le
% 5.27/5.61 thf(fact_8573_suminf__le,axiom,
% 5.27/5.61 ! [F: nat > nat,G: nat > nat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( summable_nat @ F )
% 5.27/5.61 => ( ( summable_nat @ G )
% 5.27/5.61 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_le
% 5.27/5.61 thf(fact_8574_suminf__le,axiom,
% 5.27/5.61 ! [F: nat > int,G: nat > int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( summable_int @ F )
% 5.27/5.61 => ( ( summable_int @ G )
% 5.27/5.61 => ( ord_less_eq_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_le
% 5.27/5.61 thf(fact_8575_Reals__power,axiom,
% 5.27/5.61 ! [A: real,N2: nat] :
% 5.27/5.61 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.27/5.61 => ( member_real @ ( power_power_real @ A @ N2 ) @ real_V470468836141973256s_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_power
% 5.27/5.61 thf(fact_8576_Reals__power,axiom,
% 5.27/5.61 ! [A: complex,N2: nat] :
% 5.27/5.61 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( member_complex @ ( power_power_complex @ A @ N2 ) @ real_V2521375963428798218omplex ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_power
% 5.27/5.61 thf(fact_8577_Reals__divide,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.27/5.61 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.27/5.61 => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_divide
% 5.27/5.61 thf(fact_8578_Reals__divide,axiom,
% 5.27/5.61 ! [A: complex,B: complex] :
% 5.27/5.61 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_divide
% 5.27/5.61 thf(fact_8579_Reals__add,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.27/5.61 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.27/5.61 => ( member_real @ ( plus_plus_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_add
% 5.27/5.61 thf(fact_8580_Reals__add,axiom,
% 5.27/5.61 ! [A: complex,B: complex] :
% 5.27/5.61 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( member_complex @ ( plus_plus_complex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_add
% 5.27/5.61 thf(fact_8581_Reals__1,axiom,
% 5.27/5.61 member_real @ one_one_real @ real_V470468836141973256s_real ).
% 5.27/5.61
% 5.27/5.61 % Reals_1
% 5.27/5.61 thf(fact_8582_Reals__1,axiom,
% 5.27/5.61 member_complex @ one_one_complex @ real_V2521375963428798218omplex ).
% 5.27/5.61
% 5.27/5.61 % Reals_1
% 5.27/5.61 thf(fact_8583_Reals__numeral,axiom,
% 5.27/5.61 ! [W: num] : ( member_complex @ ( numera6690914467698888265omplex @ W ) @ real_V2521375963428798218omplex ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_numeral
% 5.27/5.61 thf(fact_8584_Reals__numeral,axiom,
% 5.27/5.61 ! [W: num] : ( member_real @ ( numeral_numeral_real @ W ) @ real_V470468836141973256s_real ) ).
% 5.27/5.61
% 5.27/5.61 % Reals_numeral
% 5.27/5.61 thf(fact_8585_summable__divide,axiom,
% 5.27/5.61 ! [F: nat > real,C: real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_divide
% 5.27/5.61 thf(fact_8586_summable__divide,axiom,
% 5.27/5.61 ! [F: nat > complex,C: complex] :
% 5.27/5.61 ( ( summable_complex @ F )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_divide
% 5.27/5.61 thf(fact_8587_summable__ignore__initial__segment,axiom,
% 5.27/5.61 ! [F: nat > real,K: nat] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_ignore_initial_segment
% 5.27/5.61 thf(fact_8588_summable__add,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_add
% 5.27/5.61 thf(fact_8589_summable__add,axiom,
% 5.27/5.61 ! [F: nat > nat,G: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ( summable_nat @ G )
% 5.27/5.61 => ( summable_nat
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_add
% 5.27/5.61 thf(fact_8590_summable__add,axiom,
% 5.27/5.61 ! [F: nat > int,G: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ( summable_int @ G )
% 5.27/5.61 => ( summable_int
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_add
% 5.27/5.61 thf(fact_8591_summable__Suc__iff,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.27/5.61 = ( summable_real @ F ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_Suc_iff
% 5.27/5.61 thf(fact_8592_summable__zero__power,axiom,
% 5.27/5.61 summable_real @ ( power_power_real @ zero_zero_real ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power
% 5.27/5.61 thf(fact_8593_summable__zero__power,axiom,
% 5.27/5.61 summable_int @ ( power_power_int @ zero_zero_int ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power
% 5.27/5.61 thf(fact_8594_summable__zero__power,axiom,
% 5.27/5.61 summable_complex @ ( power_power_complex @ zero_zero_complex ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power
% 5.27/5.61 thf(fact_8595_suminf__add,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( ( plus_plus_real @ ( suminf_real @ F ) @ ( suminf_real @ G ) )
% 5.27/5.61 = ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_add
% 5.27/5.61 thf(fact_8596_suminf__add,axiom,
% 5.27/5.61 ! [F: nat > nat,G: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ( summable_nat @ G )
% 5.27/5.61 => ( ( plus_plus_nat @ ( suminf_nat @ F ) @ ( suminf_nat @ G ) )
% 5.27/5.61 = ( suminf_nat
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_add
% 5.27/5.61 thf(fact_8597_suminf__add,axiom,
% 5.27/5.61 ! [F: nat > int,G: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ( summable_int @ G )
% 5.27/5.61 => ( ( plus_plus_int @ ( suminf_int @ F ) @ ( suminf_int @ G ) )
% 5.27/5.61 = ( suminf_int
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_add
% 5.27/5.61 thf(fact_8598_suminf__divide,axiom,
% 5.27/5.61 ! [F: nat > real,C: real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C ) )
% 5.27/5.61 = ( divide_divide_real @ ( suminf_real @ F ) @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_divide
% 5.27/5.61 thf(fact_8599_suminf__divide,axiom,
% 5.27/5.61 ! [F: nat > complex,C: complex] :
% 5.27/5.61 ( ( summable_complex @ F )
% 5.27/5.61 => ( ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C ) )
% 5.27/5.61 = ( divide1717551699836669952omplex @ ( suminf_complex @ F ) @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_divide
% 5.27/5.61 thf(fact_8600_series__comparison__complex,axiom,
% 5.27/5.61 ! [G: nat > complex,N4: nat,F: nat > real] :
% 5.27/5.61 ( ( summable_complex @ G )
% 5.27/5.61 => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 5.27/5.61 => ( summable_real @ F ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % series_comparison_complex
% 5.27/5.61 thf(fact_8601_series__comparison__complex,axiom,
% 5.27/5.61 ! [G: nat > complex,N4: nat,F: nat > complex] :
% 5.27/5.61 ( ( summable_complex @ G )
% 5.27/5.61 => ( ! [N3: nat] : ( member_complex @ ( G @ N3 ) @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( real_V1022390504157884413omplex @ ( G @ N3 ) ) ) )
% 5.27/5.61 => ( summable_complex @ F ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % series_comparison_complex
% 5.27/5.61 thf(fact_8602_powser__insidea,axiom,
% 5.27/5.61 ! [F: nat > real,X4: real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_insidea
% 5.27/5.61 thf(fact_8603_powser__insidea,axiom,
% 5.27/5.61 ! [F: nat > complex,X4: complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_insidea
% 5.27/5.61 thf(fact_8604_suminf__nonneg,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_nonneg
% 5.27/5.61 thf(fact_8605_suminf__nonneg,axiom,
% 5.27/5.61 ! [F: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_eq_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_nonneg
% 5.27/5.61 thf(fact_8606_suminf__nonneg,axiom,
% 5.27/5.61 ! [F: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_eq_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_nonneg
% 5.27/5.61 thf(fact_8607_suminf__eq__zero__iff,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ( suminf_real @ F )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 = ( ! [N: nat] :
% 5.27/5.61 ( ( F @ N )
% 5.27/5.61 = zero_zero_real ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_eq_zero_iff
% 5.27/5.61 thf(fact_8608_suminf__eq__zero__iff,axiom,
% 5.27/5.61 ! [F: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ( suminf_nat @ F )
% 5.27/5.61 = zero_zero_nat )
% 5.27/5.61 = ( ! [N: nat] :
% 5.27/5.61 ( ( F @ N )
% 5.27/5.61 = zero_zero_nat ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_eq_zero_iff
% 5.27/5.61 thf(fact_8609_suminf__eq__zero__iff,axiom,
% 5.27/5.61 ! [F: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ( suminf_int @ F )
% 5.27/5.61 = zero_zero_int )
% 5.27/5.61 = ( ! [N: nat] :
% 5.27/5.61 ( ( F @ N )
% 5.27/5.61 = zero_zero_int ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_eq_zero_iff
% 5.27/5.61 thf(fact_8610_suminf__pos,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos
% 5.27/5.61 thf(fact_8611_suminf__pos,axiom,
% 5.27/5.61 ! [F: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos
% 5.27/5.61 thf(fact_8612_suminf__pos,axiom,
% 5.27/5.61 ! [F: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.61 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos
% 5.27/5.61 thf(fact_8613_summable__0__powser,axiom,
% 5.27/5.61 ! [F: nat > complex] :
% 5.27/5.61 ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_0_powser
% 5.27/5.61 thf(fact_8614_summable__0__powser,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_0_powser
% 5.27/5.61 thf(fact_8615_summable__zero__power_H,axiom,
% 5.27/5.61 ! [F: nat > complex] :
% 5.27/5.61 ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power'
% 5.27/5.61 thf(fact_8616_summable__zero__power_H,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ zero_zero_real @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power'
% 5.27/5.61 thf(fact_8617_summable__zero__power_H,axiom,
% 5.27/5.61 ! [F: nat > int] :
% 5.27/5.61 ( summable_int
% 5.27/5.61 @ ^ [N: nat] : ( times_times_int @ ( F @ N ) @ ( power_power_int @ zero_zero_int @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_zero_power'
% 5.27/5.61 thf(fact_8618_summable__powser__split__head,axiom,
% 5.27/5.61 ! [F: nat > complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 = ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_powser_split_head
% 5.27/5.61 thf(fact_8619_summable__powser__split__head,axiom,
% 5.27/5.61 ! [F: nat > real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 = ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_powser_split_head
% 5.27/5.61 thf(fact_8620_powser__split__head_I3_J,axiom,
% 5.27/5.61 ! [F: nat > complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(3)
% 5.27/5.61 thf(fact_8621_powser__split__head_I3_J,axiom,
% 5.27/5.61 ! [F: nat > real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(3)
% 5.27/5.61 thf(fact_8622_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_real,N2: nat,X4: real] :
% 5.27/5.61 ( ( ( size_size_list_real @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: real] :
% 5.27/5.61 ( ( member_real @ Y3 @ ( set_real2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_real @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8623_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_complex,N2: nat,X4: complex] :
% 5.27/5.61 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: complex] :
% 5.27/5.61 ( ( member_complex @ Y3 @ ( set_complex2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_complex @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8624_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_P6011104703257516679at_nat,N2: nat,X4: product_prod_nat_nat] :
% 5.27/5.61 ( ( ( size_s5460976970255530739at_nat @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: product_prod_nat_nat] :
% 5.27/5.61 ( ( member8440522571783428010at_nat @ Y3 @ ( set_Pr5648618587558075414at_nat @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replic4235873036481779905at_nat @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8625_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_VEBT_VEBT,N2: nat,X4: vEBT_VEBT] :
% 5.27/5.61 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: vEBT_VEBT] :
% 5.27/5.61 ( ( member_VEBT_VEBT @ Y3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_VEBT_VEBT @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8626_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_o,N2: nat,X4: $o] :
% 5.27/5.61 ( ( ( size_size_list_o @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: $o] :
% 5.27/5.61 ( ( member_o @ Y3 @ ( set_o2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_o @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8627_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_nat,N2: nat,X4: nat] :
% 5.27/5.61 ( ( ( size_size_list_nat @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: nat] :
% 5.27/5.61 ( ( member_nat @ Y3 @ ( set_nat2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_nat @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8628_replicate__eqI,axiom,
% 5.27/5.61 ! [Xs: list_int,N2: nat,X4: int] :
% 5.27/5.61 ( ( ( size_size_list_int @ Xs )
% 5.27/5.61 = N2 )
% 5.27/5.61 => ( ! [Y3: int] :
% 5.27/5.61 ( ( member_int @ Y3 @ ( set_int2 @ Xs ) )
% 5.27/5.61 => ( Y3 = X4 ) )
% 5.27/5.61 => ( Xs
% 5.27/5.61 = ( replicate_int @ N2 @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_eqI
% 5.27/5.61 thf(fact_8629_replicate__length__same,axiom,
% 5.27/5.61 ! [Xs: list_VEBT_VEBT,X4: vEBT_VEBT] :
% 5.27/5.61 ( ! [X5: vEBT_VEBT] :
% 5.27/5.61 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.27/5.61 => ( X5 = X4 ) )
% 5.27/5.61 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X4 )
% 5.27/5.61 = Xs ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_length_same
% 5.27/5.61 thf(fact_8630_replicate__length__same,axiom,
% 5.27/5.61 ! [Xs: list_o,X4: $o] :
% 5.27/5.61 ( ! [X5: $o] :
% 5.27/5.61 ( ( member_o @ X5 @ ( set_o2 @ Xs ) )
% 5.27/5.61 => ( X5 = X4 ) )
% 5.27/5.61 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X4 )
% 5.27/5.61 = Xs ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_length_same
% 5.27/5.61 thf(fact_8631_replicate__length__same,axiom,
% 5.27/5.61 ! [Xs: list_nat,X4: nat] :
% 5.27/5.61 ( ! [X5: nat] :
% 5.27/5.61 ( ( member_nat @ X5 @ ( set_nat2 @ Xs ) )
% 5.27/5.61 => ( X5 = X4 ) )
% 5.27/5.61 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X4 )
% 5.27/5.61 = Xs ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_length_same
% 5.27/5.61 thf(fact_8632_replicate__length__same,axiom,
% 5.27/5.61 ! [Xs: list_int,X4: int] :
% 5.27/5.61 ( ! [X5: int] :
% 5.27/5.61 ( ( member_int @ X5 @ ( set_int2 @ Xs ) )
% 5.27/5.61 => ( X5 = X4 ) )
% 5.27/5.61 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X4 )
% 5.27/5.61 = Xs ) ) ).
% 5.27/5.61
% 5.27/5.61 % replicate_length_same
% 5.27/5.61 thf(fact_8633_summable__powser__ignore__initial__segment,axiom,
% 5.27/5.61 ! [F: nat > complex,M: nat,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 = ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_powser_ignore_initial_segment
% 5.27/5.61 thf(fact_8634_summable__powser__ignore__initial__segment,axiom,
% 5.27/5.61 ! [F: nat > real,M: nat,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ ( plus_plus_nat @ N @ M ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 = ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_powser_ignore_initial_segment
% 5.27/5.61 thf(fact_8635_summable__norm__comparison__test,axiom,
% 5.27/5.61 ! [F: nat > complex,G: nat > real] :
% 5.27/5.61 ( ? [N7: nat] :
% 5.27/5.61 ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_comparison_test
% 5.27/5.61 thf(fact_8636_summable__rabs__comparison__test,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real] :
% 5.27/5.61 ( ? [N7: nat] :
% 5.27/5.61 ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.27/5.61 => ( ( summable_real @ G )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_rabs_comparison_test
% 5.27/5.61 thf(fact_8637_nonzero__Reals__divide,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( member_real @ A @ real_V470468836141973256s_real )
% 5.27/5.61 => ( ( member_real @ B @ real_V470468836141973256s_real )
% 5.27/5.61 => ( ( B != zero_zero_real )
% 5.27/5.61 => ( member_real @ ( divide_divide_real @ A @ B ) @ real_V470468836141973256s_real ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % nonzero_Reals_divide
% 5.27/5.61 thf(fact_8638_nonzero__Reals__divide,axiom,
% 5.27/5.61 ! [A: complex,B: complex] :
% 5.27/5.61 ( ( member_complex @ A @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( member_complex @ B @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( B != zero_zero_complex )
% 5.27/5.61 => ( member_complex @ ( divide1717551699836669952omplex @ A @ B ) @ real_V2521375963428798218omplex ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % nonzero_Reals_divide
% 5.27/5.61 thf(fact_8639_summable__rabs,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( abs_abs_real @ ( F @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_rabs
% 5.27/5.61 thf(fact_8640_suminf__pos2,axiom,
% 5.27/5.61 ! [F: nat > real,I2: nat] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.27/5.61 => ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos2
% 5.27/5.61 thf(fact_8641_suminf__pos2,axiom,
% 5.27/5.61 ! [F: nat > nat,I2: nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.27/5.61 => ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos2
% 5.27/5.61 thf(fact_8642_suminf__pos2,axiom,
% 5.27/5.61 ! [F: nat > int,I2: nat] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.27/5.61 => ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos2
% 5.27/5.61 thf(fact_8643_suminf__pos__iff,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_real @ zero_zero_real @ ( suminf_real @ F ) )
% 5.27/5.61 = ( ? [I3: nat] : ( ord_less_real @ zero_zero_real @ ( F @ I3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos_iff
% 5.27/5.61 thf(fact_8644_suminf__pos__iff,axiom,
% 5.27/5.61 ! [F: nat > nat] :
% 5.27/5.61 ( ( summable_nat @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_nat @ zero_zero_nat @ ( suminf_nat @ F ) )
% 5.27/5.61 = ( ? [I3: nat] : ( ord_less_nat @ zero_zero_nat @ ( F @ I3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos_iff
% 5.27/5.61 thf(fact_8645_suminf__pos__iff,axiom,
% 5.27/5.61 ! [F: nat > int] :
% 5.27/5.61 ( ( summable_int @ F )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.61 => ( ( ord_less_int @ zero_zero_int @ ( suminf_int @ F ) )
% 5.27/5.61 = ( ? [I3: nat] : ( ord_less_int @ zero_zero_int @ ( F @ I3 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_pos_iff
% 5.27/5.61 thf(fact_8646_summable__geometric,axiom,
% 5.27/5.61 ! [C: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.27/5.61 => ( summable_real @ ( power_power_real @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_geometric
% 5.27/5.61 thf(fact_8647_summable__geometric,axiom,
% 5.27/5.61 ! [C: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.27/5.61 => ( summable_complex @ ( power_power_complex @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_geometric
% 5.27/5.61 thf(fact_8648_complete__algebra__summable__geometric,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ one_one_real )
% 5.27/5.61 => ( summable_real @ ( power_power_real @ X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % complete_algebra_summable_geometric
% 5.27/5.61 thf(fact_8649_complete__algebra__summable__geometric,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ one_one_real )
% 5.27/5.61 => ( summable_complex @ ( power_power_complex @ X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % complete_algebra_summable_geometric
% 5.27/5.61 thf(fact_8650_suminf__split__head,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real @ F )
% 5.27/5.61 => ( ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) ) )
% 5.27/5.61 = ( minus_minus_real @ ( suminf_real @ F ) @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_split_head
% 5.27/5.61 thf(fact_8651_summable__norm,axiom,
% 5.27/5.61 ! [F: nat > real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( suminf_real @ F ) )
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( F @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm
% 5.27/5.61 thf(fact_8652_summable__norm,axiom,
% 5.27/5.61 ! [F: nat > complex] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( suminf_complex @ F ) )
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( F @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm
% 5.27/5.61 thf(fact_8653_powser__inside,axiom,
% 5.27/5.61 ! [F: nat > real,X4: real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ ( real_V7735802525324610683m_real @ X4 ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_inside
% 5.27/5.61 thf(fact_8654_powser__inside,axiom,
% 5.27/5.61 ! [F: nat > complex,X4: complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ ( real_V1022390504157884413omplex @ X4 ) )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_inside
% 5.27/5.61 thf(fact_8655_summable__exp,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( invers8013647133539491842omplex @ ( semiri5044797733671781792omplex @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_exp
% 5.27/5.61 thf(fact_8656_summable__exp,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_exp
% 5.27/5.61 thf(fact_8657_powser__split__head_I1_J,axiom,
% 5.27/5.61 ! [F: nat > complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 => ( ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 = ( plus_plus_complex @ ( F @ zero_zero_nat )
% 5.27/5.61 @ ( times_times_complex
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 @ Z ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(1)
% 5.27/5.61 thf(fact_8658_powser__split__head_I1_J,axiom,
% 5.27/5.61 ! [F: nat > real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 => ( ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 = ( plus_plus_real @ ( F @ zero_zero_nat )
% 5.27/5.61 @ ( times_times_real
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 @ Z ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(1)
% 5.27/5.61 thf(fact_8659_powser__split__head_I2_J,axiom,
% 5.27/5.61 ! [F: nat > complex,Z: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 => ( ( times_times_complex
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 @ Z )
% 5.27/5.61 = ( minus_minus_complex
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( F @ N ) @ ( power_power_complex @ Z @ N ) ) )
% 5.27/5.61 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(2)
% 5.27/5.61 thf(fact_8660_powser__split__head_I2_J,axiom,
% 5.27/5.61 ! [F: nat > real,Z: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 => ( ( times_times_real
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 @ Z )
% 5.27/5.61 = ( minus_minus_real
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ Z @ N ) ) )
% 5.27/5.61 @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_split_head(2)
% 5.27/5.61 thf(fact_8661_suminf__exist__split,axiom,
% 5.27/5.61 ! [R3: real,F: nat > real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.27/5.61 => ( ( summable_real @ F )
% 5.27/5.61 => ? [N8: nat] :
% 5.27/5.61 ! [N6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N8 @ N6 )
% 5.27/5.61 => ( ord_less_real
% 5.27/5.61 @ ( real_V7735802525324610683m_real
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 5.27/5.61 @ R3 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_exist_split
% 5.27/5.61 thf(fact_8662_suminf__exist__split,axiom,
% 5.27/5.61 ! [R3: real,F: nat > complex] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ R3 )
% 5.27/5.61 => ( ( summable_complex @ F )
% 5.27/5.61 => ? [N8: nat] :
% 5.27/5.61 ! [N6: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N8 @ N6 )
% 5.27/5.61 => ( ord_less_real
% 5.27/5.61 @ ( real_V1022390504157884413omplex
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N6 ) ) ) )
% 5.27/5.61 @ R3 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % suminf_exist_split
% 5.27/5.61 thf(fact_8663_summable__power__series,axiom,
% 5.27/5.61 ! [F: nat > real,Z: real] :
% 5.27/5.61 ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 5.27/5.61 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.27/5.61 => ( ( ord_less_real @ Z @ one_one_real )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( F @ I3 ) @ ( power_power_real @ Z @ I3 ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_power_series
% 5.27/5.61 thf(fact_8664_Abel__lemma,axiom,
% 5.27/5.61 ! [R3: real,R0: real,A: nat > complex,M7: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ R3 )
% 5.27/5.61 => ( ( ord_less_real @ R3 @ R0 )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N3 ) ) @ ( power_power_real @ R0 @ N3 ) ) @ M7 )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( real_V1022390504157884413omplex @ ( A @ N ) ) @ ( power_power_real @ R3 @ N ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Abel_lemma
% 5.27/5.61 thf(fact_8665_summable__ratio__test,axiom,
% 5.27/5.61 ! [C: real,N4: nat,F: nat > real] :
% 5.27/5.61 ( ( ord_less_real @ C @ one_one_real )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V7735802525324610683m_real @ ( F @ N3 ) ) ) ) )
% 5.27/5.61 => ( summable_real @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_ratio_test
% 5.27/5.61 thf(fact_8666_summable__ratio__test,axiom,
% 5.27/5.61 ! [C: real,N4: nat,F: nat > complex] :
% 5.27/5.61 ( ( ord_less_real @ C @ one_one_real )
% 5.27/5.61 => ( ! [N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ N4 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ ( suc @ N3 ) ) ) @ ( times_times_real @ C @ ( real_V1022390504157884413omplex @ ( F @ N3 ) ) ) ) )
% 5.27/5.61 => ( summable_complex @ F ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_ratio_test
% 5.27/5.61 thf(fact_8667_Re__Reals__divide,axiom,
% 5.27/5.61 ! [R3: complex,Z: complex] :
% 5.27/5.61 ( ( member_complex @ R3 @ real_V2521375963428798218omplex )
% 5.27/5.61 => ( ( re @ ( divide1717551699836669952omplex @ R3 @ Z ) )
% 5.27/5.61 = ( divide_divide_real @ ( times_times_real @ ( re @ R3 ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Re_Reals_divide
% 5.27/5.61 thf(fact_8668_vebt__buildup_Osimps_I3_J,axiom,
% 5.27/5.61 ! [Va: nat] :
% 5.27/5.61 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.27/5.61 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.27/5.61 = ( 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 ) ) ) ) ) ) )
% 5.27/5.61 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.27/5.61 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.27/5.61 = ( 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 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % vebt_buildup.simps(3)
% 5.27/5.61 thf(fact_8669_sin__paired,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.27/5.61 @ ( sin_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_paired
% 5.27/5.61 thf(fact_8670_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.61 ( ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.61 = Y )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.61 => ( ~ Y
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.27/5.61 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.27/5.61 => ( ~ Y
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 ) ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 )
% 5.27/5.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) ) ) )
% 5.27/5.61 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.pelims(1)
% 5.27/5.61 thf(fact_8671_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ~ ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) )
% 5.27/5.61 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.27/5.61 => ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 ) ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 5.27/5.61 => ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 )
% 5.27/5.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.27/5.61 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 5.27/5.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.pelims(3)
% 5.27/5.61 thf(fact_8672_geometric__deriv__sums,axiom,
% 5.27/5.61 ! [Z: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Z ) @ one_one_real )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( power_power_real @ Z @ N ) )
% 5.27/5.61 @ ( divide_divide_real @ one_one_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % geometric_deriv_sums
% 5.27/5.61 thf(fact_8673_geometric__deriv__sums,axiom,
% 5.27/5.61 ! [Z: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.27/5.61 => ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( power_power_complex @ Z @ N ) )
% 5.27/5.61 @ ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ ( minus_minus_complex @ one_one_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % geometric_deriv_sums
% 5.27/5.61 thf(fact_8674_powser__sums__zero__iff,axiom,
% 5.27/5.61 ! [A: nat > complex,X4: complex] :
% 5.27/5.61 ( ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.27/5.61 @ X4 )
% 5.27/5.61 = ( ( A @ zero_zero_nat )
% 5.27/5.61 = X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_zero_iff
% 5.27/5.61 thf(fact_8675_powser__sums__zero__iff,axiom,
% 5.27/5.61 ! [A: nat > real,X4: real] :
% 5.27/5.61 ( ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.27/5.61 @ X4 )
% 5.27/5.61 = ( ( A @ zero_zero_nat )
% 5.27/5.61 = X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_zero_iff
% 5.27/5.61 thf(fact_8676_sums__le,axiom,
% 5.27/5.61 ! [F: nat > real,G: nat > real,S: real,T2: real] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( sums_real @ F @ S )
% 5.27/5.61 => ( ( sums_real @ G @ T2 )
% 5.27/5.61 => ( ord_less_eq_real @ S @ T2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_le
% 5.27/5.61 thf(fact_8677_sums__le,axiom,
% 5.27/5.61 ! [F: nat > nat,G: nat > nat,S: nat,T2: nat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( sums_nat @ F @ S )
% 5.27/5.61 => ( ( sums_nat @ G @ T2 )
% 5.27/5.61 => ( ord_less_eq_nat @ S @ T2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_le
% 5.27/5.61 thf(fact_8678_sums__le,axiom,
% 5.27/5.61 ! [F: nat > int,G: nat > int,S: int,T2: int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.61 => ( ( sums_int @ F @ S )
% 5.27/5.61 => ( ( sums_int @ G @ T2 )
% 5.27/5.61 => ( ord_less_eq_int @ S @ T2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_le
% 5.27/5.61 thf(fact_8679_sums__divide,axiom,
% 5.27/5.61 ! [F: nat > real,A: real,C: real] :
% 5.27/5.61 ( ( sums_real @ F @ A )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ C )
% 5.27/5.61 @ ( divide_divide_real @ A @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_divide
% 5.27/5.61 thf(fact_8680_sums__divide,axiom,
% 5.27/5.61 ! [F: nat > complex,A: complex,C: complex] :
% 5.27/5.61 ( ( sums_complex @ F @ A )
% 5.27/5.61 => ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( divide1717551699836669952omplex @ ( F @ N ) @ C )
% 5.27/5.61 @ ( divide1717551699836669952omplex @ A @ C ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_divide
% 5.27/5.61 thf(fact_8681_sums__add,axiom,
% 5.27/5.61 ! [F: nat > real,A: real,G: nat > real,B: real] :
% 5.27/5.61 ( ( sums_real @ F @ A )
% 5.27/5.61 => ( ( sums_real @ G @ B )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_real @ ( F @ N ) @ ( G @ N ) )
% 5.27/5.61 @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_add
% 5.27/5.61 thf(fact_8682_sums__add,axiom,
% 5.27/5.61 ! [F: nat > nat,A: nat,G: nat > nat,B: nat] :
% 5.27/5.61 ( ( sums_nat @ F @ A )
% 5.27/5.61 => ( ( sums_nat @ G @ B )
% 5.27/5.61 => ( sums_nat
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_nat @ ( F @ N ) @ ( G @ N ) )
% 5.27/5.61 @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_add
% 5.27/5.61 thf(fact_8683_sums__add,axiom,
% 5.27/5.61 ! [F: nat > int,A: int,G: nat > int,B: int] :
% 5.27/5.61 ( ( sums_int @ F @ A )
% 5.27/5.61 => ( ( sums_int @ G @ B )
% 5.27/5.61 => ( sums_int
% 5.27/5.61 @ ^ [N: nat] : ( plus_plus_int @ ( F @ N ) @ ( G @ N ) )
% 5.27/5.61 @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_add
% 5.27/5.61 thf(fact_8684_sums__mult__D,axiom,
% 5.27/5.61 ! [C: real,F: nat > real,A: real] :
% 5.27/5.61 ( ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ C @ ( F @ N ) )
% 5.27/5.61 @ A )
% 5.27/5.61 => ( ( C != zero_zero_real )
% 5.27/5.61 => ( sums_real @ F @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_mult_D
% 5.27/5.61 thf(fact_8685_sums__mult__D,axiom,
% 5.27/5.61 ! [C: complex,F: nat > complex,A: complex] :
% 5.27/5.61 ( ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ C @ ( F @ N ) )
% 5.27/5.61 @ A )
% 5.27/5.61 => ( ( C != zero_zero_complex )
% 5.27/5.61 => ( sums_complex @ F @ ( divide1717551699836669952omplex @ A @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_mult_D
% 5.27/5.61 thf(fact_8686_sums__Suc__imp,axiom,
% 5.27/5.61 ! [F: nat > complex,S: complex] :
% 5.27/5.61 ( ( ( F @ zero_zero_nat )
% 5.27/5.61 = zero_zero_complex )
% 5.27/5.61 => ( ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ S )
% 5.27/5.61 => ( sums_complex @ F @ S ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc_imp
% 5.27/5.61 thf(fact_8687_sums__Suc__imp,axiom,
% 5.27/5.61 ! [F: nat > real,S: real] :
% 5.27/5.61 ( ( ( F @ zero_zero_nat )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 => ( ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ S )
% 5.27/5.61 => ( sums_real @ F @ S ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc_imp
% 5.27/5.61 thf(fact_8688_sums__Suc__iff,axiom,
% 5.27/5.61 ! [F: nat > real,S: real] :
% 5.27/5.61 ( ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ S )
% 5.27/5.61 = ( sums_real @ F @ ( plus_plus_real @ S @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc_iff
% 5.27/5.61 thf(fact_8689_sums__Suc,axiom,
% 5.27/5.61 ! [F: nat > real,L: real] :
% 5.27/5.61 ( ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ L )
% 5.27/5.61 => ( sums_real @ F @ ( plus_plus_real @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc
% 5.27/5.61 thf(fact_8690_sums__Suc,axiom,
% 5.27/5.61 ! [F: nat > nat,L: nat] :
% 5.27/5.61 ( ( sums_nat
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ L )
% 5.27/5.61 => ( sums_nat @ F @ ( plus_plus_nat @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc
% 5.27/5.61 thf(fact_8691_sums__Suc,axiom,
% 5.27/5.61 ! [F: nat > int,L: int] :
% 5.27/5.61 ( ( sums_int
% 5.27/5.61 @ ^ [N: nat] : ( F @ ( suc @ N ) )
% 5.27/5.61 @ L )
% 5.27/5.61 => ( sums_int @ F @ ( plus_plus_int @ L @ ( F @ zero_zero_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_Suc
% 5.27/5.61 thf(fact_8692_sums__zero__iff__shift,axiom,
% 5.27/5.61 ! [N2: nat,F: nat > complex,S: complex] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ I4 @ N2 )
% 5.27/5.61 => ( ( F @ I4 )
% 5.27/5.61 = zero_zero_complex ) )
% 5.27/5.61 => ( ( sums_complex
% 5.27/5.61 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.27/5.61 @ S )
% 5.27/5.61 = ( sums_complex @ F @ S ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_zero_iff_shift
% 5.27/5.61 thf(fact_8693_sums__zero__iff__shift,axiom,
% 5.27/5.61 ! [N2: nat,F: nat > real,S: real] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ I4 @ N2 )
% 5.27/5.61 => ( ( F @ I4 )
% 5.27/5.61 = zero_zero_real ) )
% 5.27/5.61 => ( ( sums_real
% 5.27/5.61 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.27/5.61 @ S )
% 5.27/5.61 = ( sums_real @ F @ S ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_zero_iff_shift
% 5.27/5.61 thf(fact_8694_powser__sums__if,axiom,
% 5.27/5.61 ! [M: nat,Z: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( if_complex @ ( N = M ) @ one_one_complex @ zero_zero_complex ) @ ( power_power_complex @ Z @ N ) )
% 5.27/5.61 @ ( power_power_complex @ Z @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_if
% 5.27/5.61 thf(fact_8695_powser__sums__if,axiom,
% 5.27/5.61 ! [M: nat,Z: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( if_real @ ( N = M ) @ one_one_real @ zero_zero_real ) @ ( power_power_real @ Z @ N ) )
% 5.27/5.61 @ ( power_power_real @ Z @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_if
% 5.27/5.61 thf(fact_8696_powser__sums__if,axiom,
% 5.27/5.61 ! [M: nat,Z: int] :
% 5.27/5.61 ( sums_int
% 5.27/5.61 @ ^ [N: nat] : ( times_times_int @ ( if_int @ ( N = M ) @ one_one_int @ zero_zero_int ) @ ( power_power_int @ Z @ N ) )
% 5.27/5.61 @ ( power_power_int @ Z @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_if
% 5.27/5.61 thf(fact_8697_powser__sums__zero,axiom,
% 5.27/5.61 ! [A: nat > complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( A @ N ) @ ( power_power_complex @ zero_zero_complex @ N ) )
% 5.27/5.61 @ ( A @ zero_zero_nat ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_zero
% 5.27/5.61 thf(fact_8698_powser__sums__zero,axiom,
% 5.27/5.61 ! [A: nat > real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( A @ N ) @ ( power_power_real @ zero_zero_real @ N ) )
% 5.27/5.61 @ ( A @ zero_zero_nat ) ) ).
% 5.27/5.61
% 5.27/5.61 % powser_sums_zero
% 5.27/5.61 thf(fact_8699_geometric__sums,axiom,
% 5.27/5.61 ! [C: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ C ) @ one_one_real )
% 5.27/5.61 => ( sums_real @ ( power_power_real @ C ) @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % geometric_sums
% 5.27/5.61 thf(fact_8700_geometric__sums,axiom,
% 5.27/5.61 ! [C: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ C ) @ one_one_real )
% 5.27/5.61 => ( sums_complex @ ( power_power_complex @ C ) @ ( divide1717551699836669952omplex @ one_one_complex @ ( minus_minus_complex @ one_one_complex @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % geometric_sums
% 5.27/5.61 thf(fact_8701_power__half__series,axiom,
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N ) )
% 5.27/5.61 @ one_one_real ) ).
% 5.27/5.61
% 5.27/5.61 % power_half_series
% 5.27/5.61 thf(fact_8702_sums__if_H,axiom,
% 5.27/5.61 ! [G: nat > real,X4: real] :
% 5.27/5.61 ( ( sums_real @ G @ X4 )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_if'
% 5.27/5.61 thf(fact_8703_sums__if,axiom,
% 5.27/5.61 ! [G: nat > real,X4: real,F: nat > real,Y: real] :
% 5.27/5.61 ( ( sums_real @ G @ X4 )
% 5.27/5.61 => ( ( sums_real @ F @ Y )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( F @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.61 @ ( plus_plus_real @ X4 @ Y ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_if
% 5.27/5.61 thf(fact_8704_cos__paired,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ ( power_power_real @ X4 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.61 @ ( cos_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_paired
% 5.27/5.61 thf(fact_8705_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ( vEBT_VEBT_membermima @ X4 @ Xa )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa ) )
% 5.27/5.61 => ~ ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 ) ) ) )
% 5.27/5.61 => ( ! [Mi3: nat,Ma3: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc ) @ Xa ) )
% 5.27/5.61 => ~ ( ( Xa = Mi3 )
% 5.27/5.61 | ( Xa = Ma3 )
% 5.27/5.61 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.27/5.61 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd ) @ Xa ) )
% 5.27/5.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.membermima.pelims(2)
% 5.27/5.61 thf(fact_8706_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ~ ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.27/5.61 => ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.27/5.61 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.27/5.61 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.pelims(3)
% 5.27/5.61 thf(fact_8707_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.61 ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) )
% 5.27/5.61 => ~ ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) ) )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) )
% 5.27/5.61 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.pelims(2)
% 5.27/5.61 thf(fact_8708_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.27/5.61 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.61 ( ( ( vEBT_V5719532721284313246member @ X4 @ Xa )
% 5.27/5.61 = Y )
% 5.27/5.61 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.61 => ( ! [A5: $o,B5: $o] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( ( ( Xa = zero_zero_nat )
% 5.27/5.61 => A5 )
% 5.27/5.61 & ( ( Xa != zero_zero_nat )
% 5.27/5.61 => ( ( ( Xa = one_one_nat )
% 5.27/5.61 => B5 )
% 5.27/5.61 & ( Xa = one_one_nat ) ) ) ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa ) ) ) )
% 5.27/5.61 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.27/5.61 => ( ~ Y
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa ) ) ) )
% 5.27/5.61 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.27/5.61 ( ( X4
% 5.27/5.61 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.27/5.61 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.61 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.27/5.61 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % VEBT_internal.naive_member.pelims(1)
% 5.27/5.61 thf(fact_8709_diffs__equiv,axiom,
% 5.27/5.61 ! [C: nat > complex,X4: complex] :
% 5.27/5.61 ( ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) )
% 5.27/5.61 => ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( C @ N ) ) @ ( power_power_complex @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diffs_equiv
% 5.27/5.61 thf(fact_8710_diffs__equiv,axiom,
% 5.27/5.61 ! [C: nat > real,X4: real] :
% 5.27/5.61 ( ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) )
% 5.27/5.61 => ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( C @ N ) ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diffs_equiv
% 5.27/5.61 thf(fact_8711_diffs__def,axiom,
% 5.27/5.61 ( diffs_complex
% 5.27/5.61 = ( ^ [C2: nat > complex,N: nat] : ( times_times_complex @ ( semiri8010041392384452111omplex @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diffs_def
% 5.27/5.61 thf(fact_8712_diffs__def,axiom,
% 5.27/5.61 ( diffs_real
% 5.27/5.61 = ( ^ [C2: nat > real,N: nat] : ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diffs_def
% 5.27/5.61 thf(fact_8713_diffs__def,axiom,
% 5.27/5.61 ( diffs_int
% 5.27/5.61 = ( ^ [C2: nat > int,N: nat] : ( times_times_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) @ ( C2 @ ( suc @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % diffs_def
% 5.27/5.61 thf(fact_8714_termdiff__converges__all,axiom,
% 5.27/5.61 ! [C: nat > complex,X4: complex] :
% 5.27/5.61 ( ! [X5: complex] :
% 5.27/5.61 ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % termdiff_converges_all
% 5.27/5.61 thf(fact_8715_termdiff__converges__all,axiom,
% 5.27/5.61 ! [C: nat > real,X4: real] :
% 5.27/5.61 ( ! [X5: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % termdiff_converges_all
% 5.27/5.61 thf(fact_8716_termdiff__converges,axiom,
% 5.27/5.61 ! [X4: real,K5: real,C: nat > real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X4 ) @ K5 )
% 5.27/5.61 => ( ! [X5: real] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X5 ) @ K5 )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( C @ N ) @ ( power_power_real @ X5 @ N ) ) ) )
% 5.27/5.61 => ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( times_times_real @ ( diffs_real @ C @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % termdiff_converges
% 5.27/5.61 thf(fact_8717_termdiff__converges,axiom,
% 5.27/5.61 ! [X4: complex,K5: real,C: nat > complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X4 ) @ K5 )
% 5.27/5.61 => ( ! [X5: complex] :
% 5.27/5.61 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X5 ) @ K5 )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( C @ N ) @ ( power_power_complex @ X5 @ N ) ) ) )
% 5.27/5.61 => ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( times_times_complex @ ( diffs_complex @ C @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % termdiff_converges
% 5.27/5.61 thf(fact_8718_exp__first__two__terms,axiom,
% 5.27/5.61 ( exp_real
% 5.27/5.61 = ( ^ [X: real] :
% 5.27/5.61 ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X )
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_first_two_terms
% 5.27/5.61 thf(fact_8719_exp__first__two__terms,axiom,
% 5.27/5.61 ( exp_complex
% 5.27/5.61 = ( ^ [X: complex] :
% 5.27/5.61 ( plus_plus_complex @ ( plus_plus_complex @ one_one_complex @ X )
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_first_two_terms
% 5.27/5.61 thf(fact_8720_monoseq__def,axiom,
% 5.27/5.61 ( topolo6980174941875973593q_real
% 5.27/5.61 = ( ^ [X3: nat > real] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_real @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8721_monoseq__def,axiom,
% 5.27/5.61 ( topolo3100542954746470799et_int
% 5.27/5.61 = ( ^ [X3: nat > set_int] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_set_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8722_monoseq__def,axiom,
% 5.27/5.61 ( topolo4267028734544971653eq_rat
% 5.27/5.61 = ( ^ [X3: nat > rat] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_rat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8723_monoseq__def,axiom,
% 5.27/5.61 ( topolo1459490580787246023eq_num
% 5.27/5.61 = ( ^ [X3: nat > num] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_num @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8724_monoseq__def,axiom,
% 5.27/5.61 ( topolo4902158794631467389eq_nat
% 5.27/5.61 = ( ^ [X3: nat > nat] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_nat @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8725_monoseq__def,axiom,
% 5.27/5.61 ( topolo4899668324122417113eq_int
% 5.27/5.61 = ( ^ [X3: nat > int] :
% 5.27/5.61 ( ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_int @ ( X3 @ M6 ) @ ( X3 @ N ) ) )
% 5.27/5.61 | ! [M6: nat,N: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.61 => ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ M6 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_def
% 5.27/5.61 thf(fact_8726_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > real] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8727_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > set_int] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8728_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > rat] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8729_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > num] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8730_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > nat] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8731_monoI2,axiom,
% 5.27/5.61 ! [X8: nat > int] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ M5 ) ) )
% 5.27/5.61 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI2
% 5.27/5.61 thf(fact_8732_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > real] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_real @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8733_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > set_int] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_set_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8734_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > rat] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_rat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8735_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > num] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_num @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8736_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > nat] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_nat @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8737_monoI1,axiom,
% 5.27/5.61 ! [X8: nat > int] :
% 5.27/5.61 ( ! [M5: nat,N3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M5 @ N3 )
% 5.27/5.61 => ( ord_less_eq_int @ ( X8 @ M5 ) @ ( X8 @ N3 ) ) )
% 5.27/5.61 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoI1
% 5.27/5.61 thf(fact_8738_scaleR__eq__iff,axiom,
% 5.27/5.61 ! [B: real,U: real,A: real] :
% 5.27/5.61 ( ( ( plus_plus_real @ B @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.27/5.61 = ( plus_plus_real @ A @ ( real_V1485227260804924795R_real @ U @ B ) ) )
% 5.27/5.61 = ( ( A = B )
% 5.27/5.61 | ( U = one_one_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_eq_iff
% 5.27/5.61 thf(fact_8739_scaleR__power,axiom,
% 5.27/5.61 ! [X4: real,Y: real,N2: nat] :
% 5.27/5.61 ( ( power_power_real @ ( real_V1485227260804924795R_real @ X4 @ Y ) @ N2 )
% 5.27/5.61 = ( real_V1485227260804924795R_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_power
% 5.27/5.61 thf(fact_8740_scaleR__power,axiom,
% 5.27/5.61 ! [X4: real,Y: complex,N2: nat] :
% 5.27/5.61 ( ( power_power_complex @ ( real_V2046097035970521341omplex @ X4 @ Y ) @ N2 )
% 5.27/5.61 = ( real_V2046097035970521341omplex @ ( power_power_real @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_power
% 5.27/5.61 thf(fact_8741_scaleR__minus1__left,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.61 = ( uminus_uminus_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_minus1_left
% 5.27/5.61 thf(fact_8742_scaleR__minus1__left,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( ( real_V2046097035970521341omplex @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.61 = ( uminus1482373934393186551omplex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_minus1_left
% 5.27/5.61 thf(fact_8743_scaleR__collapse,axiom,
% 5.27/5.61 ! [U: real,A: real] :
% 5.27/5.61 ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ one_one_real @ U ) @ A ) @ ( real_V1485227260804924795R_real @ U @ A ) )
% 5.27/5.61 = A ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_collapse
% 5.27/5.61 thf(fact_8744_scaleR__times,axiom,
% 5.27/5.61 ! [U: num,W: num,A: complex] :
% 5.27/5.61 ( ( real_V2046097035970521341omplex @ ( numeral_numeral_real @ U ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.27/5.61 = ( real_V2046097035970521341omplex @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_times
% 5.27/5.61 thf(fact_8745_scaleR__times,axiom,
% 5.27/5.61 ! [U: num,W: num,A: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ U ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.27/5.61 = ( real_V1485227260804924795R_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_times
% 5.27/5.61 thf(fact_8746_inverse__scaleR__times,axiom,
% 5.27/5.61 ! [V: num,W: num,A: complex] :
% 5.27/5.61 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.27/5.61 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % inverse_scaleR_times
% 5.27/5.61 thf(fact_8747_inverse__scaleR__times,axiom,
% 5.27/5.61 ! [V: num,W: num,A: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.27/5.61 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ W ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % inverse_scaleR_times
% 5.27/5.61 thf(fact_8748_fraction__scaleR__times,axiom,
% 5.27/5.61 ! [U: num,V: num,W: num,A: complex] :
% 5.27/5.61 ( ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.27/5.61 = ( real_V2046097035970521341omplex @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % fraction_scaleR_times
% 5.27/5.61 thf(fact_8749_fraction__scaleR__times,axiom,
% 5.27/5.61 ! [U: num,V: num,W: num,A: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.27/5.61 = ( real_V1485227260804924795R_real @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ W ) ) @ ( numeral_numeral_real @ V ) ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % fraction_scaleR_times
% 5.27/5.61 thf(fact_8750_scaleR__half__double,axiom,
% 5.27/5.61 ! [A: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ A @ A ) )
% 5.27/5.61 = A ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_half_double
% 5.27/5.61 thf(fact_8751_scaleR__right__distrib,axiom,
% 5.27/5.61 ! [A: real,X4: real,Y: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ A @ ( plus_plus_real @ X4 @ Y ) )
% 5.27/5.61 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ A @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_right_distrib
% 5.27/5.61 thf(fact_8752_scaleR__left__distrib,axiom,
% 5.27/5.61 ! [A: real,B: real,X4: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ A @ B ) @ X4 )
% 5.27/5.61 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_left_distrib
% 5.27/5.61 thf(fact_8753_scaleR__left_Oadd,axiom,
% 5.27/5.61 ! [X4: real,Y: real,Xa: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( plus_plus_real @ X4 @ Y ) @ Xa )
% 5.27/5.61 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ X4 @ Xa ) @ ( real_V1485227260804924795R_real @ Y @ Xa ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_left.add
% 5.27/5.61 thf(fact_8754_of__real__def,axiom,
% 5.27/5.61 ( real_V1803761363581548252l_real
% 5.27/5.61 = ( ^ [R5: real] : ( real_V1485227260804924795R_real @ R5 @ one_one_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_real_def
% 5.27/5.61 thf(fact_8755_of__real__def,axiom,
% 5.27/5.61 ( real_V4546457046886955230omplex
% 5.27/5.61 = ( ^ [R5: real] : ( real_V2046097035970521341omplex @ R5 @ one_one_complex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_real_def
% 5.27/5.61 thf(fact_8756_scaleR__right__mono,axiom,
% 5.27/5.61 ! [A: real,B: real,X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_right_mono
% 5.27/5.61 thf(fact_8757_scaleR__right__mono__neg,axiom,
% 5.27/5.61 ! [B: real,A: real,C: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ B @ A )
% 5.27/5.61 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ C ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_right_mono_neg
% 5.27/5.61 thf(fact_8758_Real__Vector__Spaces_Ole__add__iff2,axiom,
% 5.27/5.61 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 5.27/5.61 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ B @ A ) @ E2 ) @ D ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Real_Vector_Spaces.le_add_iff2
% 5.27/5.61 thf(fact_8759_Real__Vector__Spaces_Ole__add__iff1,axiom,
% 5.27/5.61 ! [A: real,E2: real,C: real,B: real,D: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ A @ E2 ) @ C ) @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ B @ E2 ) @ D ) )
% 5.27/5.61 = ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1485227260804924795R_real @ ( minus_minus_real @ A @ B ) @ E2 ) @ C ) @ D ) ) ).
% 5.27/5.61
% 5.27/5.61 % Real_Vector_Spaces.le_add_iff1
% 5.27/5.61 thf(fact_8760_zero__le__scaleR__iff,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) )
% 5.27/5.61 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.27/5.61 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.27/5.61 | ( A = zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % zero_le_scaleR_iff
% 5.27/5.61 thf(fact_8761_scaleR__le__0__iff,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ B ) @ zero_zero_real )
% 5.27/5.61 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.61 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.27/5.61 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.27/5.61 | ( A = zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_le_0_iff
% 5.27/5.61 thf(fact_8762_scaleR__nonpos__nonpos,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_nonpos_nonpos
% 5.27/5.61 thf(fact_8763_scaleR__nonpos__nonneg,axiom,
% 5.27/5.61 ! [A: real,X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_nonpos_nonneg
% 5.27/5.61 thf(fact_8764_scaleR__nonneg__nonpos,axiom,
% 5.27/5.61 ! [A: real,X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.61 => ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_nonneg_nonpos
% 5.27/5.61 thf(fact_8765_scaleR__nonneg__nonneg,axiom,
% 5.27/5.61 ! [A: real,X4: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ X4 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_nonneg_nonneg
% 5.27/5.61 thf(fact_8766_split__scaleR__pos__le,axiom,
% 5.27/5.61 ! [A: real,B: real] :
% 5.27/5.61 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.27/5.61 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( real_V1485227260804924795R_real @ A @ B ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % split_scaleR_pos_le
% 5.27/5.61 thf(fact_8767_split__scaleR__neg__le,axiom,
% 5.27/5.61 ! [A: real,X4: real] :
% 5.27/5.61 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.61 & ( ord_less_eq_real @ X4 @ zero_zero_real ) )
% 5.27/5.61 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.27/5.61 & ( ord_less_eq_real @ zero_zero_real @ X4 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ zero_zero_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % split_scaleR_neg_le
% 5.27/5.61 thf(fact_8768_scaleR__mono_H,axiom,
% 5.27/5.61 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.61 => ( ( ord_less_eq_real @ C @ D )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ C ) @ ( real_V1485227260804924795R_real @ B @ D ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_mono'
% 5.27/5.61 thf(fact_8769_scaleR__mono,axiom,
% 5.27/5.61 ! [A: real,B: real,X4: real,Y: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.61 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.27/5.61 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ ( real_V1485227260804924795R_real @ B @ Y ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_mono
% 5.27/5.61 thf(fact_8770_scaleR__left__le__one__le,axiom,
% 5.27/5.61 ! [X4: real,A: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.61 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ A @ X4 ) @ X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_left_le_one_le
% 5.27/5.61 thf(fact_8771_scaleR__2,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( ( real_V1485227260804924795R_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.61 = ( plus_plus_real @ X4 @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % scaleR_2
% 5.27/5.61 thf(fact_8772_real__vector__affinity__eq,axiom,
% 5.27/5.61 ! [M: real,X4: real,C: real,Y: real] :
% 5.27/5.61 ( ( M != zero_zero_real )
% 5.27/5.61 => ( ( ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C )
% 5.27/5.61 = Y )
% 5.27/5.61 = ( X4
% 5.27/5.61 = ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % real_vector_affinity_eq
% 5.27/5.61 thf(fact_8773_real__vector__eq__affinity,axiom,
% 5.27/5.61 ! [M: real,Y: real,X4: real,C: real] :
% 5.27/5.61 ( ( M != zero_zero_real )
% 5.27/5.61 => ( ( Y
% 5.27/5.61 = ( plus_plus_real @ ( real_V1485227260804924795R_real @ M @ X4 ) @ C ) )
% 5.27/5.61 = ( ( minus_minus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ Y ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ M ) @ C ) )
% 5.27/5.61 = X4 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % real_vector_eq_affinity
% 5.27/5.61 thf(fact_8774_neg__less__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.27/5.61 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_less_divideR_eq
% 5.27/5.61 thf(fact_8775_neg__divideR__less__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.27/5.61 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_divideR_less_eq
% 5.27/5.61 thf(fact_8776_pos__less__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_real @ A @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) )
% 5.27/5.61 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ B ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_less_divideR_eq
% 5.27/5.61 thf(fact_8777_pos__divideR__less__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) @ A )
% 5.27/5.61 = ( ord_less_real @ B @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_divideR_less_eq
% 5.27/5.61 thf(fact_8778_summable__exp__generic,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_exp_generic
% 5.27/5.61 thf(fact_8779_summable__exp__generic,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( summable_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_exp_generic
% 5.27/5.61 thf(fact_8780_sin__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 5.27/5.61 @ ( sin_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_converges
% 5.27/5.61 thf(fact_8781_sin__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 5.27/5.61 @ ( sin_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_converges
% 5.27/5.61 thf(fact_8782_sin__def,axiom,
% 5.27/5.61 ( sin_real
% 5.27/5.61 = ( ^ [X: real] :
% 5.27/5.61 ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_def
% 5.27/5.61 thf(fact_8783_sin__def,axiom,
% 5.27/5.61 ( sin_complex
% 5.27/5.61 = ( ^ [X: complex] :
% 5.27/5.61 ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_def
% 5.27/5.61 thf(fact_8784_cos__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) )
% 5.27/5.61 @ ( cos_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_converges
% 5.27/5.61 thf(fact_8785_cos__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) )
% 5.27/5.61 @ ( cos_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_converges
% 5.27/5.61 thf(fact_8786_cos__def,axiom,
% 5.27/5.61 ( cos_real
% 5.27/5.61 = ( ^ [X: real] :
% 5.27/5.61 ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_def
% 5.27/5.61 thf(fact_8787_cos__def,axiom,
% 5.27/5.61 ( cos_complex
% 5.27/5.61 = ( ^ [X: complex] :
% 5.27/5.61 ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_def
% 5.27/5.61 thf(fact_8788_summable__norm__sin,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_sin
% 5.27/5.61 thf(fact_8789_summable__norm__sin,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_sin
% 5.27/5.61 thf(fact_8790_summable__norm__cos,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_cos
% 5.27/5.61 thf(fact_8791_summable__norm__cos,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_cos
% 5.27/5.61 thf(fact_8792_pos__le__minus__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.27/5.61 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_le_minus_divideR_eq
% 5.27/5.61 thf(fact_8793_pos__minus__divideR__le__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.27/5.61 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_minus_divideR_le_eq
% 5.27/5.61 thf(fact_8794_neg__le__minus__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.27/5.61 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_le_minus_divideR_eq
% 5.27/5.61 thf(fact_8795_neg__minus__divideR__le__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.27/5.61 = ( ord_less_eq_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_minus_divideR_le_eq
% 5.27/5.61 thf(fact_8796_neg__minus__divideR__less__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.27/5.61 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_minus_divideR_less_eq
% 5.27/5.61 thf(fact_8797_neg__less__minus__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ C @ zero_zero_real )
% 5.27/5.61 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.27/5.61 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % neg_less_minus_divideR_eq
% 5.27/5.61 thf(fact_8798_pos__minus__divideR__less__eq,axiom,
% 5.27/5.61 ! [C: real,B: real,A: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_real @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) @ A )
% 5.27/5.61 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( real_V1485227260804924795R_real @ C @ A ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_minus_divideR_less_eq
% 5.27/5.61 thf(fact_8799_pos__less__minus__divideR__eq,axiom,
% 5.27/5.61 ! [C: real,A: real,B: real] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.61 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ C ) @ B ) ) )
% 5.27/5.61 = ( ord_less_real @ ( real_V1485227260804924795R_real @ C @ A ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pos_less_minus_divideR_eq
% 5.27/5.61 thf(fact_8800_exp__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) )
% 5.27/5.61 @ ( exp_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_converges
% 5.27/5.61 thf(fact_8801_exp__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) )
% 5.27/5.61 @ ( exp_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_converges
% 5.27/5.61 thf(fact_8802_exp__def,axiom,
% 5.27/5.61 ( exp_real
% 5.27/5.61 = ( ^ [X: real] :
% 5.27/5.61 ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_def
% 5.27/5.61 thf(fact_8803_exp__def,axiom,
% 5.27/5.61 ( exp_complex
% 5.27/5.61 = ( ^ [X: complex] :
% 5.27/5.61 ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_def
% 5.27/5.61 thf(fact_8804_summable__norm__exp,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V7735802525324610683m_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_exp
% 5.27/5.61 thf(fact_8805_summable__norm__exp,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( summable_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1022390504157884413omplex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % summable_norm_exp
% 5.27/5.61 thf(fact_8806_sin__minus__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( uminus_uminus_real @ ( real_V1485227260804924795R_real @ ( sin_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) ) )
% 5.27/5.61 @ ( sin_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_minus_converges
% 5.27/5.61 thf(fact_8807_sin__minus__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( uminus1482373934393186551omplex @ ( real_V2046097035970521341omplex @ ( sin_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) ) )
% 5.27/5.61 @ ( sin_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_minus_converges
% 5.27/5.61 thf(fact_8808_cos__minus__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( cos_coeff @ N ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ N ) )
% 5.27/5.61 @ ( cos_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_minus_converges
% 5.27/5.61 thf(fact_8809_cos__minus__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( cos_coeff @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ N ) )
% 5.27/5.61 @ ( cos_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_minus_converges
% 5.27/5.61 thf(fact_8810_cosh__def,axiom,
% 5.27/5.61 ( cosh_real
% 5.27/5.61 = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cosh_def
% 5.27/5.61 thf(fact_8811_cosh__def,axiom,
% 5.27/5.61 ( cosh_complex
% 5.27/5.61 = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cosh_def
% 5.27/5.61 thf(fact_8812_sinh__def,axiom,
% 5.27/5.61 ( sinh_real
% 5.27/5.61 = ( ^ [X: real] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sinh_def
% 5.27/5.61 thf(fact_8813_sinh__def,axiom,
% 5.27/5.61 ( sinh_complex
% 5.27/5.61 = ( ^ [X: complex] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( minus_minus_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sinh_def
% 5.27/5.61 thf(fact_8814_exp__first__term,axiom,
% 5.27/5.61 ( exp_real
% 5.27/5.61 = ( ^ [X: real] :
% 5.27/5.61 ( plus_plus_real @ one_one_real
% 5.27/5.61 @ ( suminf_real
% 5.27/5.61 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_first_term
% 5.27/5.61 thf(fact_8815_exp__first__term,axiom,
% 5.27/5.61 ( exp_complex
% 5.27/5.61 = ( ^ [X: complex] :
% 5.27/5.61 ( plus_plus_complex @ one_one_complex
% 5.27/5.61 @ ( suminf_complex
% 5.27/5.61 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( suc @ N ) ) ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_first_term
% 5.27/5.61 thf(fact_8816_cosh__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) @ zero_zero_real )
% 5.27/5.61 @ ( cosh_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cosh_converges
% 5.27/5.61 thf(fact_8817_cosh__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) @ zero_zero_complex )
% 5.27/5.61 @ ( cosh_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % cosh_converges
% 5.27/5.61 thf(fact_8818_sinh__converges,axiom,
% 5.27/5.61 ! [X4: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X4 @ N ) ) )
% 5.27/5.61 @ ( sinh_real @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sinh_converges
% 5.27/5.61 thf(fact_8819_sinh__converges,axiom,
% 5.27/5.61 ! [X4: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ zero_zero_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X4 @ N ) ) )
% 5.27/5.61 @ ( sinh_complex @ X4 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sinh_converges
% 5.27/5.61 thf(fact_8820_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > real] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8821_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > set_int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8822_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > rat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8823_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > num] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8824_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > nat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8825_mono__SucI1,axiom,
% 5.27/5.61 ! [X8: nat > int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ N3 ) @ ( X8 @ ( suc @ N3 ) ) )
% 5.27/5.61 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI1
% 5.27/5.61 thf(fact_8826_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > real] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo6980174941875973593q_real @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8827_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > set_int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo3100542954746470799et_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8828_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > rat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_rat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo4267028734544971653eq_rat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8829_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > num] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_num @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo1459490580787246023eq_num @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8830_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > nat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo4902158794631467389eq_nat @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8831_mono__SucI2,axiom,
% 5.27/5.61 ! [X8: nat > int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ ( X8 @ ( suc @ N3 ) ) @ ( X8 @ N3 ) )
% 5.27/5.61 => ( topolo4899668324122417113eq_int @ X8 ) ) ).
% 5.27/5.61
% 5.27/5.61 % mono_SucI2
% 5.27/5.61 thf(fact_8832_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo6980174941875973593q_real
% 5.27/5.61 = ( ^ [X3: nat > real] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_real @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_real @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8833_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo3100542954746470799et_int
% 5.27/5.61 = ( ^ [X3: nat > set_int] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_set_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8834_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo4267028734544971653eq_rat
% 5.27/5.61 = ( ^ [X3: nat > rat] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_rat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8835_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo1459490580787246023eq_num
% 5.27/5.61 = ( ^ [X3: nat > num] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_num @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_num @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8836_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo4902158794631467389eq_nat
% 5.27/5.61 = ( ^ [X3: nat > nat] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_nat @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8837_monoseq__Suc,axiom,
% 5.27/5.61 ( topolo4899668324122417113eq_int
% 5.27/5.61 = ( ^ [X3: nat > int] :
% 5.27/5.61 ( ! [N: nat] : ( ord_less_eq_int @ ( X3 @ N ) @ ( X3 @ ( suc @ N ) ) )
% 5.27/5.61 | ! [N: nat] : ( ord_less_eq_int @ ( X3 @ ( suc @ N ) ) @ ( X3 @ N ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % monoseq_Suc
% 5.27/5.61 thf(fact_8838_of__nat__code,axiom,
% 5.27/5.61 ( semiri8010041392384452111omplex
% 5.27/5.61 = ( ^ [N: nat] :
% 5.27/5.61 ( semiri2816024913162550771omplex
% 5.27/5.61 @ ^ [I3: complex] : ( plus_plus_complex @ I3 @ one_one_complex )
% 5.27/5.61 @ N
% 5.27/5.61 @ zero_zero_complex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_code
% 5.27/5.61 thf(fact_8839_of__nat__code,axiom,
% 5.27/5.61 ( semiri681578069525770553at_rat
% 5.27/5.61 = ( ^ [N: nat] :
% 5.27/5.61 ( semiri7787848453975740701ux_rat
% 5.27/5.61 @ ^ [I3: rat] : ( plus_plus_rat @ I3 @ one_one_rat )
% 5.27/5.61 @ N
% 5.27/5.61 @ zero_zero_rat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_code
% 5.27/5.61 thf(fact_8840_of__nat__code,axiom,
% 5.27/5.61 ( semiri5074537144036343181t_real
% 5.27/5.61 = ( ^ [N: nat] :
% 5.27/5.61 ( semiri7260567687927622513x_real
% 5.27/5.61 @ ^ [I3: real] : ( plus_plus_real @ I3 @ one_one_real )
% 5.27/5.61 @ N
% 5.27/5.61 @ zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_code
% 5.27/5.61 thf(fact_8841_of__nat__code,axiom,
% 5.27/5.61 ( semiri1314217659103216013at_int
% 5.27/5.61 = ( ^ [N: nat] :
% 5.27/5.61 ( semiri8420488043553186161ux_int
% 5.27/5.61 @ ^ [I3: int] : ( plus_plus_int @ I3 @ one_one_int )
% 5.27/5.61 @ N
% 5.27/5.61 @ zero_zero_int ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_code
% 5.27/5.61 thf(fact_8842_of__nat__code,axiom,
% 5.27/5.61 ( semiri1316708129612266289at_nat
% 5.27/5.61 = ( ^ [N: nat] :
% 5.27/5.61 ( semiri8422978514062236437ux_nat
% 5.27/5.61 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ one_one_nat )
% 5.27/5.61 @ N
% 5.27/5.61 @ zero_zero_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_code
% 5.27/5.61 thf(fact_8843_Arg__def,axiom,
% 5.27/5.61 ( arg
% 5.27/5.61 = ( ^ [Z5: complex] :
% 5.27/5.61 ( if_real @ ( Z5 = zero_zero_complex ) @ zero_zero_real
% 5.27/5.61 @ ( fChoice_real
% 5.27/5.61 @ ^ [A3: real] :
% 5.27/5.61 ( ( ( sgn_sgn_complex @ Z5 )
% 5.27/5.61 = ( cis @ A3 ) )
% 5.27/5.61 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.27/5.61 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Arg_def
% 5.27/5.61 thf(fact_8844_set__vebt__def,axiom,
% 5.27/5.61 ( vEBT_set_vebt
% 5.27/5.61 = ( ^ [T: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % set_vebt_def
% 5.27/5.61 thf(fact_8845_sin__x__sin__y,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [N: nat] :
% 5.27/5.61 ( if_complex
% 5.27/5.61 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.27/5.61 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.27/5.61 @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.27/5.61 @ zero_zero_complex )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( times_times_complex @ ( sin_complex @ X4 ) @ ( sin_complex @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_x_sin_y
% 5.27/5.61 thf(fact_8846_sin__x__sin__y,axiom,
% 5.27/5.61 ! [X4: real,Y: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [N: nat] :
% 5.27/5.61 ( if_real
% 5.27/5.61 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.27/5.61 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.27/5.61 @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.27/5.61 @ zero_zero_real )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( times_times_real @ ( sin_real @ X4 ) @ ( sin_real @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sin_x_sin_y
% 5.27/5.61 thf(fact_8847_atMost__eq__iff,axiom,
% 5.27/5.61 ! [X4: nat,Y: nat] :
% 5.27/5.61 ( ( ( set_ord_atMost_nat @ X4 )
% 5.27/5.61 = ( set_ord_atMost_nat @ Y ) )
% 5.27/5.61 = ( X4 = Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_eq_iff
% 5.27/5.61 thf(fact_8848_atMost__eq__iff,axiom,
% 5.27/5.61 ! [X4: int,Y: int] :
% 5.27/5.61 ( ( ( set_ord_atMost_int @ X4 )
% 5.27/5.61 = ( set_ord_atMost_int @ Y ) )
% 5.27/5.61 = ( X4 = Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_eq_iff
% 5.27/5.61 thf(fact_8849_atMost__iff,axiom,
% 5.27/5.61 ! [I2: real,K: real] :
% 5.27/5.61 ( ( member_real @ I2 @ ( set_ord_atMost_real @ K ) )
% 5.27/5.61 = ( ord_less_eq_real @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8850_atMost__iff,axiom,
% 5.27/5.61 ! [I2: set_int,K: set_int] :
% 5.27/5.61 ( ( member_set_int @ I2 @ ( set_or58775011639299419et_int @ K ) )
% 5.27/5.61 = ( ord_less_eq_set_int @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8851_atMost__iff,axiom,
% 5.27/5.61 ! [I2: rat,K: rat] :
% 5.27/5.61 ( ( member_rat @ I2 @ ( set_ord_atMost_rat @ K ) )
% 5.27/5.61 = ( ord_less_eq_rat @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8852_atMost__iff,axiom,
% 5.27/5.61 ! [I2: num,K: num] :
% 5.27/5.61 ( ( member_num @ I2 @ ( set_ord_atMost_num @ K ) )
% 5.27/5.61 = ( ord_less_eq_num @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8853_atMost__iff,axiom,
% 5.27/5.61 ! [I2: nat,K: nat] :
% 5.27/5.61 ( ( member_nat @ I2 @ ( set_ord_atMost_nat @ K ) )
% 5.27/5.61 = ( ord_less_eq_nat @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8854_atMost__iff,axiom,
% 5.27/5.61 ! [I2: int,K: int] :
% 5.27/5.61 ( ( member_int @ I2 @ ( set_ord_atMost_int @ K ) )
% 5.27/5.61 = ( ord_less_eq_int @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_iff
% 5.27/5.61 thf(fact_8855_atMost__subset__iff,axiom,
% 5.27/5.61 ! [X4: set_int,Y: set_int] :
% 5.27/5.61 ( ( ord_le4403425263959731960et_int @ ( set_or58775011639299419et_int @ X4 ) @ ( set_or58775011639299419et_int @ Y ) )
% 5.27/5.61 = ( ord_less_eq_set_int @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_subset_iff
% 5.27/5.61 thf(fact_8856_atMost__subset__iff,axiom,
% 5.27/5.61 ! [X4: rat,Y: rat] :
% 5.27/5.61 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ X4 ) @ ( set_ord_atMost_rat @ Y ) )
% 5.27/5.61 = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_subset_iff
% 5.27/5.61 thf(fact_8857_atMost__subset__iff,axiom,
% 5.27/5.61 ! [X4: num,Y: num] :
% 5.27/5.61 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ X4 ) @ ( set_ord_atMost_num @ Y ) )
% 5.27/5.61 = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_subset_iff
% 5.27/5.61 thf(fact_8858_atMost__subset__iff,axiom,
% 5.27/5.61 ! [X4: nat,Y: nat] :
% 5.27/5.61 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ X4 ) @ ( set_ord_atMost_nat @ Y ) )
% 5.27/5.61 = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_subset_iff
% 5.27/5.61 thf(fact_8859_atMost__subset__iff,axiom,
% 5.27/5.61 ! [X4: int,Y: int] :
% 5.27/5.61 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ X4 ) @ ( set_ord_atMost_int @ Y ) )
% 5.27/5.61 = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_subset_iff
% 5.27/5.61 thf(fact_8860_sum_OatMost__Suc,axiom,
% 5.27/5.61 ! [G: nat > rat,N2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc
% 5.27/5.61 thf(fact_8861_sum_OatMost__Suc,axiom,
% 5.27/5.61 ! [G: nat > int,N2: nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc
% 5.27/5.61 thf(fact_8862_sum_OatMost__Suc,axiom,
% 5.27/5.61 ! [G: nat > nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc
% 5.27/5.61 thf(fact_8863_sum_OatMost__Suc,axiom,
% 5.27/5.61 ! [G: nat > real,N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc
% 5.27/5.61 thf(fact_8864_norm__sum,axiom,
% 5.27/5.61 ! [F: nat > complex,A2: set_nat] :
% 5.27/5.61 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % norm_sum
% 5.27/5.61 thf(fact_8865_norm__sum,axiom,
% 5.27/5.61 ! [F: nat > real,A2: set_nat] :
% 5.27/5.61 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( real_V7735802525324610683m_real @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % norm_sum
% 5.27/5.61 thf(fact_8866_norm__sum,axiom,
% 5.27/5.61 ! [F: complex > complex,A2: set_complex] :
% 5.27/5.61 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.27/5.61 @ ( groups5808333547571424918x_real
% 5.27/5.61 @ ^ [I3: complex] : ( real_V1022390504157884413omplex @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % norm_sum
% 5.27/5.61 thf(fact_8867_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_real,F: real > complex,G: real > real] :
% 5.27/5.61 ( ! [X5: real] :
% 5.27/5.61 ( ( member_real @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8868_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_int,F: int > complex,G: int > real] :
% 5.27/5.61 ( ! [X5: int] :
% 5.27/5.61 ( ( member_int @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8869_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_Pr1261947904930325089at_nat,F: product_prod_nat_nat > complex,G: product_prod_nat_nat > real] :
% 5.27/5.61 ( ! [X5: product_prod_nat_nat] :
% 5.27/5.61 ( ( member8440522571783428010at_nat @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups6381953495645901045omplex @ F @ S2 ) ) @ ( groups4567486121110086003t_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8870_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 5.27/5.61 ( ! [X5: nat] :
% 5.27/5.61 ( ( member_nat @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8871_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_nat,F: nat > real,G: nat > real] :
% 5.27/5.61 ( ! [X5: nat] :
% 5.27/5.61 ( ( member_nat @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8872_sum__norm__le,axiom,
% 5.27/5.61 ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 5.27/5.61 ( ! [X5: complex] :
% 5.27/5.61 ( ( member_complex @ X5 @ S2 )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X5 ) ) @ ( G @ X5 ) ) )
% 5.27/5.61 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_norm_le
% 5.27/5.61 thf(fact_8873_sum__choose__upper,axiom,
% 5.27/5.61 ! [M: nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( binomial @ K3 @ M )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( binomial @ ( suc @ N2 ) @ ( suc @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_choose_upper
% 5.27/5.61 thf(fact_8874_mod__sum__eq,axiom,
% 5.27/5.61 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.27/5.61 ( ( modulo_modulo_nat
% 5.27/5.61 @ ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.27/5.61 @ A2 )
% 5.27/5.61 @ A )
% 5.27/5.61 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % mod_sum_eq
% 5.27/5.61 thf(fact_8875_mod__sum__eq,axiom,
% 5.27/5.61 ! [F: int > int,A: int,A2: set_int] :
% 5.27/5.61 ( ( modulo_modulo_int
% 5.27/5.61 @ ( groups4538972089207619220nt_int
% 5.27/5.61 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.27/5.61 @ A2 )
% 5.27/5.61 @ A )
% 5.27/5.61 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.27/5.61
% 5.27/5.61 % mod_sum_eq
% 5.27/5.61 thf(fact_8876_sum_OatMost__Suc__shift,axiom,
% 5.27/5.61 ! [G: nat > rat,N2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc_shift
% 5.27/5.61 thf(fact_8877_sum_OatMost__Suc__shift,axiom,
% 5.27/5.61 ! [G: nat > int,N2: nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc_shift
% 5.27/5.61 thf(fact_8878_sum_OatMost__Suc__shift,axiom,
% 5.27/5.61 ! [G: nat > nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.27/5.61 @ ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc_shift
% 5.27/5.61 thf(fact_8879_sum_OatMost__Suc__shift,axiom,
% 5.27/5.61 ! [G: nat > real,N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.atMost_Suc_shift
% 5.27/5.61 thf(fact_8880_sum__telescope,axiom,
% 5.27/5.61 ! [F: nat > rat,I2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ I2 ) )
% 5.27/5.61 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_telescope
% 5.27/5.61 thf(fact_8881_sum__telescope,axiom,
% 5.27/5.61 ! [F: nat > int,I2: nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ I2 ) )
% 5.27/5.61 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_telescope
% 5.27/5.61 thf(fact_8882_sum__telescope,axiom,
% 5.27/5.61 ! [F: nat > real,I2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ I3 ) @ ( F @ ( suc @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ I2 ) )
% 5.27/5.61 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ ( suc @ I2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_telescope
% 5.27/5.61 thf(fact_8883_polyfun__eq__coeffs,axiom,
% 5.27/5.61 ! [C: nat > complex,N2: nat,D: nat > complex] :
% 5.27/5.61 ( ( ! [X: complex] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( D @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.27/5.61 = ( ! [I3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.27/5.61 => ( ( C @ I3 )
% 5.27/5.61 = ( D @ I3 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_eq_coeffs
% 5.27/5.61 thf(fact_8884_polyfun__eq__coeffs,axiom,
% 5.27/5.61 ! [C: nat > real,N2: nat,D: nat > real] :
% 5.27/5.61 ( ( ! [X: real] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( D @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) )
% 5.27/5.61 = ( ! [I3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.27/5.61 => ( ( C @ I3 )
% 5.27/5.61 = ( D @ I3 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_eq_coeffs
% 5.27/5.61 thf(fact_8885_bounded__imp__summable,axiom,
% 5.27/5.61 ! [A: nat > int,B3: int] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( A @ N3 ) )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.27/5.61 => ( summable_int @ A ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % bounded_imp_summable
% 5.27/5.61 thf(fact_8886_bounded__imp__summable,axiom,
% 5.27/5.61 ! [A: nat > nat,B3: nat] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( A @ N3 ) )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.27/5.61 => ( summable_nat @ A ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % bounded_imp_summable
% 5.27/5.61 thf(fact_8887_bounded__imp__summable,axiom,
% 5.27/5.61 ! [A: nat > real,B3: real] :
% 5.27/5.61 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.61 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ A @ ( set_ord_atMost_nat @ N3 ) ) @ B3 )
% 5.27/5.61 => ( summable_real @ A ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % bounded_imp_summable
% 5.27/5.61 thf(fact_8888_atMost__def,axiom,
% 5.27/5.61 ( set_ord_atMost_real
% 5.27/5.61 = ( ^ [U2: real] :
% 5.27/5.61 ( collect_real
% 5.27/5.61 @ ^ [X: real] : ( ord_less_eq_real @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8889_atMost__def,axiom,
% 5.27/5.61 ( set_or58775011639299419et_int
% 5.27/5.61 = ( ^ [U2: set_int] :
% 5.27/5.61 ( collect_set_int
% 5.27/5.61 @ ^ [X: set_int] : ( ord_less_eq_set_int @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8890_atMost__def,axiom,
% 5.27/5.61 ( set_ord_atMost_rat
% 5.27/5.61 = ( ^ [U2: rat] :
% 5.27/5.61 ( collect_rat
% 5.27/5.61 @ ^ [X: rat] : ( ord_less_eq_rat @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8891_atMost__def,axiom,
% 5.27/5.61 ( set_ord_atMost_num
% 5.27/5.61 = ( ^ [U2: num] :
% 5.27/5.61 ( collect_num
% 5.27/5.61 @ ^ [X: num] : ( ord_less_eq_num @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8892_atMost__def,axiom,
% 5.27/5.61 ( set_ord_atMost_nat
% 5.27/5.61 = ( ^ [U2: nat] :
% 5.27/5.61 ( collect_nat
% 5.27/5.61 @ ^ [X: nat] : ( ord_less_eq_nat @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8893_atMost__def,axiom,
% 5.27/5.61 ( set_ord_atMost_int
% 5.27/5.61 = ( ^ [U2: int] :
% 5.27/5.61 ( collect_int
% 5.27/5.61 @ ^ [X: int] : ( ord_less_eq_int @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % atMost_def
% 5.27/5.61 thf(fact_8894_sum__choose__lower,axiom,
% 5.27/5.61 ! [R3: nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( binomial @ ( plus_plus_nat @ R3 @ K3 ) @ K3 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( binomial @ ( suc @ ( plus_plus_nat @ R3 @ N2 ) ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_choose_lower
% 5.27/5.61 thf(fact_8895_choose__rising__sum_I2_J,axiom,
% 5.27/5.61 ! [N2: nat,M: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_rising_sum(2)
% 5.27/5.61 thf(fact_8896_choose__rising__sum_I1_J,axiom,
% 5.27/5.61 ! [N2: nat,M: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N2 @ J3 ) @ N2 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N2 @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_rising_sum(1)
% 5.27/5.61 thf(fact_8897_polyfun__eq__0,axiom,
% 5.27/5.61 ! [C: nat > complex,N2: nat] :
% 5.27/5.61 ( ( ! [X: complex] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_complex ) )
% 5.27/5.61 = ( ! [I3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.27/5.61 => ( ( C @ I3 )
% 5.27/5.61 = zero_zero_complex ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_eq_0
% 5.27/5.61 thf(fact_8898_polyfun__eq__0,axiom,
% 5.27/5.61 ! [C: nat > real,N2: nat] :
% 5.27/5.61 ( ( ! [X: real] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_real ) )
% 5.27/5.61 = ( ! [I3: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ I3 @ N2 )
% 5.27/5.61 => ( ( C @ I3 )
% 5.27/5.61 = zero_zero_real ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_eq_0
% 5.27/5.61 thf(fact_8899_zero__polynom__imp__zero__coeffs,axiom,
% 5.27/5.61 ! [C: nat > complex,N2: nat,K: nat] :
% 5.27/5.61 ( ! [W2: complex] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ W2 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_complex )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.61 => ( ( C @ K )
% 5.27/5.61 = zero_zero_complex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % zero_polynom_imp_zero_coeffs
% 5.27/5.61 thf(fact_8900_zero__polynom__imp__zero__coeffs,axiom,
% 5.27/5.61 ! [C: nat > real,N2: nat,K: nat] :
% 5.27/5.61 ( ! [W2: real] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ W2 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_real )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ N2 )
% 5.27/5.61 => ( ( C @ K )
% 5.27/5.61 = zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % zero_polynom_imp_zero_coeffs
% 5.27/5.61 thf(fact_8901_gbinomial__parallel__sum,axiom,
% 5.27/5.61 ! [A: complex,N2: nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( gbinomial_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ K3 ) ) @ K3 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( gbinomial_complex @ ( plus_plus_complex @ ( plus_plus_complex @ A @ ( semiri8010041392384452111omplex @ N2 ) ) @ one_one_complex ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_parallel_sum
% 5.27/5.61 thf(fact_8902_gbinomial__parallel__sum,axiom,
% 5.27/5.61 ! [A: rat,N2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( gbinomial_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ K3 ) ) @ K3 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( gbinomial_rat @ ( plus_plus_rat @ ( plus_plus_rat @ A @ ( semiri681578069525770553at_rat @ N2 ) ) @ one_one_rat ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_parallel_sum
% 5.27/5.61 thf(fact_8903_gbinomial__parallel__sum,axiom,
% 5.27/5.61 ! [A: real,N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( gbinomial_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ K3 ) ) @ K3 )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( gbinomial_real @ ( plus_plus_real @ ( plus_plus_real @ A @ ( semiri5074537144036343181t_real @ N2 ) ) @ one_one_real ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_parallel_sum
% 5.27/5.61 thf(fact_8904_sum__choose__diagonal,axiom,
% 5.27/5.61 ! [M: nat,N2: nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.61 => ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( binomial @ ( minus_minus_nat @ N2 @ K3 ) @ ( minus_minus_nat @ M @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( binomial @ ( suc @ N2 ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_choose_diagonal
% 5.27/5.61 thf(fact_8905_vandermonde,axiom,
% 5.27/5.61 ! [M: nat,N2: nat,R3: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_nat @ ( binomial @ M @ K3 ) @ ( binomial @ N2 @ ( minus_minus_nat @ R3 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R3 ) )
% 5.27/5.61 = ( binomial @ ( plus_plus_nat @ M @ N2 ) @ R3 ) ) ).
% 5.27/5.61
% 5.27/5.61 % vandermonde
% 5.27/5.61 thf(fact_8906_sum__gp__basic,axiom,
% 5.27/5.61 ! [X4: rat,N2: nat] :
% 5.27/5.61 ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp_basic
% 5.27/5.61 thf(fact_8907_sum__gp__basic,axiom,
% 5.27/5.61 ! [X4: complex,N2: nat] :
% 5.27/5.61 ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp_basic
% 5.27/5.61 thf(fact_8908_sum__gp__basic,axiom,
% 5.27/5.61 ! [X4: int,N2: nat] :
% 5.27/5.61 ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp_basic
% 5.27/5.61 thf(fact_8909_sum__gp__basic,axiom,
% 5.27/5.61 ! [X4: real,N2: nat] :
% 5.27/5.61 ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp_basic
% 5.27/5.61 thf(fact_8910_choose__row__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ ( binomial @ N2 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_row_sum
% 5.27/5.61 thf(fact_8911_binomial,axiom,
% 5.27/5.61 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.61 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial
% 5.27/5.61 thf(fact_8912_sum_Oin__pairs__0,axiom,
% 5.27/5.61 ! [G: nat > rat,N2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [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 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.in_pairs_0
% 5.27/5.61 thf(fact_8913_sum_Oin__pairs__0,axiom,
% 5.27/5.61 ! [G: nat > int,N2: nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.61 = ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [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 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.in_pairs_0
% 5.27/5.61 thf(fact_8914_sum_Oin__pairs__0,axiom,
% 5.27/5.61 ! [G: nat > nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [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 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.in_pairs_0
% 5.27/5.61 thf(fact_8915_sum_Oin__pairs__0,axiom,
% 5.27/5.61 ! [G: nat > real,N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [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 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.in_pairs_0
% 5.27/5.61 thf(fact_8916_polynomial__product,axiom,
% 5.27/5.61 ! [M: nat,A: nat > rat,N2: nat,B: nat > rat,X4: rat] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ M @ I4 )
% 5.27/5.61 => ( ( A @ I4 )
% 5.27/5.61 = zero_zero_rat ) )
% 5.27/5.61 => ( ! [J2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ N2 @ J2 )
% 5.27/5.61 => ( ( B @ J2 )
% 5.27/5.61 = zero_zero_rat ) )
% 5.27/5.61 => ( ( times_times_rat
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [J3: nat] : ( times_times_rat @ ( B @ J3 ) @ ( power_power_rat @ X4 @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [R5: nat] :
% 5.27/5.61 ( times_times_rat
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R5 ) )
% 5.27/5.61 @ ( power_power_rat @ X4 @ R5 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polynomial_product
% 5.27/5.61 thf(fact_8917_polynomial__product,axiom,
% 5.27/5.61 ! [M: nat,A: nat > complex,N2: nat,B: nat > complex,X4: complex] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ M @ I4 )
% 5.27/5.61 => ( ( A @ I4 )
% 5.27/5.61 = zero_zero_complex ) )
% 5.27/5.61 => ( ! [J2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ N2 @ J2 )
% 5.27/5.61 => ( ( B @ J2 )
% 5.27/5.61 = zero_zero_complex ) )
% 5.27/5.61 => ( ( times_times_complex
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [J3: nat] : ( times_times_complex @ ( B @ J3 ) @ ( power_power_complex @ X4 @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [R5: nat] :
% 5.27/5.61 ( times_times_complex
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R5 ) )
% 5.27/5.61 @ ( power_power_complex @ X4 @ R5 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polynomial_product
% 5.27/5.61 thf(fact_8918_polynomial__product,axiom,
% 5.27/5.61 ! [M: nat,A: nat > int,N2: nat,B: nat > int,X4: int] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ M @ I4 )
% 5.27/5.61 => ( ( A @ I4 )
% 5.27/5.61 = zero_zero_int ) )
% 5.27/5.61 => ( ! [J2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ N2 @ J2 )
% 5.27/5.61 => ( ( B @ J2 )
% 5.27/5.61 = zero_zero_int ) )
% 5.27/5.61 => ( ( times_times_int
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [J3: nat] : ( times_times_int @ ( B @ J3 ) @ ( power_power_int @ X4 @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [R5: nat] :
% 5.27/5.61 ( times_times_int
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_int @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R5 ) )
% 5.27/5.61 @ ( power_power_int @ X4 @ R5 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polynomial_product
% 5.27/5.61 thf(fact_8919_polynomial__product,axiom,
% 5.27/5.61 ! [M: nat,A: nat > real,N2: nat,B: nat > real,X4: real] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ M @ I4 )
% 5.27/5.61 => ( ( A @ I4 )
% 5.27/5.61 = zero_zero_real ) )
% 5.27/5.61 => ( ! [J2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ N2 @ J2 )
% 5.27/5.61 => ( ( B @ J2 )
% 5.27/5.61 = zero_zero_real ) )
% 5.27/5.61 => ( ( times_times_real
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [J3: nat] : ( times_times_real @ ( B @ J3 ) @ ( power_power_real @ X4 @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [R5: nat] :
% 5.27/5.61 ( times_times_real
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R5 ) )
% 5.27/5.61 @ ( power_power_real @ X4 @ R5 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polynomial_product
% 5.27/5.61 thf(fact_8920_gbinomial__sum__lower__neg,axiom,
% 5.27/5.61 ! [A: complex,M: nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ M ) @ ( gbinomial_complex @ ( minus_minus_complex @ A @ one_one_complex ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_sum_lower_neg
% 5.27/5.61 thf(fact_8921_gbinomial__sum__lower__neg,axiom,
% 5.27/5.61 ! [A: rat,M: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ M ) @ ( gbinomial_rat @ ( minus_minus_rat @ A @ one_one_rat ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_sum_lower_neg
% 5.27/5.61 thf(fact_8922_gbinomial__sum__lower__neg,axiom,
% 5.27/5.61 ! [A: real,M: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ M ) @ ( gbinomial_real @ ( minus_minus_real @ A @ one_one_real ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_sum_lower_neg
% 5.27/5.61 thf(fact_8923_binomial__ring,axiom,
% 5.27/5.61 ! [A: rat,B: rat,N2: nat] :
% 5.27/5.61 ( ( power_power_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_rat @ A @ K3 ) ) @ ( power_power_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_ring
% 5.27/5.61 thf(fact_8924_binomial__ring,axiom,
% 5.27/5.61 ! [A: complex,B: complex,N2: nat] :
% 5.27/5.61 ( ( power_power_complex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( power_power_complex @ A @ K3 ) ) @ ( power_power_complex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_ring
% 5.27/5.61 thf(fact_8925_binomial__ring,axiom,
% 5.27/5.61 ! [A: int,B: int,N2: nat] :
% 5.27/5.61 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( power_power_int @ A @ K3 ) ) @ ( power_power_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_ring
% 5.27/5.61 thf(fact_8926_binomial__ring,axiom,
% 5.27/5.61 ! [A: nat,B: nat,N2: nat] :
% 5.27/5.61 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N2 @ K3 ) ) @ ( power_power_nat @ A @ K3 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_ring
% 5.27/5.61 thf(fact_8927_binomial__ring,axiom,
% 5.27/5.61 ! [A: real,B: real,N2: nat] :
% 5.27/5.61 ( ( power_power_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( power_power_real @ A @ K3 ) ) @ ( power_power_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_ring
% 5.27/5.61 thf(fact_8928_polynomial__product__nat,axiom,
% 5.27/5.61 ! [M: nat,A: nat > nat,N2: nat,B: nat > nat,X4: nat] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( ord_less_nat @ M @ I4 )
% 5.27/5.61 => ( ( A @ I4 )
% 5.27/5.61 = zero_zero_nat ) )
% 5.27/5.61 => ( ! [J2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ N2 @ J2 )
% 5.27/5.61 => ( ( B @ J2 )
% 5.27/5.61 = zero_zero_nat ) )
% 5.27/5.61 => ( ( times_times_nat
% 5.27/5.61 @ ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( power_power_nat @ X4 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 @ ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X4 @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [R5: nat] :
% 5.27/5.61 ( times_times_nat
% 5.27/5.61 @ ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_nat @ ( A @ K3 ) @ ( B @ ( minus_minus_nat @ R5 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ R5 ) )
% 5.27/5.61 @ ( power_power_nat @ X4 @ R5 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polynomial_product_nat
% 5.27/5.61 thf(fact_8929_choose__square__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [K3: nat] : ( power_power_nat @ ( binomial @ N2 @ K3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ N2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_square_sum
% 5.27/5.61 thf(fact_8930_pochhammer__binomial__sum,axiom,
% 5.27/5.61 ! [A: rat,B: rat,N2: nat] :
% 5.27/5.61 ( ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ A @ K3 ) ) @ ( comm_s4028243227959126397er_rat @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_binomial_sum
% 5.27/5.61 thf(fact_8931_pochhammer__binomial__sum,axiom,
% 5.27/5.61 ! [A: complex,B: complex,N2: nat] :
% 5.27/5.61 ( ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ K3 ) ) @ ( comm_s2602460028002588243omplex @ A @ K3 ) ) @ ( comm_s2602460028002588243omplex @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_binomial_sum
% 5.27/5.61 thf(fact_8932_pochhammer__binomial__sum,axiom,
% 5.27/5.61 ! [A: int,B: int,N2: nat] :
% 5.27/5.61 ( ( comm_s4660882817536571857er_int @ ( plus_plus_int @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ K3 ) ) @ ( comm_s4660882817536571857er_int @ A @ K3 ) ) @ ( comm_s4660882817536571857er_int @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_binomial_sum
% 5.27/5.61 thf(fact_8933_pochhammer__binomial__sum,axiom,
% 5.27/5.61 ! [A: real,B: real,N2: nat] :
% 5.27/5.61 ( ( comm_s7457072308508201937r_real @ ( plus_plus_real @ A @ B ) @ N2 )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ K3 ) ) @ ( comm_s7457072308508201937r_real @ A @ K3 ) ) @ ( comm_s7457072308508201937r_real @ B @ ( minus_minus_nat @ N2 @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % pochhammer_binomial_sum
% 5.27/5.61 thf(fact_8934_sum__power__add,axiom,
% 5.27/5.61 ! [X4: complex,M: nat,I5: set_nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ I5 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_power_add
% 5.27/5.61 thf(fact_8935_sum__power__add,axiom,
% 5.27/5.61 ! [X4: int,M: nat,I5: set_nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( power_power_int @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ I5 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_power_add
% 5.27/5.61 thf(fact_8936_sum__power__add,axiom,
% 5.27/5.61 ! [X4: real,M: nat,I5: set_nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( power_power_real @ X4 @ ( plus_plus_nat @ M @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ I5 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_power_add
% 5.27/5.61 thf(fact_8937_sum_Ozero__middle,axiom,
% 5.27/5.61 ! [P2: nat,K: nat,G: nat > complex,H: nat > complex] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.27/5.61 => ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_complex @ ( J3 = K ) @ zero_zero_complex @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P2 ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [J3: nat] : ( if_complex @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.zero_middle
% 5.27/5.61 thf(fact_8938_sum_Ozero__middle,axiom,
% 5.27/5.61 ! [P2: nat,K: nat,G: nat > rat,H: nat > rat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.27/5.61 => ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_rat @ ( J3 = K ) @ zero_zero_rat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P2 ) )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [J3: nat] : ( if_rat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.zero_middle
% 5.27/5.61 thf(fact_8939_sum_Ozero__middle,axiom,
% 5.27/5.61 ! [P2: nat,K: nat,G: nat > int,H: nat > int] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.27/5.61 => ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_int @ ( J3 = K ) @ zero_zero_int @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P2 ) )
% 5.27/5.61 = ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [J3: nat] : ( if_int @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.zero_middle
% 5.27/5.61 thf(fact_8940_sum_Ozero__middle,axiom,
% 5.27/5.61 ! [P2: nat,K: nat,G: nat > nat,H: nat > nat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.27/5.61 => ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_nat @ ( J3 = K ) @ zero_zero_nat @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P2 ) )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [J3: nat] : ( if_nat @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.zero_middle
% 5.27/5.61 thf(fact_8941_sum_Ozero__middle,axiom,
% 5.27/5.61 ! [P2: nat,K: nat,G: nat > real,H: nat > real] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ P2 )
% 5.27/5.61 => ( ( ord_less_eq_nat @ K @ P2 )
% 5.27/5.61 => ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( if_real @ ( J3 = K ) @ zero_zero_real @ ( H @ ( minus_minus_nat @ J3 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P2 ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [J3: nat] : ( if_real @ ( ord_less_nat @ J3 @ K ) @ ( G @ J3 ) @ ( H @ J3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ ( minus_minus_nat @ P2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.zero_middle
% 5.27/5.61 thf(fact_8942_gbinomial__partial__sum__poly,axiom,
% 5.27/5.61 ! [M: nat,A: complex,X4: complex,Y: complex] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( uminus1482373934393186551omplex @ A ) @ K3 ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ X4 ) @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly
% 5.27/5.61 thf(fact_8943_gbinomial__partial__sum__poly,axiom,
% 5.27/5.61 ! [M: nat,A: rat,X4: rat,Y: rat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( uminus_uminus_rat @ A ) @ K3 ) @ ( power_power_rat @ ( uminus_uminus_rat @ X4 ) @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly
% 5.27/5.61 thf(fact_8944_gbinomial__partial__sum__poly,axiom,
% 5.27/5.61 ! [M: nat,A: real,X4: real,Y: real] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( uminus_uminus_real @ A ) @ K3 ) @ ( power_power_real @ ( uminus_uminus_real @ X4 ) @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly
% 5.27/5.61 thf(fact_8945_exp__series__add__commuting,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex,N2: nat] :
% 5.27/5.61 ( ( ( times_times_complex @ X4 @ Y )
% 5.27/5.61 = ( times_times_complex @ Y @ X4 ) )
% 5.27/5.61 => ( ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ N2 ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_complex @ X4 @ I3 ) ) @ ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_series_add_commuting
% 5.27/5.61 thf(fact_8946_exp__series__add__commuting,axiom,
% 5.27/5.61 ! [X4: real,Y: real,N2: nat] :
% 5.27/5.61 ( ( ( times_times_real @ X4 @ Y )
% 5.27/5.61 = ( times_times_real @ Y @ X4 ) )
% 5.27/5.61 => ( ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ N2 ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ I3 ) ) @ ( power_power_real @ X4 @ I3 ) ) @ ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ I3 ) ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ I3 ) ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % exp_series_add_commuting
% 5.27/5.61 thf(fact_8947_root__polyfun,axiom,
% 5.27/5.61 ! [N2: nat,Z: int,A: int] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.61 => ( ( ( power_power_int @ Z @ N2 )
% 5.27/5.61 = A )
% 5.27/5.61 = ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_int @ ( if_int @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_int @ A ) @ ( if_int @ ( I3 = N2 ) @ one_one_int @ zero_zero_int ) ) @ ( power_power_int @ Z @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_int ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % root_polyfun
% 5.27/5.61 thf(fact_8948_root__polyfun,axiom,
% 5.27/5.61 ! [N2: nat,Z: complex,A: complex] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.61 => ( ( ( power_power_complex @ Z @ N2 )
% 5.27/5.61 = A )
% 5.27/5.61 = ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( if_complex @ ( I3 = zero_zero_nat ) @ ( uminus1482373934393186551omplex @ A ) @ ( if_complex @ ( I3 = N2 ) @ one_one_complex @ zero_zero_complex ) ) @ ( power_power_complex @ Z @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_complex ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % root_polyfun
% 5.27/5.61 thf(fact_8949_root__polyfun,axiom,
% 5.27/5.61 ! [N2: nat,Z: code_integer,A: code_integer] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.61 => ( ( ( power_8256067586552552935nteger @ Z @ N2 )
% 5.27/5.61 = A )
% 5.27/5.61 = ( ( groups7501900531339628137nteger
% 5.27/5.61 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( if_Code_integer @ ( I3 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ A ) @ ( if_Code_integer @ ( I3 = N2 ) @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) @ ( power_8256067586552552935nteger @ Z @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_z3403309356797280102nteger ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % root_polyfun
% 5.27/5.61 thf(fact_8950_root__polyfun,axiom,
% 5.27/5.61 ! [N2: nat,Z: rat,A: rat] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.61 => ( ( ( power_power_rat @ Z @ N2 )
% 5.27/5.61 = A )
% 5.27/5.61 = ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_rat @ ( if_rat @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_rat @ A ) @ ( if_rat @ ( I3 = N2 ) @ one_one_rat @ zero_zero_rat ) ) @ ( power_power_rat @ Z @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_rat ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % root_polyfun
% 5.27/5.61 thf(fact_8951_root__polyfun,axiom,
% 5.27/5.61 ! [N2: nat,Z: real,A: real] :
% 5.27/5.61 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.61 => ( ( ( power_power_real @ Z @ N2 )
% 5.27/5.61 = A )
% 5.27/5.61 = ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( if_real @ ( I3 = zero_zero_nat ) @ ( uminus_uminus_real @ A ) @ ( if_real @ ( I3 = N2 ) @ one_one_real @ zero_zero_real ) ) @ ( power_power_real @ Z @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_real ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % root_polyfun
% 5.27/5.61 thf(fact_8952_sum__gp0,axiom,
% 5.27/5.61 ! [X4: rat,N2: nat] :
% 5.27/5.61 ( ( ( X4 = one_one_rat )
% 5.27/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( semiri681578069525770553at_rat @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.27/5.61 & ( ( X4 != one_one_rat )
% 5.27/5.61 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp0
% 5.27/5.61 thf(fact_8953_sum__gp0,axiom,
% 5.27/5.61 ! [X4: complex,N2: nat] :
% 5.27/5.61 ( ( ( X4 = one_one_complex )
% 5.27/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( semiri8010041392384452111omplex @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.27/5.61 & ( ( X4 != one_one_complex )
% 5.27/5.61 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp0
% 5.27/5.61 thf(fact_8954_sum__gp0,axiom,
% 5.27/5.61 ! [X4: real,N2: nat] :
% 5.27/5.61 ( ( ( X4 = one_one_real )
% 5.27/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) )
% 5.27/5.61 & ( ( X4 != one_one_real )
% 5.27/5.61 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_gp0
% 5.27/5.61 thf(fact_8955_choose__alternating__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( N2 != one_one_nat )
% 5.27/5.61 => ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ I3 ) ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_complex ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_linear_sum
% 5.27/5.61 thf(fact_8956_choose__alternating__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( N2 != one_one_nat )
% 5.27/5.61 => ( ( groups7501900531339628137nteger
% 5.27/5.61 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ I3 ) ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_linear_sum
% 5.27/5.61 thf(fact_8957_choose__alternating__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( N2 != one_one_nat )
% 5.27/5.61 => ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_rat @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ I3 ) ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_rat ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_linear_sum
% 5.27/5.61 thf(fact_8958_choose__alternating__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( N2 != one_one_nat )
% 5.27/5.61 => ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_int @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ I3 ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_int ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_linear_sum
% 5.27/5.61 thf(fact_8959_choose__alternating__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( N2 != one_one_nat )
% 5.27/5.61 => ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ I3 ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_linear_sum
% 5.27/5.61 thf(fact_8960_gbinomial__sum__nat__pow2,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( divide1717551699836669952omplex @ ( gbinomial_complex @ ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_sum_nat_pow2
% 5.27/5.61 thf(fact_8961_gbinomial__sum__nat__pow2,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( divide_divide_real @ ( gbinomial_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ K3 ) ) @ K3 ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ K3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ M ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_sum_nat_pow2
% 5.27/5.61 thf(fact_8962_gbinomial__partial__sum__poly__xpos,axiom,
% 5.27/5.61 ! [M: nat,A: rat,X4: rat,Y: rat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( times_times_rat @ ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ A ) @ K3 ) @ ( power_power_rat @ X4 @ K3 ) ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [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 @ X4 @ K3 ) ) @ ( power_power_rat @ ( plus_plus_rat @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly_xpos
% 5.27/5.61 thf(fact_8963_gbinomial__partial__sum__poly__xpos,axiom,
% 5.27/5.61 ! [M: nat,A: complex,X4: complex,Y: complex] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( times_times_complex @ ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ A ) @ K3 ) @ ( power_power_complex @ X4 @ K3 ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [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 @ X4 @ K3 ) ) @ ( power_power_complex @ ( plus_plus_complex @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly_xpos
% 5.27/5.61 thf(fact_8964_gbinomial__partial__sum__poly__xpos,axiom,
% 5.27/5.61 ! [M: nat,A: real,X4: real,Y: real] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( times_times_real @ ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ A ) @ K3 ) @ ( power_power_real @ X4 @ K3 ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [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 @ X4 @ K3 ) ) @ ( power_power_real @ ( plus_plus_real @ X4 @ Y ) @ ( minus_minus_nat @ M @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_sum_poly_xpos
% 5.27/5.61 thf(fact_8965_binomial__r__part__sum,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % binomial_r_part_sum
% 5.27/5.61 thf(fact_8966_choose__linear__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_nat @ I3 @ ( binomial @ N2 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = ( times_times_nat @ N2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_linear_sum
% 5.27/5.61 thf(fact_8967_choose__alternating__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_complex ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_sum
% 5.27/5.61 thf(fact_8968_choose__alternating__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( groups7501900531339628137nteger
% 5.27/5.61 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ I3 ) @ ( semiri4939895301339042750nteger @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_z3403309356797280102nteger ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_sum
% 5.27/5.61 thf(fact_8969_choose__alternating__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_rat ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_sum
% 5.27/5.61 thf(fact_8970_choose__alternating__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_int ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_sum
% 5.27/5.61 thf(fact_8971_choose__alternating__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.61 = zero_zero_real ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_alternating_sum
% 5.27/5.61 thf(fact_8972_polyfun__extremal__lemma,axiom,
% 5.27/5.61 ! [E2: real,C: nat > complex,N2: nat] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.61 => ? [M9: real] :
% 5.27/5.61 ! [Z3: complex] :
% 5.27/5.61 ( ( ord_less_eq_real @ M9 @ ( real_V1022390504157884413omplex @ Z3 ) )
% 5.27/5.61 => ( ord_less_eq_real
% 5.27/5.61 @ ( real_V1022390504157884413omplex
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_extremal_lemma
% 5.27/5.61 thf(fact_8973_polyfun__extremal__lemma,axiom,
% 5.27/5.61 ! [E2: real,C: nat > real,N2: nat] :
% 5.27/5.61 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.61 => ? [M9: real] :
% 5.27/5.61 ! [Z3: real] :
% 5.27/5.61 ( ( ord_less_eq_real @ M9 @ ( real_V7735802525324610683m_real @ Z3 ) )
% 5.27/5.61 => ( ord_less_eq_real
% 5.27/5.61 @ ( real_V7735802525324610683m_real
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 @ ( times_times_real @ E2 @ ( power_power_real @ ( real_V7735802525324610683m_real @ Z3 ) @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % polyfun_extremal_lemma
% 5.27/5.61 thf(fact_8974_gbinomial__r__part__sum,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( 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 ) )
% 5.27/5.61 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_r_part_sum
% 5.27/5.61 thf(fact_8975_gbinomial__r__part__sum,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex @ ( gbinomial_complex @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M ) ) @ one_one_complex ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_r_part_sum
% 5.27/5.61 thf(fact_8976_gbinomial__r__part__sum,axiom,
% 5.27/5.61 ! [M: nat] :
% 5.27/5.61 ( ( 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 ) )
% 5.27/5.61 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_r_part_sum
% 5.27/5.61 thf(fact_8977_choose__odd__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] :
% 5.27/5.61 ( if_rat
% 5.27/5.61 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.61 @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) )
% 5.27/5.61 @ zero_zero_rat )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_odd_sum
% 5.27/5.61 thf(fact_8978_choose__odd__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] :
% 5.27/5.61 ( if_complex
% 5.27/5.61 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.61 @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) )
% 5.27/5.61 @ zero_zero_complex )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_odd_sum
% 5.27/5.61 thf(fact_8979_choose__odd__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] :
% 5.27/5.61 ( if_int
% 5.27/5.61 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.61 @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) )
% 5.27/5.61 @ zero_zero_int )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_odd_sum
% 5.27/5.61 thf(fact_8980_choose__odd__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] :
% 5.27/5.61 ( if_real
% 5.27/5.61 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 )
% 5.27/5.61 @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) )
% 5.27/5.61 @ zero_zero_real )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_odd_sum
% 5.27/5.61 thf(fact_8981_choose__even__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( if_rat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri681578069525770553at_rat @ ( binomial @ N2 @ I3 ) ) @ zero_zero_rat )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_even_sum
% 5.27/5.61 thf(fact_8982_choose__even__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [I3: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri8010041392384452111omplex @ ( binomial @ N2 @ I3 ) ) @ zero_zero_complex )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_even_sum
% 5.27/5.61 thf(fact_8983_choose__even__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups3539618377306564664at_int
% 5.27/5.61 @ ^ [I3: nat] : ( if_int @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri1314217659103216013at_int @ ( binomial @ N2 @ I3 ) ) @ zero_zero_int )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_even_sum
% 5.27/5.61 thf(fact_8984_choose__even__sum,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( semiri5074537144036343181t_real @ ( binomial @ N2 @ I3 ) ) @ zero_zero_real )
% 5.27/5.61 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.61 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % choose_even_sum
% 5.27/5.61 thf(fact_8985_gbinomial__partial__row__sum,axiom,
% 5.27/5.61 ! [A: rat,M: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ A @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( 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 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_row_sum
% 5.27/5.61 thf(fact_8986_gbinomial__partial__row__sum,axiom,
% 5.27/5.61 ! [A: complex,M: nat] :
% 5.27/5.61 ( ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ A @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( 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 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_row_sum
% 5.27/5.61 thf(fact_8987_gbinomial__partial__row__sum,axiom,
% 5.27/5.61 ! [A: real,M: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ A @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.27/5.61 @ ( set_ord_atMost_nat @ M ) )
% 5.27/5.61 = ( 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 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % gbinomial_partial_row_sum
% 5.27/5.61 thf(fact_8988_mask__eq__sum__exp,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int )
% 5.27/5.61 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.61 @ ( collect_nat
% 5.27/5.61 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % mask_eq_sum_exp
% 5.27/5.61 thf(fact_8989_mask__eq__sum__exp,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat )
% 5.27/5.61 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.61 @ ( collect_nat
% 5.27/5.61 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % mask_eq_sum_exp
% 5.27/5.61 thf(fact_8990_mask__eq__sum__exp__nat,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.61 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.27/5.61 @ ( collect_nat
% 5.27/5.61 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % mask_eq_sum_exp_nat
% 5.27/5.61 thf(fact_8991_cos__x__cos__y,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [N: nat] :
% 5.27/5.61 ( if_complex
% 5.27/5.61 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.27/5.61 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.27/5.61 @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.27/5.61 @ zero_zero_complex )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( times_times_complex @ ( cos_complex @ X4 ) @ ( cos_complex @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_x_cos_y
% 5.27/5.61 thf(fact_8992_cos__x__cos__y,axiom,
% 5.27/5.61 ! [X4: real,Y: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [N: nat] :
% 5.27/5.61 ( if_real
% 5.27/5.61 @ ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 )
% 5.27/5.61 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.27/5.61 @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) )
% 5.27/5.61 @ zero_zero_real )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( times_times_real @ ( cos_real @ X4 ) @ ( cos_real @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % cos_x_cos_y
% 5.27/5.61 thf(fact_8993_sums__cos__x__plus__y,axiom,
% 5.27/5.61 ! [X4: complex,Y: complex] :
% 5.27/5.61 ( sums_complex
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups2073611262835488442omplex
% 5.27/5.61 @ ^ [N: nat] : ( if_complex @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_complex @ X4 @ N ) ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_complex )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( cos_complex @ ( plus_plus_complex @ X4 @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_cos_x_plus_y
% 5.27/5.61 thf(fact_8994_sums__cos__x__plus__y,axiom,
% 5.27/5.61 ! [X4: real,Y: real] :
% 5.27/5.61 ( sums_real
% 5.27/5.61 @ ^ [P5: nat] :
% 5.27/5.61 ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [N: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ P5 ) @ ( 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 @ P5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri1314217659103216013at_int @ ( binomial @ P5 @ N ) ) ) ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ X4 @ N ) ) @ ( power_power_real @ Y @ ( minus_minus_nat @ P5 @ N ) ) ) @ zero_zero_real )
% 5.27/5.61 @ ( set_ord_atMost_nat @ P5 ) )
% 5.27/5.61 @ ( cos_real @ ( plus_plus_real @ X4 @ Y ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sums_cos_x_plus_y
% 5.27/5.61 thf(fact_8995_sum__abs__ge__zero,axiom,
% 5.27/5.61 ! [F: nat > real,A2: set_nat] :
% 5.27/5.61 ( ord_less_eq_real @ zero_zero_real
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_abs_ge_zero
% 5.27/5.61 thf(fact_8996_sum__abs__ge__zero,axiom,
% 5.27/5.61 ! [F: int > int,A2: set_int] :
% 5.27/5.61 ( ord_less_eq_int @ zero_zero_int
% 5.27/5.61 @ ( groups4538972089207619220nt_int
% 5.27/5.61 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_abs_ge_zero
% 5.27/5.61 thf(fact_8997_sum__abs,axiom,
% 5.27/5.61 ! [F: nat > real,A2: set_nat] :
% 5.27/5.61 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [I3: nat] : ( abs_abs_real @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_abs
% 5.27/5.61 thf(fact_8998_sum__abs,axiom,
% 5.27/5.61 ! [F: int > int,A2: set_int] :
% 5.27/5.61 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.27/5.61 @ ( groups4538972089207619220nt_int
% 5.27/5.61 @ ^ [I3: int] : ( abs_abs_int @ ( F @ I3 ) )
% 5.27/5.61 @ A2 ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_abs
% 5.27/5.61 thf(fact_8999_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_real,X4: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.27/5.61 ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups7713935264441627589nteger @ X4 @ I5 )
% 5.27/5.61 = one_one_Code_integer )
% 5.27/5.61 => ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_le3102999989581377725nteger
% 5.27/5.61 @ ( abs_abs_Code_integer
% 5.27/5.61 @ ( minus_8373710615458151222nteger
% 5.27/5.61 @ ( groups7713935264441627589nteger
% 5.27/5.61 @ ^ [I3: real] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9000_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_nat,X4: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( member_nat @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups7501900531339628137nteger @ X4 @ I5 )
% 5.27/5.61 = one_one_Code_integer )
% 5.27/5.61 => ( ! [I4: nat] :
% 5.27/5.61 ( ( member_nat @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_le3102999989581377725nteger
% 5.27/5.61 @ ( abs_abs_Code_integer
% 5.27/5.61 @ ( minus_8373710615458151222nteger
% 5.27/5.61 @ ( groups7501900531339628137nteger
% 5.27/5.61 @ ^ [I3: nat] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9001_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_complex,X4: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.27/5.61 ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups6621422865394947399nteger @ X4 @ I5 )
% 5.27/5.61 = one_one_Code_integer )
% 5.27/5.61 => ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_le3102999989581377725nteger
% 5.27/5.61 @ ( abs_abs_Code_integer
% 5.27/5.61 @ ( minus_8373710615458151222nteger
% 5.27/5.61 @ ( groups6621422865394947399nteger
% 5.27/5.61 @ ^ [I3: complex] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9002_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_int,X4: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.27/5.61 ( ! [I4: int] :
% 5.27/5.61 ( ( member_int @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups7873554091576472773nteger @ X4 @ I5 )
% 5.27/5.61 = one_one_Code_integer )
% 5.27/5.61 => ( ! [I4: int] :
% 5.27/5.61 ( ( member_int @ I4 @ I5 )
% 5.27/5.61 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_le3102999989581377725nteger
% 5.27/5.61 @ ( abs_abs_Code_integer
% 5.27/5.61 @ ( minus_8373710615458151222nteger
% 5.27/5.61 @ ( groups7873554091576472773nteger
% 5.27/5.61 @ ^ [I3: int] : ( times_3573771949741848930nteger @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9003_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_real,X4: real > real,A: real > real,B: real,Delta: real] :
% 5.27/5.61 ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups8097168146408367636l_real @ X4 @ I5 )
% 5.27/5.61 = one_one_real )
% 5.27/5.61 => ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_real
% 5.27/5.61 @ ( abs_abs_real
% 5.27/5.61 @ ( minus_minus_real
% 5.27/5.61 @ ( groups8097168146408367636l_real
% 5.27/5.61 @ ^ [I3: real] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9004_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_complex,X4: complex > real,A: complex > real,B: real,Delta: real] :
% 5.27/5.61 ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups5808333547571424918x_real @ X4 @ I5 )
% 5.27/5.61 = one_one_real )
% 5.27/5.61 => ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_real
% 5.27/5.61 @ ( abs_abs_real
% 5.27/5.61 @ ( minus_minus_real
% 5.27/5.61 @ ( groups5808333547571424918x_real
% 5.27/5.61 @ ^ [I3: complex] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9005_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_int,X4: int > real,A: int > real,B: real,Delta: real] :
% 5.27/5.61 ( ! [I4: int] :
% 5.27/5.61 ( ( member_int @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ zero_zero_real @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups8778361861064173332t_real @ X4 @ I5 )
% 5.27/5.61 = one_one_real )
% 5.27/5.61 => ( ! [I4: int] :
% 5.27/5.61 ( ( member_int @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_real
% 5.27/5.61 @ ( abs_abs_real
% 5.27/5.61 @ ( minus_minus_real
% 5.27/5.61 @ ( groups8778361861064173332t_real
% 5.27/5.61 @ ^ [I3: int] : ( times_times_real @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9006_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_real,X4: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.27/5.61 ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups1300246762558778688al_rat @ X4 @ I5 )
% 5.27/5.61 = one_one_rat )
% 5.27/5.61 => ( ! [I4: real] :
% 5.27/5.61 ( ( member_real @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_rat
% 5.27/5.61 @ ( abs_abs_rat
% 5.27/5.61 @ ( minus_minus_rat
% 5.27/5.61 @ ( groups1300246762558778688al_rat
% 5.27/5.61 @ ^ [I3: real] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9007_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_nat,X4: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.27/5.61 ( ! [I4: nat] :
% 5.27/5.61 ( ( member_nat @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups2906978787729119204at_rat @ X4 @ I5 )
% 5.27/5.61 = one_one_rat )
% 5.27/5.61 => ( ! [I4: nat] :
% 5.27/5.61 ( ( member_nat @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_rat
% 5.27/5.61 @ ( abs_abs_rat
% 5.27/5.61 @ ( minus_minus_rat
% 5.27/5.61 @ ( groups2906978787729119204at_rat
% 5.27/5.61 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9008_convex__sum__bound__le,axiom,
% 5.27/5.61 ! [I5: set_complex,X4: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.27/5.61 ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ zero_zero_rat @ ( X4 @ I4 ) ) )
% 5.27/5.61 => ( ( ( groups5058264527183730370ex_rat @ X4 @ I5 )
% 5.27/5.61 = one_one_rat )
% 5.27/5.61 => ( ! [I4: complex] :
% 5.27/5.61 ( ( member_complex @ I4 @ I5 )
% 5.27/5.61 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.27/5.61 => ( ord_less_eq_rat
% 5.27/5.61 @ ( abs_abs_rat
% 5.27/5.61 @ ( minus_minus_rat
% 5.27/5.61 @ ( groups5058264527183730370ex_rat
% 5.27/5.61 @ ^ [I3: complex] : ( times_times_rat @ ( A @ I3 ) @ ( X4 @ I3 ) )
% 5.27/5.61 @ I5 )
% 5.27/5.61 @ B ) )
% 5.27/5.61 @ Delta ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % convex_sum_bound_le
% 5.27/5.61 thf(fact_9009_Maclaurin__minus__cos__expansion,axiom,
% 5.27/5.61 ! [N2: nat,X4: real] :
% 5.27/5.61 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.61 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.61 => ? [T3: real] :
% 5.27/5.61 ( ( ord_less_real @ X4 @ T3 )
% 5.27/5.61 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.27/5.61 & ( ( cos_real @ X4 )
% 5.27/5.61 = ( plus_plus_real
% 5.27/5.61 @ ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.61 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.61 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % Maclaurin_minus_cos_expansion
% 5.27/5.61 thf(fact_9010_lessThan__eq__iff,axiom,
% 5.27/5.61 ! [X4: nat,Y: nat] :
% 5.27/5.61 ( ( ( set_ord_lessThan_nat @ X4 )
% 5.27/5.61 = ( set_ord_lessThan_nat @ Y ) )
% 5.27/5.61 = ( X4 = Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_eq_iff
% 5.27/5.61 thf(fact_9011_lessThan__eq__iff,axiom,
% 5.27/5.61 ! [X4: int,Y: int] :
% 5.27/5.61 ( ( ( set_ord_lessThan_int @ X4 )
% 5.27/5.61 = ( set_ord_lessThan_int @ Y ) )
% 5.27/5.61 = ( X4 = Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_eq_iff
% 5.27/5.61 thf(fact_9012_lessThan__eq__iff,axiom,
% 5.27/5.61 ! [X4: real,Y: real] :
% 5.27/5.61 ( ( ( set_or5984915006950818249n_real @ X4 )
% 5.27/5.61 = ( set_or5984915006950818249n_real @ Y ) )
% 5.27/5.61 = ( X4 = Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_eq_iff
% 5.27/5.61 thf(fact_9013_of__nat__id,axiom,
% 5.27/5.61 ( semiri1316708129612266289at_nat
% 5.27/5.61 = ( ^ [N: nat] : N ) ) ).
% 5.27/5.61
% 5.27/5.61 % of_nat_id
% 5.27/5.61 thf(fact_9014_lessThan__iff,axiom,
% 5.27/5.61 ! [I2: rat,K: rat] :
% 5.27/5.61 ( ( member_rat @ I2 @ ( set_ord_lessThan_rat @ K ) )
% 5.27/5.61 = ( ord_less_rat @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_iff
% 5.27/5.61 thf(fact_9015_lessThan__iff,axiom,
% 5.27/5.61 ! [I2: num,K: num] :
% 5.27/5.61 ( ( member_num @ I2 @ ( set_ord_lessThan_num @ K ) )
% 5.27/5.61 = ( ord_less_num @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_iff
% 5.27/5.61 thf(fact_9016_lessThan__iff,axiom,
% 5.27/5.61 ! [I2: nat,K: nat] :
% 5.27/5.61 ( ( member_nat @ I2 @ ( set_ord_lessThan_nat @ K ) )
% 5.27/5.61 = ( ord_less_nat @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_iff
% 5.27/5.61 thf(fact_9017_lessThan__iff,axiom,
% 5.27/5.61 ! [I2: int,K: int] :
% 5.27/5.61 ( ( member_int @ I2 @ ( set_ord_lessThan_int @ K ) )
% 5.27/5.61 = ( ord_less_int @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_iff
% 5.27/5.61 thf(fact_9018_lessThan__iff,axiom,
% 5.27/5.61 ! [I2: real,K: real] :
% 5.27/5.61 ( ( member_real @ I2 @ ( set_or5984915006950818249n_real @ K ) )
% 5.27/5.61 = ( ord_less_real @ I2 @ K ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_iff
% 5.27/5.61 thf(fact_9019_lessThan__subset__iff,axiom,
% 5.27/5.61 ! [X4: rat,Y: rat] :
% 5.27/5.61 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X4 ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.27/5.61 = ( ord_less_eq_rat @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_subset_iff
% 5.27/5.61 thf(fact_9020_lessThan__subset__iff,axiom,
% 5.27/5.61 ! [X4: num,Y: num] :
% 5.27/5.61 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X4 ) @ ( set_ord_lessThan_num @ Y ) )
% 5.27/5.61 = ( ord_less_eq_num @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_subset_iff
% 5.27/5.61 thf(fact_9021_lessThan__subset__iff,axiom,
% 5.27/5.61 ! [X4: nat,Y: nat] :
% 5.27/5.61 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X4 ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.27/5.61 = ( ord_less_eq_nat @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_subset_iff
% 5.27/5.61 thf(fact_9022_lessThan__subset__iff,axiom,
% 5.27/5.61 ! [X4: int,Y: int] :
% 5.27/5.61 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X4 ) @ ( set_ord_lessThan_int @ Y ) )
% 5.27/5.61 = ( ord_less_eq_int @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_subset_iff
% 5.27/5.61 thf(fact_9023_lessThan__subset__iff,axiom,
% 5.27/5.61 ! [X4: real,Y: real] :
% 5.27/5.61 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X4 ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.27/5.61 = ( ord_less_eq_real @ X4 @ Y ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_subset_iff
% 5.27/5.61 thf(fact_9024_sum_OlessThan__Suc,axiom,
% 5.27/5.61 ! [G: nat > rat,N2: nat] :
% 5.27/5.61 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.lessThan_Suc
% 5.27/5.61 thf(fact_9025_sum_OlessThan__Suc,axiom,
% 5.27/5.61 ! [G: nat > int,N2: nat] :
% 5.27/5.61 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.lessThan_Suc
% 5.27/5.61 thf(fact_9026_sum_OlessThan__Suc,axiom,
% 5.27/5.61 ! [G: nat > nat,N2: nat] :
% 5.27/5.61 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.lessThan_Suc
% 5.27/5.61 thf(fact_9027_sum_OlessThan__Suc,axiom,
% 5.27/5.61 ! [G: nat > real,N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum.lessThan_Suc
% 5.27/5.61 thf(fact_9028_sumr__cos__zero__one,axiom,
% 5.27/5.61 ! [N2: nat] :
% 5.27/5.61 ( ( groups6591440286371151544t_real
% 5.27/5.61 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ zero_zero_real @ M6 ) )
% 5.27/5.61 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.61 = one_one_real ) ).
% 5.27/5.61
% 5.27/5.61 % sumr_cos_zero_one
% 5.27/5.61 thf(fact_9029_sum__diff__distrib,axiom,
% 5.27/5.61 ! [Q: int > nat,P: int > nat,N2: int] :
% 5.27/5.61 ( ! [X5: int] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.27/5.61 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N2 ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N2 ) ) )
% 5.27/5.61 = ( groups4541462559716669496nt_nat
% 5.27/5.61 @ ^ [X: int] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.27/5.61 @ ( set_ord_lessThan_int @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_diff_distrib
% 5.27/5.61 thf(fact_9030_sum__diff__distrib,axiom,
% 5.27/5.61 ! [Q: real > nat,P: real > nat,N2: real] :
% 5.27/5.61 ( ! [X5: real] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.27/5.61 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N2 ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N2 ) ) )
% 5.27/5.61 = ( groups1935376822645274424al_nat
% 5.27/5.61 @ ^ [X: real] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.27/5.61 @ ( set_or5984915006950818249n_real @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_diff_distrib
% 5.27/5.61 thf(fact_9031_sum__diff__distrib,axiom,
% 5.27/5.61 ! [Q: nat > nat,P: nat > nat,N2: nat] :
% 5.27/5.61 ( ! [X5: nat] : ( ord_less_eq_nat @ ( Q @ X5 ) @ ( P @ X5 ) )
% 5.27/5.61 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.27/5.61 = ( groups3542108847815614940at_nat
% 5.27/5.61 @ ^ [X: nat] : ( minus_minus_nat @ ( P @ X ) @ ( Q @ X ) )
% 5.27/5.61 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % sum_diff_distrib
% 5.27/5.61 thf(fact_9032_lessThan__def,axiom,
% 5.27/5.61 ( set_ord_lessThan_rat
% 5.27/5.61 = ( ^ [U2: rat] :
% 5.27/5.61 ( collect_rat
% 5.27/5.61 @ ^ [X: rat] : ( ord_less_rat @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_def
% 5.27/5.61 thf(fact_9033_lessThan__def,axiom,
% 5.27/5.61 ( set_ord_lessThan_num
% 5.27/5.61 = ( ^ [U2: num] :
% 5.27/5.61 ( collect_num
% 5.27/5.61 @ ^ [X: num] : ( ord_less_num @ X @ U2 ) ) ) ) ).
% 5.27/5.61
% 5.27/5.61 % lessThan_def
% 5.27/5.62 thf(fact_9034_lessThan__def,axiom,
% 5.27/5.62 ( set_ord_lessThan_nat
% 5.27/5.62 = ( ^ [U2: nat] :
% 5.27/5.62 ( collect_nat
% 5.27/5.62 @ ^ [X: nat] : ( ord_less_nat @ X @ U2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_def
% 5.27/5.62 thf(fact_9035_lessThan__def,axiom,
% 5.27/5.62 ( set_ord_lessThan_int
% 5.27/5.62 = ( ^ [U2: int] :
% 5.27/5.62 ( collect_int
% 5.27/5.62 @ ^ [X: int] : ( ord_less_int @ X @ U2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_def
% 5.27/5.62 thf(fact_9036_lessThan__def,axiom,
% 5.27/5.62 ( set_or5984915006950818249n_real
% 5.27/5.62 = ( ^ [U2: real] :
% 5.27/5.62 ( collect_real
% 5.27/5.62 @ ^ [X: real] : ( ord_less_real @ X @ U2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_def
% 5.27/5.62 thf(fact_9037_sum__subtractf__nat,axiom,
% 5.27/5.62 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ( groups1935376822645274424al_nat
% 5.27/5.62 @ ^ [X: real] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_subtractf_nat
% 5.27/5.62 thf(fact_9038_sum__subtractf__nat,axiom,
% 5.27/5.62 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ( groups5693394587270226106ex_nat
% 5.27/5.62 @ ^ [X: complex] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_subtractf_nat
% 5.27/5.62 thf(fact_9039_sum__subtractf__nat,axiom,
% 5.27/5.62 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ( groups4541462559716669496nt_nat
% 5.27/5.62 @ ^ [X: int] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_subtractf_nat
% 5.27/5.62 thf(fact_9040_sum__subtractf__nat,axiom,
% 5.27/5.62 ! [A2: set_Pr1261947904930325089at_nat,G: product_prod_nat_nat > nat,F: product_prod_nat_nat > nat] :
% 5.27/5.62 ( ! [X5: product_prod_nat_nat] :
% 5.27/5.62 ( ( member8440522571783428010at_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ( groups977919841031483927at_nat
% 5.27/5.62 @ ^ [X: product_prod_nat_nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( minus_minus_nat @ ( groups977919841031483927at_nat @ F @ A2 ) @ ( groups977919841031483927at_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_subtractf_nat
% 5.27/5.62 thf(fact_9041_sum__subtractf__nat,axiom,
% 5.27/5.62 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( G @ X5 ) @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [X: nat] : ( minus_minus_nat @ ( F @ X ) @ ( G @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_subtractf_nat
% 5.27/5.62 thf(fact_9042_sum__SucD,axiom,
% 5.27/5.62 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.27/5.62 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.27/5.62 = ( suc @ N2 ) )
% 5.27/5.62 => ? [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 & ( ord_less_nat @ zero_zero_nat @ ( F @ X5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_SucD
% 5.27/5.62 thf(fact_9043_lessThan__strict__subset__iff,axiom,
% 5.27/5.62 ! [M: rat,N2: rat] :
% 5.27/5.62 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N2 ) )
% 5.27/5.62 = ( ord_less_rat @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_strict_subset_iff
% 5.27/5.62 thf(fact_9044_lessThan__strict__subset__iff,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N2 ) )
% 5.27/5.62 = ( ord_less_num @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_strict_subset_iff
% 5.27/5.62 thf(fact_9045_lessThan__strict__subset__iff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_strict_subset_iff
% 5.27/5.62 thf(fact_9046_lessThan__strict__subset__iff,axiom,
% 5.27/5.62 ! [M: int,N2: int] :
% 5.27/5.62 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N2 ) )
% 5.27/5.62 = ( ord_less_int @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_strict_subset_iff
% 5.27/5.62 thf(fact_9047_lessThan__strict__subset__iff,axiom,
% 5.27/5.62 ! [M: real,N2: real] :
% 5.27/5.62 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N2 ) )
% 5.27/5.62 = ( ord_less_real @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_strict_subset_iff
% 5.27/5.62 thf(fact_9048_lessThan__Suc__atMost,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.27/5.62 = ( set_ord_atMost_nat @ K ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_Suc_atMost
% 5.27/5.62 thf(fact_9049_Iic__subset__Iio__iff,axiom,
% 5.27/5.62 ! [A: rat,B: rat] :
% 5.27/5.62 ( ( ord_less_eq_set_rat @ ( set_ord_atMost_rat @ A ) @ ( set_ord_lessThan_rat @ B ) )
% 5.27/5.62 = ( ord_less_rat @ A @ B ) ) ).
% 5.27/5.62
% 5.27/5.62 % Iic_subset_Iio_iff
% 5.27/5.62 thf(fact_9050_Iic__subset__Iio__iff,axiom,
% 5.27/5.62 ! [A: num,B: num] :
% 5.27/5.62 ( ( ord_less_eq_set_num @ ( set_ord_atMost_num @ A ) @ ( set_ord_lessThan_num @ B ) )
% 5.27/5.62 = ( ord_less_num @ A @ B ) ) ).
% 5.27/5.62
% 5.27/5.62 % Iic_subset_Iio_iff
% 5.27/5.62 thf(fact_9051_Iic__subset__Iio__iff,axiom,
% 5.27/5.62 ! [A: nat,B: nat] :
% 5.27/5.62 ( ( ord_less_eq_set_nat @ ( set_ord_atMost_nat @ A ) @ ( set_ord_lessThan_nat @ B ) )
% 5.27/5.62 = ( ord_less_nat @ A @ B ) ) ).
% 5.27/5.62
% 5.27/5.62 % Iic_subset_Iio_iff
% 5.27/5.62 thf(fact_9052_Iic__subset__Iio__iff,axiom,
% 5.27/5.62 ! [A: int,B: int] :
% 5.27/5.62 ( ( ord_less_eq_set_int @ ( set_ord_atMost_int @ A ) @ ( set_ord_lessThan_int @ B ) )
% 5.27/5.62 = ( ord_less_int @ A @ B ) ) ).
% 5.27/5.62
% 5.27/5.62 % Iic_subset_Iio_iff
% 5.27/5.62 thf(fact_9053_Iic__subset__Iio__iff,axiom,
% 5.27/5.62 ! [A: real,B: real] :
% 5.27/5.62 ( ( ord_less_eq_set_real @ ( set_ord_atMost_real @ A ) @ ( set_or5984915006950818249n_real @ B ) )
% 5.27/5.62 = ( ord_less_real @ A @ B ) ) ).
% 5.27/5.62
% 5.27/5.62 % Iic_subset_Iio_iff
% 5.27/5.62 thf(fact_9054_sum_Onat__diff__reindex,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_diff_reindex
% 5.27/5.62 thf(fact_9055_sum_Onat__diff__reindex,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_diff_reindex
% 5.27/5.62 thf(fact_9056_suminf__le__const,axiom,
% 5.27/5.62 ! [F: nat > int,X4: int] :
% 5.27/5.62 ( ( summable_int @ F )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( ord_less_eq_int @ ( suminf_int @ F ) @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % suminf_le_const
% 5.27/5.62 thf(fact_9057_suminf__le__const,axiom,
% 5.27/5.62 ! [F: nat > nat,X4: nat] :
% 5.27/5.62 ( ( summable_nat @ F )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( suminf_nat @ F ) @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % suminf_le_const
% 5.27/5.62 thf(fact_9058_suminf__le__const,axiom,
% 5.27/5.62 ! [F: nat > real,X4: real] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( ord_less_eq_real @ ( suminf_real @ F ) @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % suminf_le_const
% 5.27/5.62 thf(fact_9059_sum_OlessThan__Suc__shift,axiom,
% 5.27/5.62 ! [G: nat > rat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.lessThan_Suc_shift
% 5.27/5.62 thf(fact_9060_sum_OlessThan__Suc__shift,axiom,
% 5.27/5.62 ! [G: nat > int,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.lessThan_Suc_shift
% 5.27/5.62 thf(fact_9061_sum_OlessThan__Suc__shift,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.lessThan_Suc_shift
% 5.27/5.62 thf(fact_9062_sum_OlessThan__Suc__shift,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.lessThan_Suc_shift
% 5.27/5.62 thf(fact_9063_sum__lessThan__telescope_H,axiom,
% 5.27/5.62 ! [F: nat > rat,M: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope'
% 5.27/5.62 thf(fact_9064_sum__lessThan__telescope_H,axiom,
% 5.27/5.62 ! [F: nat > int,M: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_int @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope'
% 5.27/5.62 thf(fact_9065_sum__lessThan__telescope_H,axiom,
% 5.27/5.62 ! [F: nat > real,M: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( F @ ( suc @ N ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope'
% 5.27/5.62 thf(fact_9066_sum__lessThan__telescope,axiom,
% 5.27/5.62 ! [F: nat > rat,M: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope
% 5.27/5.62 thf(fact_9067_sum__lessThan__telescope,axiom,
% 5.27/5.62 ! [F: nat > int,M: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope
% 5.27/5.62 thf(fact_9068_sum__lessThan__telescope,axiom,
% 5.27/5.62 ! [F: nat > real,M: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [N: nat] : ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ N ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_lessThan_telescope
% 5.27/5.62 thf(fact_9069_summableI__nonneg__bounded,axiom,
% 5.27/5.62 ! [F: nat > int,X4: int] :
% 5.27/5.62 ( ! [N3: nat] : ( ord_less_eq_int @ zero_zero_int @ ( F @ N3 ) )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( summable_int @ F ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % summableI_nonneg_bounded
% 5.27/5.62 thf(fact_9070_summableI__nonneg__bounded,axiom,
% 5.27/5.62 ! [F: nat > nat,X4: nat] :
% 5.27/5.62 ( ! [N3: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( F @ N3 ) )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( summable_nat @ F ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % summableI_nonneg_bounded
% 5.27/5.62 thf(fact_9071_summableI__nonneg__bounded,axiom,
% 5.27/5.62 ! [F: nat > real,X4: real] :
% 5.27/5.62 ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ N3 ) )
% 5.27/5.62 => ( ! [N3: nat] : ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N3 ) ) @ X4 )
% 5.27/5.62 => ( summable_real @ F ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % summableI_nonneg_bounded
% 5.27/5.62 thf(fact_9072_sums__iff__shift,axiom,
% 5.27/5.62 ! [F: nat > real,N2: nat,S: real] :
% 5.27/5.62 ( ( sums_real
% 5.27/5.62 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.27/5.62 @ S )
% 5.27/5.62 = ( sums_real @ F @ ( plus_plus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sums_iff_shift
% 5.27/5.62 thf(fact_9073_sums__iff__shift_H,axiom,
% 5.27/5.62 ! [F: nat > real,N2: nat,S: real] :
% 5.27/5.62 ( ( sums_real
% 5.27/5.62 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.27/5.62 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.27/5.62 = ( sums_real @ F @ S ) ) ).
% 5.27/5.62
% 5.27/5.62 % sums_iff_shift'
% 5.27/5.62 thf(fact_9074_sums__split__initial__segment,axiom,
% 5.27/5.62 ! [F: nat > real,S: real,N2: nat] :
% 5.27/5.62 ( ( sums_real @ F @ S )
% 5.27/5.62 => ( sums_real
% 5.27/5.62 @ ^ [I3: nat] : ( F @ ( plus_plus_nat @ I3 @ N2 ) )
% 5.27/5.62 @ ( minus_minus_real @ S @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sums_split_initial_segment
% 5.27/5.62 thf(fact_9075_sum__nth__roots,axiom,
% 5.27/5.62 ! [N2: nat,C: complex] :
% 5.27/5.62 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( groups7754918857620584856omplex
% 5.27/5.62 @ ^ [X: complex] : X
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = C ) ) )
% 5.27/5.62 = zero_zero_complex ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nth_roots
% 5.27/5.62 thf(fact_9076_power__diff__1__eq,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat] :
% 5.27/5.62 ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ X4 @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_1_eq
% 5.27/5.62 thf(fact_9077_power__diff__1__eq,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat] :
% 5.27/5.62 ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ X4 @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_1_eq
% 5.27/5.62 thf(fact_9078_power__diff__1__eq,axiom,
% 5.27/5.62 ! [X4: int,N2: nat] :
% 5.27/5.62 ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ one_one_int )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ X4 @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_1_eq
% 5.27/5.62 thf(fact_9079_power__diff__1__eq,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ X4 @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_1_eq
% 5.27/5.62 thf(fact_9080_one__diff__power__eq,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat] :
% 5.27/5.62 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq
% 5.27/5.62 thf(fact_9081_one__diff__power__eq,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat] :
% 5.27/5.62 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq
% 5.27/5.62 thf(fact_9082_one__diff__power__eq,axiom,
% 5.27/5.62 ! [X4: int,N2: nat] :
% 5.27/5.62 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq
% 5.27/5.62 thf(fact_9083_one__diff__power__eq,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq
% 5.27/5.62 thf(fact_9084_geometric__sum,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat] :
% 5.27/5.62 ( ( X4 != one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ one_one_rat ) @ ( minus_minus_rat @ X4 @ one_one_rat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % geometric_sum
% 5.27/5.62 thf(fact_9085_geometric__sum,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat] :
% 5.27/5.62 ( ( X4 != one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ one_one_complex ) @ ( minus_minus_complex @ X4 @ one_one_complex ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % geometric_sum
% 5.27/5.62 thf(fact_9086_geometric__sum,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( X4 != one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ one_one_real ) @ ( minus_minus_real @ X4 @ one_one_real ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % geometric_sum
% 5.27/5.62 thf(fact_9087_sum_OatMost__shift,axiom,
% 5.27/5.62 ! [G: nat > rat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atMost_shift
% 5.27/5.62 thf(fact_9088_sum_OatMost__shift,axiom,
% 5.27/5.62 ! [G: nat > int,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atMost_shift
% 5.27/5.62 thf(fact_9089_sum_OatMost__shift,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atMost_shift
% 5.27/5.62 thf(fact_9090_sum_OatMost__shift,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atMost_shift
% 5.27/5.62 thf(fact_9091_suminf__split__initial__segment,axiom,
% 5.27/5.62 ! [F: nat > real,K: nat] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ( suminf_real @ F )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( suminf_real
% 5.27/5.62 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % suminf_split_initial_segment
% 5.27/5.62 thf(fact_9092_suminf__minus__initial__segment,axiom,
% 5.27/5.62 ! [F: nat > real,K: nat] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ( suminf_real
% 5.27/5.62 @ ^ [N: nat] : ( F @ ( plus_plus_nat @ N @ K ) ) )
% 5.27/5.62 = ( minus_minus_real @ ( suminf_real @ F ) @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % suminf_minus_initial_segment
% 5.27/5.62 thf(fact_9093_sum__roots__unity,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( ord_less_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( groups7754918857620584856omplex
% 5.27/5.62 @ ^ [X: complex] : X
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = one_one_complex ) ) )
% 5.27/5.62 = zero_zero_complex ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_roots_unity
% 5.27/5.62 thf(fact_9094_sum__less__suminf,axiom,
% 5.27/5.62 ! [F: nat > int,N2: nat] :
% 5.27/5.62 ( ( summable_int @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf
% 5.27/5.62 thf(fact_9095_sum__less__suminf,axiom,
% 5.27/5.62 ! [F: nat > nat,N2: nat] :
% 5.27/5.62 ( ( summable_nat @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf
% 5.27/5.62 thf(fact_9096_sum__less__suminf,axiom,
% 5.27/5.62 ! [F: nat > real,N2: nat] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf
% 5.27/5.62 thf(fact_9097_sum__gp__strict,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( semiri681578069525770553at_rat @ N2 ) ) )
% 5.27/5.62 & ( ( X4 != one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_strict
% 5.27/5.62 thf(fact_9098_sum__gp__strict,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( semiri8010041392384452111omplex @ N2 ) ) )
% 5.27/5.62 & ( ( X4 != one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_strict
% 5.27/5.62 thf(fact_9099_sum__gp__strict,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.62 & ( ( X4 != one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_strict
% 5.27/5.62 thf(fact_9100_lemma__termdiff1,axiom,
% 5.27/5.62 ! [Z: rat,H: rat,M: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [P5: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ P5 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P5 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff1
% 5.27/5.62 thf(fact_9101_lemma__termdiff1,axiom,
% 5.27/5.62 ! [Z: complex,H: complex,M: nat] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [P5: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ P5 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P5 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff1
% 5.27/5.62 thf(fact_9102_lemma__termdiff1,axiom,
% 5.27/5.62 ! [Z: int,H: int,M: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [P5: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ P5 ) ) @ ( power_power_int @ Z @ M ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ Z @ P5 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff1
% 5.27/5.62 thf(fact_9103_lemma__termdiff1,axiom,
% 5.27/5.62 ! [Z: real,H: real,M: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [P5: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ P5 ) ) @ ( power_power_real @ Z @ M ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ Z @ P5 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ ( minus_minus_nat @ M @ P5 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P5 ) ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff1
% 5.27/5.62 thf(fact_9104_diff__power__eq__sum,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat,Y: rat] :
% 5.27/5.62 ( ( minus_minus_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) @ ( power_power_rat @ Y @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_rat @ ( power_power_rat @ X4 @ P5 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % diff_power_eq_sum
% 5.27/5.62 thf(fact_9105_diff__power__eq__sum,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat,Y: complex] :
% 5.27/5.62 ( ( minus_minus_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) @ ( power_power_complex @ Y @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_complex @ ( power_power_complex @ X4 @ P5 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % diff_power_eq_sum
% 5.27/5.62 thf(fact_9106_diff__power__eq__sum,axiom,
% 5.27/5.62 ! [X4: int,N2: nat,Y: int] :
% 5.27/5.62 ( ( minus_minus_int @ ( power_power_int @ X4 @ ( suc @ N2 ) ) @ ( power_power_int @ Y @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_int @ ( power_power_int @ X4 @ P5 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % diff_power_eq_sum
% 5.27/5.62 thf(fact_9107_diff__power__eq__sum,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Y: real] :
% 5.27/5.62 ( ( minus_minus_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) @ ( power_power_real @ Y @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [P5: nat] : ( times_times_real @ ( power_power_real @ X4 @ P5 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % diff_power_eq_sum
% 5.27/5.62 thf(fact_9108_power__diff__sumr2,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat,Y: rat] :
% 5.27/5.62 ( ( minus_minus_rat @ ( power_power_rat @ X4 @ N2 ) @ ( power_power_rat @ Y @ N2 ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_rat @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_sumr2
% 5.27/5.62 thf(fact_9109_power__diff__sumr2,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat,Y: complex] :
% 5.27/5.62 ( ( minus_minus_complex @ ( power_power_complex @ X4 @ N2 ) @ ( power_power_complex @ Y @ N2 ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_complex @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_sumr2
% 5.27/5.62 thf(fact_9110_power__diff__sumr2,axiom,
% 5.27/5.62 ! [X4: int,N2: nat,Y: int] :
% 5.27/5.62 ( ( minus_minus_int @ ( power_power_int @ X4 @ N2 ) @ ( power_power_int @ Y @ N2 ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_int @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_sumr2
% 5.27/5.62 thf(fact_9111_power__diff__sumr2,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Y: real] :
% 5.27/5.62 ( ( minus_minus_real @ ( power_power_real @ X4 @ N2 ) @ ( power_power_real @ Y @ N2 ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) ) @ ( power_power_real @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % power_diff_sumr2
% 5.27/5.62 thf(fact_9112_polyfun__linear__factor__root,axiom,
% 5.27/5.62 ! [C: nat > rat,A: rat,N2: nat] :
% 5.27/5.62 ( ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = zero_zero_rat )
% 5.27/5.62 => ~ ! [B5: nat > rat] :
% 5.27/5.62 ~ ! [Z3: rat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor_root
% 5.27/5.62 thf(fact_9113_polyfun__linear__factor__root,axiom,
% 5.27/5.62 ! [C: nat > complex,A: complex,N2: nat] :
% 5.27/5.62 ( ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = zero_zero_complex )
% 5.27/5.62 => ~ ! [B5: nat > complex] :
% 5.27/5.62 ~ ! [Z3: complex] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor_root
% 5.27/5.62 thf(fact_9114_polyfun__linear__factor__root,axiom,
% 5.27/5.62 ! [C: nat > int,A: int,N2: nat] :
% 5.27/5.62 ( ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = zero_zero_int )
% 5.27/5.62 => ~ ! [B5: nat > int] :
% 5.27/5.62 ~ ! [Z3: int] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor_root
% 5.27/5.62 thf(fact_9115_polyfun__linear__factor__root,axiom,
% 5.27/5.62 ! [C: nat > real,A: real,N2: nat] :
% 5.27/5.62 ( ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = zero_zero_real )
% 5.27/5.62 => ~ ! [B5: nat > real] :
% 5.27/5.62 ~ ! [Z3: real] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor_root
% 5.27/5.62 thf(fact_9116_polyfun__linear__factor,axiom,
% 5.27/5.62 ! [C: nat > rat,N2: nat,A: rat] :
% 5.27/5.62 ? [B5: nat > rat] :
% 5.27/5.62 ! [Z3: rat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_rat
% 5.27/5.62 @ ( times_times_rat @ ( minus_minus_rat @ Z3 @ A )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( B5 @ I3 ) @ ( power_power_rat @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( C @ I3 ) @ ( power_power_rat @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor
% 5.27/5.62 thf(fact_9117_polyfun__linear__factor,axiom,
% 5.27/5.62 ! [C: nat > complex,N2: nat,A: complex] :
% 5.27/5.62 ? [B5: nat > complex] :
% 5.27/5.62 ! [Z3: complex] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_complex
% 5.27/5.62 @ ( times_times_complex @ ( minus_minus_complex @ Z3 @ A )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( B5 @ I3 ) @ ( power_power_complex @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor
% 5.27/5.62 thf(fact_9118_polyfun__linear__factor,axiom,
% 5.27/5.62 ! [C: nat > int,N2: nat,A: int] :
% 5.27/5.62 ? [B5: nat > int] :
% 5.27/5.62 ! [Z3: int] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_int
% 5.27/5.62 @ ( times_times_int @ ( minus_minus_int @ Z3 @ A )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( B5 @ I3 ) @ ( power_power_int @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( C @ I3 ) @ ( power_power_int @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor
% 5.27/5.62 thf(fact_9119_polyfun__linear__factor,axiom,
% 5.27/5.62 ! [C: nat > real,N2: nat,A: real] :
% 5.27/5.62 ? [B5: nat > real] :
% 5.27/5.62 ! [Z3: real] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( times_times_real @ ( minus_minus_real @ Z3 @ A )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( B5 @ I3 ) @ ( power_power_real @ Z3 @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ A @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_linear_factor
% 5.27/5.62 thf(fact_9120_real__sum__nat__ivl__bounded2,axiom,
% 5.27/5.62 ! [N2: nat,F: nat > rat,K5: rat,K: nat] :
% 5.27/5.62 ( ! [P7: nat] :
% 5.27/5.62 ( ( ord_less_nat @ P7 @ N2 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.27/5.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ K5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_sum_nat_ivl_bounded2
% 5.27/5.62 thf(fact_9121_real__sum__nat__ivl__bounded2,axiom,
% 5.27/5.62 ! [N2: nat,F: nat > int,K5: int,K: nat] :
% 5.27/5.62 ( ! [P7: nat] :
% 5.27/5.62 ( ( ord_less_nat @ P7 @ N2 )
% 5.27/5.62 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.27/5.62 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.27/5.62 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ K5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_sum_nat_ivl_bounded2
% 5.27/5.62 thf(fact_9122_real__sum__nat__ivl__bounded2,axiom,
% 5.27/5.62 ! [N2: nat,F: nat > nat,K5: nat,K: nat] :
% 5.27/5.62 ( ! [P7: nat] :
% 5.27/5.62 ( ( ord_less_nat @ P7 @ N2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.27/5.62 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ K5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_sum_nat_ivl_bounded2
% 5.27/5.62 thf(fact_9123_real__sum__nat__ivl__bounded2,axiom,
% 5.27/5.62 ! [N2: nat,F: nat > real,K5: real,K: nat] :
% 5.27/5.62 ( ! [P7: nat] :
% 5.27/5.62 ( ( ord_less_nat @ P7 @ N2 )
% 5.27/5.62 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.27/5.62 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.27/5.62 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ K5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_sum_nat_ivl_bounded2
% 5.27/5.62 thf(fact_9124_sum__less__suminf2,axiom,
% 5.27/5.62 ! [F: nat > int,N2: nat,I2: nat] :
% 5.27/5.62 ( ( summable_int @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.27/5.62 => ( ( ord_less_int @ zero_zero_int @ ( F @ I2 ) )
% 5.27/5.62 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_int @ F ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf2
% 5.27/5.62 thf(fact_9125_sum__less__suminf2,axiom,
% 5.27/5.62 ! [F: nat > nat,N2: nat,I2: nat] :
% 5.27/5.62 ( ( summable_nat @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.27/5.62 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I2 ) )
% 5.27/5.62 => ( ord_less_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_nat @ F ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf2
% 5.27/5.62 thf(fact_9126_sum__less__suminf2,axiom,
% 5.27/5.62 ! [F: nat > real,N2: nat,I2: nat] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M5 )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( F @ M5 ) ) )
% 5.27/5.62 => ( ( ord_less_eq_nat @ N2 @ I2 )
% 5.27/5.62 => ( ( ord_less_real @ zero_zero_real @ ( F @ I2 ) )
% 5.27/5.62 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N2 ) ) @ ( suminf_real @ F ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_less_suminf2
% 5.27/5.62 thf(fact_9127_one__diff__power__eq_H,axiom,
% 5.27/5.62 ! [X4: rat,N2: nat] :
% 5.27/5.62 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( power_power_rat @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq'
% 5.27/5.62 thf(fact_9128_one__diff__power__eq_H,axiom,
% 5.27/5.62 ! [X4: complex,N2: nat] :
% 5.27/5.62 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( power_power_complex @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq'
% 5.27/5.62 thf(fact_9129_one__diff__power__eq_H,axiom,
% 5.27/5.62 ! [X4: int,N2: nat] :
% 5.27/5.62 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( power_power_int @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq'
% 5.27/5.62 thf(fact_9130_one__diff__power__eq_H,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ I3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % one_diff_power_eq'
% 5.27/5.62 thf(fact_9131_Maclaurin__zero,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Diff: nat > complex > real] :
% 5.27/5.62 ( ( X4 = zero_zero_real )
% 5.27/5.62 => ( ( N2 != zero_zero_nat )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_complex ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( Diff @ zero_zero_nat @ zero_zero_complex ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_zero
% 5.27/5.62 thf(fact_9132_Maclaurin__zero,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Diff: nat > real > real] :
% 5.27/5.62 ( ( X4 = zero_zero_real )
% 5.27/5.62 => ( ( N2 != zero_zero_nat )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( Diff @ zero_zero_nat @ zero_zero_real ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_zero
% 5.27/5.62 thf(fact_9133_Maclaurin__zero,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Diff: nat > rat > real] :
% 5.27/5.62 ( ( X4 = zero_zero_real )
% 5.27/5.62 => ( ( N2 != zero_zero_nat )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_rat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( Diff @ zero_zero_nat @ zero_zero_rat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_zero
% 5.27/5.62 thf(fact_9134_Maclaurin__zero,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Diff: nat > nat > real] :
% 5.27/5.62 ( ( X4 = zero_zero_real )
% 5.27/5.62 => ( ( N2 != zero_zero_nat )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_nat ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( Diff @ zero_zero_nat @ zero_zero_nat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_zero
% 5.27/5.62 thf(fact_9135_Maclaurin__zero,axiom,
% 5.27/5.62 ! [X4: real,N2: nat,Diff: nat > int > real] :
% 5.27/5.62 ( ( X4 = zero_zero_real )
% 5.27/5.62 => ( ( N2 != zero_zero_nat )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_int ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 = ( Diff @ zero_zero_nat @ zero_zero_int ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_zero
% 5.27/5.62 thf(fact_9136_Maclaurin__lemma,axiom,
% 5.27/5.62 ! [H: real,F: real > real,J: nat > real,N2: nat] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ H )
% 5.27/5.62 => ? [B7: real] :
% 5.27/5.62 ( ( F @ H )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( times_times_real @ B7 @ ( divide_divide_real @ ( power_power_real @ H @ N2 ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_lemma
% 5.27/5.62 thf(fact_9137_sum__split__even__odd,axiom,
% 5.27/5.62 ! [F: nat > real,G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ ( F @ I3 ) @ ( G @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I3 ) @ one_one_nat ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_split_even_odd
% 5.27/5.62 thf(fact_9138_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.27/5.62 ( ! [I4: real] :
% 5.27/5.62 ( ( member_real @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9139_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.27/5.62 ( ! [I4: nat] :
% 5.27/5.62 ( ( member_nat @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9140_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.27/5.62 ( ! [I4: complex] :
% 5.27/5.62 ( ( member_complex @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9141_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.27/5.62 ( ! [I4: int] :
% 5.27/5.62 ( ( member_int @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9142_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.27/5.62 ( ! [I4: real] :
% 5.27/5.62 ( ( member_real @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9143_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.27/5.62 ( ! [I4: complex] :
% 5.27/5.62 ( ( member_complex @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9144_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.27/5.62 ( ! [I4: int] :
% 5.27/5.62 ( ( member_int @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9145_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_real,F: real > int,G: real > int] :
% 5.27/5.62 ( ! [I4: real] :
% 5.27/5.62 ( ( member_real @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9146_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.27/5.62 ( ! [I4: nat] :
% 5.27/5.62 ( ( member_nat @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9147_sum__mono,axiom,
% 5.27/5.62 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.27/5.62 ( ! [I4: complex] :
% 5.27/5.62 ( ( member_complex @ I4 @ K5 )
% 5.27/5.62 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_mono
% 5.27/5.62 thf(fact_9148_sum_Odistrib,axiom,
% 5.27/5.62 ! [G: nat > nat,H: nat > nat,A2: set_nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [X: nat] : ( plus_plus_nat @ ( G @ X ) @ ( H @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.distrib
% 5.27/5.62 thf(fact_9149_sum_Odistrib,axiom,
% 5.27/5.62 ! [G: nat > real,H: nat > real,A2: set_nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [X: nat] : ( plus_plus_real @ ( G @ X ) @ ( H @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.distrib
% 5.27/5.62 thf(fact_9150_sum_Odistrib,axiom,
% 5.27/5.62 ! [G: complex > complex,H: complex > complex,A2: set_complex] :
% 5.27/5.62 ( ( groups7754918857620584856omplex
% 5.27/5.62 @ ^ [X: complex] : ( plus_plus_complex @ ( G @ X ) @ ( H @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.distrib
% 5.27/5.62 thf(fact_9151_sum_Odistrib,axiom,
% 5.27/5.62 ! [G: int > int,H: int > int,A2: set_int] :
% 5.27/5.62 ( ( groups4538972089207619220nt_int
% 5.27/5.62 @ ^ [X: int] : ( plus_plus_int @ ( G @ X ) @ ( H @ X ) )
% 5.27/5.62 @ A2 )
% 5.27/5.62 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.distrib
% 5.27/5.62 thf(fact_9152_sum__divide__distrib,axiom,
% 5.27/5.62 ! [F: nat > real,A2: set_nat,R3: real] :
% 5.27/5.62 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R3 )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [N: nat] : ( divide_divide_real @ ( F @ N ) @ R3 )
% 5.27/5.62 @ A2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_divide_distrib
% 5.27/5.62 thf(fact_9153_sum__divide__distrib,axiom,
% 5.27/5.62 ! [F: complex > complex,A2: set_complex,R3: complex] :
% 5.27/5.62 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R3 )
% 5.27/5.62 = ( groups7754918857620584856omplex
% 5.27/5.62 @ ^ [N: complex] : ( divide1717551699836669952omplex @ ( F @ N ) @ R3 )
% 5.27/5.62 @ A2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_divide_distrib
% 5.27/5.62 thf(fact_9154_Maclaurin__exp__le,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ? [T3: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.62 & ( ( exp_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_exp_le
% 5.27/5.62 thf(fact_9155_polyfun__diff__alt,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_rat
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [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 @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff_alt
% 5.27/5.62 thf(fact_9156_polyfun__diff__alt,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_complex
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [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 @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff_alt
% 5.27/5.62 thf(fact_9157_polyfun__diff__alt,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_int
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [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 @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff_alt
% 5.27/5.62 thf(fact_9158_polyfun__diff__alt,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [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 @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ J3 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff_alt
% 5.27/5.62 thf(fact_9159_exp__first__terms,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( exp_complex
% 5.27/5.62 = ( ^ [X: complex] :
% 5.27/5.62 ( plus_plus_complex
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_complex @ X @ N ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ K ) )
% 5.27/5.62 @ ( suminf_complex
% 5.27/5.62 @ ^ [N: nat] : ( real_V2046097035970521341omplex @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_complex @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % exp_first_terms
% 5.27/5.62 thf(fact_9160_exp__first__terms,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( exp_real
% 5.27/5.62 = ( ^ [X: real] :
% 5.27/5.62 ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ K ) )
% 5.27/5.62 @ ( suminf_real
% 5.27/5.62 @ ^ [N: nat] : ( real_V1485227260804924795R_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ N @ K ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ N @ K ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % exp_first_terms
% 5.27/5.62 thf(fact_9161_Maclaurin__sin__bound,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ord_less_eq_real
% 5.27/5.62 @ ( abs_abs_real
% 5.27/5.62 @ ( minus_minus_real @ ( sin_real @ X4 )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) )
% 5.27/5.62 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( abs_abs_real @ X4 ) @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_sin_bound
% 5.27/5.62 thf(fact_9162_sum__pos__lt__pair,axiom,
% 5.27/5.62 ! [F: nat > real,K: nat] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ! [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 ) ) ) ) )
% 5.27/5.62 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_pos_lt_pair
% 5.27/5.62 thf(fact_9163_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > real] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.27/5.62 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9164_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > real] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.27/5.62 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9165_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > real] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ ( F @ X5 ) @ zero_zero_real ) )
% 5.27/5.62 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9166_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > rat] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9167_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > rat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9168_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > rat] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9169_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > rat] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ ( F @ X5 ) @ zero_zero_rat ) )
% 5.27/5.62 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9170_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > nat] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9171_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > nat] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9172_sum__nonpos,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > nat] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( F @ X5 ) @ zero_zero_nat ) )
% 5.27/5.62 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonpos
% 5.27/5.62 thf(fact_9173_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > real] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9174_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > real] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9175_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > real] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9176_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > rat] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9177_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > rat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9178_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > rat] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9179_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > rat] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9180_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_real,F: real > nat] :
% 5.27/5.62 ( ! [X5: real] :
% 5.27/5.62 ( ( member_real @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9181_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_complex,F: complex > nat] :
% 5.27/5.62 ( ! [X5: complex] :
% 5.27/5.62 ( ( member_complex @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9182_sum__nonneg,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > nat] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_nonneg
% 5.27/5.62 thf(fact_9183_sum__cong__Suc,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.27/5.62 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.27/5.62 => ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.27/5.62 => ( ( F @ ( suc @ X5 ) )
% 5.27/5.62 = ( G @ ( suc @ X5 ) ) ) )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.27/5.62 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_cong_Suc
% 5.27/5.62 thf(fact_9184_sum__cong__Suc,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.27/5.62 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.27/5.62 => ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ ( suc @ X5 ) @ A2 )
% 5.27/5.62 => ( ( F @ ( suc @ X5 ) )
% 5.27/5.62 = ( G @ ( suc @ X5 ) ) ) )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.27/5.62 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_cong_Suc
% 5.27/5.62 thf(fact_9185_Maclaurin__exp__lt,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( X4 != zero_zero_real )
% 5.27/5.62 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ? [T3: real] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.27/5.62 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.62 & ( ( exp_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( divide_divide_real @ ( power_power_real @ X4 @ M6 ) @ ( semiri2265585572941072030t_real @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_exp_lt
% 5.27/5.62 thf(fact_9186_lemma__termdiff2,axiom,
% 5.27/5.62 ! [H: rat,Z: rat,N2: nat] :
% 5.27/5.62 ( ( H != zero_zero_rat )
% 5.27/5.62 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ N2 ) @ ( power_power_rat @ Z @ N2 ) ) @ H ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.62 = ( times_times_rat @ H
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [P5: nat] :
% 5.27/5.62 ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff2
% 5.27/5.62 thf(fact_9187_lemma__termdiff2,axiom,
% 5.27/5.62 ! [H: complex,Z: complex,N2: nat] :
% 5.27/5.62 ( ( H != zero_zero_complex )
% 5.27/5.62 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ N2 ) @ ( power_power_complex @ Z @ N2 ) ) @ H ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.62 = ( times_times_complex @ H
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [P5: nat] :
% 5.27/5.62 ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff2
% 5.27/5.62 thf(fact_9188_lemma__termdiff2,axiom,
% 5.27/5.62 ! [H: real,Z: real,N2: nat] :
% 5.27/5.62 ( ( H != zero_zero_real )
% 5.27/5.62 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ N2 ) @ ( power_power_real @ Z @ N2 ) ) @ H ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.27/5.62 = ( times_times_real @ H
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [P5: nat] :
% 5.27/5.62 ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ P5 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % lemma_termdiff2
% 5.27/5.62 thf(fact_9189_Maclaurin__sin__expansion,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ? [T3: real] :
% 5.27/5.62 ( ( sin_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_sin_expansion
% 5.27/5.62 thf(fact_9190_Maclaurin__sin__expansion2,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ? [T3: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.62 & ( ( sin_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_sin_expansion2
% 5.27/5.62 thf(fact_9191_Maclaurin__cos__expansion,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ? [T3: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.62 & ( ( cos_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_cos_expansion
% 5.27/5.62 thf(fact_9192_Maclaurin__sin__expansion4,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.62 => ? [T3: real] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.27/5.62 & ( ord_less_eq_real @ T3 @ X4 )
% 5.27/5.62 & ( ( sin_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_sin_expansion4
% 5.27/5.62 thf(fact_9193_Maclaurin__sin__expansion3,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.62 => ? [T3: real] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.27/5.62 & ( ord_less_real @ T3 @ X4 )
% 5.27/5.62 & ( ( sin_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( sin_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_sin_expansion3
% 5.27/5.62 thf(fact_9194_Maclaurin__cos__expansion2,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.62 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ? [T3: real] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.27/5.62 & ( ord_less_real @ T3 @ X4 )
% 5.27/5.62 & ( ( cos_real @ X4 )
% 5.27/5.62 = ( plus_plus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [M6: nat] : ( times_times_real @ ( cos_coeff @ M6 ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.62 @ ( 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 @ N2 ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Maclaurin_cos_expansion2
% 5.27/5.62 thf(fact_9195_bij__betw__roots__unity,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( bij_betw_nat_complex
% 5.27/5.62 @ ^ [K3: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K3 ) ) @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 )
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = one_one_complex ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bij_betw_roots_unity
% 5.27/5.62 thf(fact_9196_sum__gp,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,X4: rat] :
% 5.27/5.62 ( ( ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_rat ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( ( X4 = one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.27/5.62 & ( ( X4 != one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp
% 5.27/5.62 thf(fact_9197_sum__gp,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,X4: complex] :
% 5.27/5.62 ( ( ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_complex ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( ( X4 = one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.27/5.62 & ( ( X4 != one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp
% 5.27/5.62 thf(fact_9198_sum__gp,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,X4: real] :
% 5.27/5.62 ( ( ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_real ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ N2 @ M )
% 5.27/5.62 => ( ( ( X4 = one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) )
% 5.27/5.62 & ( ( X4 != one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp
% 5.27/5.62 thf(fact_9199_gchoose__row__sum__weighted,axiom,
% 5.27/5.62 ! [R3: rat,M: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [K3: nat] : ( times_times_rat @ ( gbinomial_rat @ R3 @ K3 ) @ ( minus_minus_rat @ ( divide_divide_rat @ R3 @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( semiri681578069525770553at_rat @ K3 ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.27/5.62 = ( times_times_rat @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ ( suc @ M ) ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( gbinomial_rat @ R3 @ ( suc @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gchoose_row_sum_weighted
% 5.27/5.62 thf(fact_9200_gchoose__row__sum__weighted,axiom,
% 5.27/5.62 ! [R3: complex,M: nat] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [K3: nat] : ( times_times_complex @ ( gbinomial_complex @ R3 @ K3 ) @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ R3 @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( semiri8010041392384452111omplex @ K3 ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.27/5.62 = ( times_times_complex @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ ( suc @ M ) ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) @ ( gbinomial_complex @ R3 @ ( suc @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gchoose_row_sum_weighted
% 5.27/5.62 thf(fact_9201_gchoose__row__sum__weighted,axiom,
% 5.27/5.62 ! [R3: real,M: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( times_times_real @ ( gbinomial_real @ R3 @ K3 ) @ ( minus_minus_real @ ( divide_divide_real @ R3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( semiri5074537144036343181t_real @ K3 ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ M ) )
% 5.27/5.62 = ( times_times_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( gbinomial_real @ R3 @ ( suc @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gchoose_row_sum_weighted
% 5.27/5.62 thf(fact_9202_gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9203_gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9204_gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9205_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: set_int,L: set_int,U: set_int] :
% 5.27/5.62 ( ( member_set_int @ I2 @ ( set_or370866239135849197et_int @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_set_int @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_set_int @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9206_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: rat,L: rat,U: rat] :
% 5.27/5.62 ( ( member_rat @ I2 @ ( set_or633870826150836451st_rat @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_rat @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_rat @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9207_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: num,L: num,U: num] :
% 5.27/5.62 ( ( member_num @ I2 @ ( set_or7049704709247886629st_num @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_num @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_num @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9208_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: nat,L: nat,U: nat] :
% 5.27/5.62 ( ( member_nat @ I2 @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_nat @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_nat @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9209_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: int,L: int,U: int] :
% 5.27/5.62 ( ( member_int @ I2 @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_int @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_int @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9210_atLeastAtMost__iff,axiom,
% 5.27/5.62 ! [I2: real,L: real,U: real] :
% 5.27/5.62 ( ( member_real @ I2 @ ( set_or1222579329274155063t_real @ L @ U ) )
% 5.27/5.62 = ( ( ord_less_eq_real @ L @ I2 )
% 5.27/5.62 & ( ord_less_eq_real @ I2 @ U ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastAtMost_iff
% 5.27/5.62 thf(fact_9211_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: set_int,H: set_int,L3: set_int,H3: set_int] :
% 5.27/5.62 ( ( ( set_or370866239135849197et_int @ L @ H )
% 5.27/5.62 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_set_int @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9212_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: rat,H: rat,L3: rat,H3: rat] :
% 5.27/5.62 ( ( ( set_or633870826150836451st_rat @ L @ H )
% 5.27/5.62 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_rat @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9213_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: num,H: num,L3: num,H3: num] :
% 5.27/5.62 ( ( ( set_or7049704709247886629st_num @ L @ H )
% 5.27/5.62 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_num @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9214_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: nat,H: nat,L3: nat,H3: nat] :
% 5.27/5.62 ( ( ( set_or1269000886237332187st_nat @ L @ H )
% 5.27/5.62 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_nat @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9215_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: int,H: int,L3: int,H3: int] :
% 5.27/5.62 ( ( ( set_or1266510415728281911st_int @ L @ H )
% 5.27/5.62 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_int @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9216_Icc__eq__Icc,axiom,
% 5.27/5.62 ! [L: real,H: real,L3: real,H3: real] :
% 5.27/5.62 ( ( ( set_or1222579329274155063t_real @ L @ H )
% 5.27/5.62 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.27/5.62 = ( ( ( L = L3 )
% 5.27/5.62 & ( H = H3 ) )
% 5.27/5.62 | ( ~ ( ord_less_eq_real @ L @ H )
% 5.27/5.62 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_eq_Icc
% 5.27/5.62 thf(fact_9217_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.27/5.62 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_set_int @ C @ A )
% 5.27/5.62 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9218_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.62 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_rat @ C @ A )
% 5.27/5.62 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9219_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: num,B: num,C: num,D: num] :
% 5.27/5.62 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_num @ C @ A )
% 5.27/5.62 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9220_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.27/5.62 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_nat @ C @ A )
% 5.27/5.62 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9221_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.62 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_int @ C @ A )
% 5.27/5.62 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9222_atLeastatMost__subset__iff,axiom,
% 5.27/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.62 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_real @ C @ A )
% 5.27/5.62 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_subset_iff
% 5.27/5.62 thf(fact_9223_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: set_int,H: set_int,H3: set_int] :
% 5.27/5.62 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ L @ H ) @ ( set_or58775011639299419et_int @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_set_int @ L @ H )
% 5.27/5.62 | ( ord_less_eq_set_int @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9224_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: rat,H: rat,H3: rat] :
% 5.27/5.62 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ L @ H ) @ ( set_ord_atMost_rat @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_rat @ L @ H )
% 5.27/5.62 | ( ord_less_eq_rat @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9225_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: num,H: num,H3: num] :
% 5.27/5.62 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ L @ H ) @ ( set_ord_atMost_num @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_num @ L @ H )
% 5.27/5.62 | ( ord_less_eq_num @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9226_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: nat,H: nat,H3: nat] :
% 5.27/5.62 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ L @ H ) @ ( set_ord_atMost_nat @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_nat @ L @ H )
% 5.27/5.62 | ( ord_less_eq_nat @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9227_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: int,H: int,H3: int] :
% 5.27/5.62 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ L @ H ) @ ( set_ord_atMost_int @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_int @ L @ H )
% 5.27/5.62 | ( ord_less_eq_int @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9228_Icc__subset__Iic__iff,axiom,
% 5.27/5.62 ! [L: real,H: real,H3: real] :
% 5.27/5.62 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ L @ H ) @ ( set_ord_atMost_real @ H3 ) )
% 5.27/5.62 = ( ~ ( ord_less_eq_real @ L @ H )
% 5.27/5.62 | ( ord_less_eq_real @ H @ H3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Icc_subset_Iic_iff
% 5.27/5.62 thf(fact_9229_sum_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > complex] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = zero_zero_complex ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.cl_ivl_Suc
% 5.27/5.62 thf(fact_9230_sum_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > rat] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = zero_zero_rat ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.cl_ivl_Suc
% 5.27/5.62 thf(fact_9231_sum_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > int] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = zero_zero_int ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.cl_ivl_Suc
% 5.27/5.62 thf(fact_9232_sum_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > nat] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = zero_zero_nat ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.cl_ivl_Suc
% 5.27/5.62 thf(fact_9233_sum_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > real] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = zero_zero_real ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.cl_ivl_Suc
% 5.27/5.62 thf(fact_9234_not__Iic__eq__Icc,axiom,
% 5.27/5.62 ! [H3: int,L: int,H: int] :
% 5.27/5.62 ( ( set_ord_atMost_int @ H3 )
% 5.27/5.62 != ( set_or1266510415728281911st_int @ L @ H ) ) ).
% 5.27/5.62
% 5.27/5.62 % not_Iic_eq_Icc
% 5.27/5.62 thf(fact_9235_not__Iic__eq__Icc,axiom,
% 5.27/5.62 ! [H3: real,L: real,H: real] :
% 5.27/5.62 ( ( set_ord_atMost_real @ H3 )
% 5.27/5.62 != ( set_or1222579329274155063t_real @ L @ H ) ) ).
% 5.27/5.62
% 5.27/5.62 % not_Iic_eq_Icc
% 5.27/5.62 thf(fact_9236_not__Iic__le__Icc,axiom,
% 5.27/5.62 ! [H: int,L3: int,H3: int] :
% 5.27/5.62 ~ ( ord_less_eq_set_int @ ( set_ord_atMost_int @ H ) @ ( set_or1266510415728281911st_int @ L3 @ H3 ) ) ).
% 5.27/5.62
% 5.27/5.62 % not_Iic_le_Icc
% 5.27/5.62 thf(fact_9237_not__Iic__le__Icc,axiom,
% 5.27/5.62 ! [H: real,L3: real,H3: real] :
% 5.27/5.62 ~ ( ord_less_eq_set_real @ ( set_ord_atMost_real @ H ) @ ( set_or1222579329274155063t_real @ L3 @ H3 ) ) ).
% 5.27/5.62
% 5.27/5.62 % not_Iic_le_Icc
% 5.27/5.62 thf(fact_9238_all__nat__less,axiom,
% 5.27/5.62 ! [N2: nat,P: nat > $o] :
% 5.27/5.62 ( ( ! [M6: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.27/5.62 => ( P @ M6 ) ) )
% 5.27/5.62 = ( ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 => ( P @ X ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % all_nat_less
% 5.27/5.62 thf(fact_9239_ex__nat__less,axiom,
% 5.27/5.62 ! [N2: nat,P: nat > $o] :
% 5.27/5.62 ( ( ? [M6: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M6 @ N2 )
% 5.27/5.62 & ( P @ M6 ) ) )
% 5.27/5.62 = ( ? [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 & ( P @ X ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % ex_nat_less
% 5.27/5.62 thf(fact_9240_atMost__atLeast0,axiom,
% 5.27/5.62 ( set_ord_atMost_nat
% 5.27/5.62 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % atMost_atLeast0
% 5.27/5.62 thf(fact_9241_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.27/5.62 ! [G: nat > nat,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.shift_bounds_cl_Suc_ivl
% 5.27/5.62 thf(fact_9242_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.27/5.62 ! [G: nat > real,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.shift_bounds_cl_Suc_ivl
% 5.27/5.62 thf(fact_9243_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.27/5.62 ! [G: nat > nat,M: nat,K: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.shift_bounds_cl_nat_ivl
% 5.27/5.62 thf(fact_9244_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.27/5.62 ! [G: nat > real,M: nat,K: nat,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N2 @ K ) ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( plus_plus_nat @ I3 @ K ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.shift_bounds_cl_nat_ivl
% 5.27/5.62 thf(fact_9245_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.27/5.62 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_set_int @ C @ A )
% 5.27/5.62 & ( ord_less_eq_set_int @ B @ D )
% 5.27/5.62 & ( ( ord_less_set_int @ C @ A )
% 5.27/5.62 | ( ord_less_set_int @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9246_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.27/5.62 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_rat @ C @ A )
% 5.27/5.62 & ( ord_less_eq_rat @ B @ D )
% 5.27/5.62 & ( ( ord_less_rat @ C @ A )
% 5.27/5.62 | ( ord_less_rat @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9247_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: num,B: num,C: num,D: num] :
% 5.27/5.62 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_num @ C @ A )
% 5.27/5.62 & ( ord_less_eq_num @ B @ D )
% 5.27/5.62 & ( ( ord_less_num @ C @ A )
% 5.27/5.62 | ( ord_less_num @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9248_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.27/5.62 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_nat @ C @ A )
% 5.27/5.62 & ( ord_less_eq_nat @ B @ D )
% 5.27/5.62 & ( ( ord_less_nat @ C @ A )
% 5.27/5.62 | ( ord_less_nat @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9249_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.27/5.62 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_int @ C @ A )
% 5.27/5.62 & ( ord_less_eq_int @ B @ D )
% 5.27/5.62 & ( ( ord_less_int @ C @ A )
% 5.27/5.62 | ( ord_less_int @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9250_atLeastatMost__psubset__iff,axiom,
% 5.27/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.27/5.62 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.27/5.62 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.27/5.62 | ( ( ord_less_eq_real @ C @ A )
% 5.27/5.62 & ( ord_less_eq_real @ B @ D )
% 5.27/5.62 & ( ( ord_less_real @ C @ A )
% 5.27/5.62 | ( ord_less_real @ B @ D ) ) ) )
% 5.27/5.62 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastatMost_psubset_iff
% 5.27/5.62 thf(fact_9251_sum_OatLeastAtMost__rev,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat,M: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeastAtMost_rev
% 5.27/5.62 thf(fact_9252_sum_OatLeastAtMost__rev,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat,M: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N2 @ M ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N2 ) @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeastAtMost_rev
% 5.27/5.62 thf(fact_9253_sum__shift__lb__Suc0__0,axiom,
% 5.27/5.62 ! [F: nat > complex,K: nat] :
% 5.27/5.62 ( ( ( F @ zero_zero_nat )
% 5.27/5.62 = zero_zero_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.27/5.62 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_shift_lb_Suc0_0
% 5.27/5.62 thf(fact_9254_sum__shift__lb__Suc0__0,axiom,
% 5.27/5.62 ! [F: nat > rat,K: nat] :
% 5.27/5.62 ( ( ( F @ zero_zero_nat )
% 5.27/5.62 = zero_zero_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.27/5.62 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_shift_lb_Suc0_0
% 5.27/5.62 thf(fact_9255_sum__shift__lb__Suc0__0,axiom,
% 5.27/5.62 ! [F: nat > int,K: nat] :
% 5.27/5.62 ( ( ( F @ zero_zero_nat )
% 5.27/5.62 = zero_zero_int )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.27/5.62 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_shift_lb_Suc0_0
% 5.27/5.62 thf(fact_9256_sum__shift__lb__Suc0__0,axiom,
% 5.27/5.62 ! [F: nat > nat,K: nat] :
% 5.27/5.62 ( ( ( F @ zero_zero_nat )
% 5.27/5.62 = zero_zero_nat )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_shift_lb_Suc0_0
% 5.27/5.62 thf(fact_9257_sum__shift__lb__Suc0__0,axiom,
% 5.27/5.62 ! [F: nat > real,K: nat] :
% 5.27/5.62 ( ( ( F @ zero_zero_nat )
% 5.27/5.62 = zero_zero_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.27/5.62 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_shift_lb_Suc0_0
% 5.27/5.62 thf(fact_9258_sum_OatLeast0__atMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > rat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast0_atMost_Suc
% 5.27/5.62 thf(fact_9259_sum_OatLeast0__atMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > int,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast0_atMost_Suc
% 5.27/5.62 thf(fact_9260_sum_OatLeast0__atMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast0_atMost_Suc
% 5.27/5.62 thf(fact_9261_sum_OatLeast0__atMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast0_atMost_Suc
% 5.27/5.62 thf(fact_9262_sum_OatLeast__Suc__atMost,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast_Suc_atMost
% 5.27/5.62 thf(fact_9263_sum_OatLeast__Suc__atMost,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast_Suc_atMost
% 5.27/5.62 thf(fact_9264_sum_OatLeast__Suc__atMost,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast_Suc_atMost
% 5.27/5.62 thf(fact_9265_sum_OatLeast__Suc__atMost,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast_Suc_atMost
% 5.27/5.62 thf(fact_9266_sum_Onat__ivl__Suc_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( G @ ( suc @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_ivl_Suc'
% 5.27/5.62 thf(fact_9267_sum_Onat__ivl__Suc_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( G @ ( suc @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_ivl_Suc'
% 5.27/5.62 thf(fact_9268_sum_Onat__ivl__Suc_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( G @ ( suc @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_ivl_Suc'
% 5.27/5.62 thf(fact_9269_sum_Onat__ivl__Suc_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( G @ ( suc @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nat_ivl_Suc'
% 5.27/5.62 thf(fact_9270_sum_OSuc__reindex__ivl,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( G @ M )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.Suc_reindex_ivl
% 5.27/5.62 thf(fact_9271_sum_OSuc__reindex__ivl,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( G @ M )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.Suc_reindex_ivl
% 5.27/5.62 thf(fact_9272_sum_OSuc__reindex__ivl,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( G @ M )
% 5.27/5.62 @ ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.Suc_reindex_ivl
% 5.27/5.62 thf(fact_9273_sum_OSuc__reindex__ivl,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( G @ M )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( G @ ( suc @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.Suc_reindex_ivl
% 5.27/5.62 thf(fact_9274_sum__Suc__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( minus_minus_rat @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_Suc_diff
% 5.27/5.62 thf(fact_9275_sum__Suc__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( minus_minus_int @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_Suc_diff
% 5.27/5.62 thf(fact_9276_sum__Suc__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( minus_minus_real @ ( F @ ( suc @ I3 ) ) @ ( F @ I3 ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_Suc_diff
% 5.27/5.62 thf(fact_9277_sum_OatLeast1__atMost__eq,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast1_atMost_eq
% 5.27/5.62 thf(fact_9278_sum_OatLeast1__atMost__eq,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( G @ ( suc @ K3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.atLeast1_atMost_eq
% 5.27/5.62 thf(fact_9279_sum__bounds__lt__plus1,axiom,
% 5.27/5.62 ! [F: nat > nat,Mm: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_bounds_lt_plus1
% 5.27/5.62 thf(fact_9280_sum__bounds__lt__plus1,axiom,
% 5.27/5.62 ! [F: nat > real,Mm: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( F @ ( suc @ K3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ Mm ) )
% 5.27/5.62 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ one_one_nat @ Mm ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_bounds_lt_plus1
% 5.27/5.62 thf(fact_9281_sum_Onested__swap_H,axiom,
% 5.27/5.62 ! [A: nat > nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( groups3542108847815614940at_nat @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nested_swap'
% 5.27/5.62 thf(fact_9282_sum_Onested__swap_H,axiom,
% 5.27/5.62 ! [A: nat > nat > real,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ ( A @ I3 ) @ ( set_ord_lessThan_nat @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( A @ I3 @ J3 )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.nested_swap'
% 5.27/5.62 thf(fact_9283_sum__atLeastAtMost__code,axiom,
% 5.27/5.62 ! [F: nat > complex,A: nat,B: nat] :
% 5.27/5.62 ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.62 = ( set_fo1517530859248394432omplex
% 5.27/5.62 @ ^ [A3: nat] : ( plus_plus_complex @ ( F @ A3 ) )
% 5.27/5.62 @ A
% 5.27/5.62 @ B
% 5.27/5.62 @ zero_zero_complex ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_atLeastAtMost_code
% 5.27/5.62 thf(fact_9284_sum__atLeastAtMost__code,axiom,
% 5.27/5.62 ! [F: nat > rat,A: nat,B: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.62 = ( set_fo1949268297981939178at_rat
% 5.27/5.62 @ ^ [A3: nat] : ( plus_plus_rat @ ( F @ A3 ) )
% 5.27/5.62 @ A
% 5.27/5.62 @ B
% 5.27/5.62 @ zero_zero_rat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_atLeastAtMost_code
% 5.27/5.62 thf(fact_9285_sum__atLeastAtMost__code,axiom,
% 5.27/5.62 ! [F: nat > int,A: nat,B: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.62 = ( set_fo2581907887559384638at_int
% 5.27/5.62 @ ^ [A3: nat] : ( plus_plus_int @ ( F @ A3 ) )
% 5.27/5.62 @ A
% 5.27/5.62 @ B
% 5.27/5.62 @ zero_zero_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_atLeastAtMost_code
% 5.27/5.62 thf(fact_9286_sum__atLeastAtMost__code,axiom,
% 5.27/5.62 ! [F: nat > nat,A: nat,B: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.62 = ( set_fo2584398358068434914at_nat
% 5.27/5.62 @ ^ [A3: nat] : ( plus_plus_nat @ ( F @ A3 ) )
% 5.27/5.62 @ A
% 5.27/5.62 @ B
% 5.27/5.62 @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_atLeastAtMost_code
% 5.27/5.62 thf(fact_9287_sum__atLeastAtMost__code,axiom,
% 5.27/5.62 ! [F: nat > real,A: nat,B: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.62 = ( set_fo3111899725591712190t_real
% 5.27/5.62 @ ^ [A3: nat] : ( plus_plus_real @ ( F @ A3 ) )
% 5.27/5.62 @ A
% 5.27/5.62 @ B
% 5.27/5.62 @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_atLeastAtMost_code
% 5.27/5.62 thf(fact_9288_sum_Oub__add__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > rat,P2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.ub_add_nat
% 5.27/5.62 thf(fact_9289_sum_Oub__add__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > int,P2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.ub_add_nat
% 5.27/5.62 thf(fact_9290_sum_Oub__add__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > nat,P2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.27/5.62 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.ub_add_nat
% 5.27/5.62 thf(fact_9291_sum_Oub__add__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,G: nat > real,P2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N2 @ one_one_nat ) )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N2 @ P2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ ( plus_plus_nat @ N2 @ P2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.ub_add_nat
% 5.27/5.62 thf(fact_9292_sum__up__index__split,axiom,
% 5.27/5.62 ! [F: nat > rat,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_up_index_split
% 5.27/5.62 thf(fact_9293_sum__up__index__split,axiom,
% 5.27/5.62 ! [F: nat > int,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_up_index_split
% 5.27/5.62 thf(fact_9294_sum__up__index__split,axiom,
% 5.27/5.62 ! [F: nat > nat,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_up_index_split
% 5.27/5.62 thf(fact_9295_sum__up__index__split,axiom,
% 5.27/5.62 ! [F: nat > real,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_atMost_nat @ M ) ) @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( plus_plus_nat @ M @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_up_index_split
% 5.27/5.62 thf(fact_9296_sum__natinterval__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > complex] :
% 5.27/5.62 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_complex @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_natinterval_diff
% 5.27/5.62 thf(fact_9297_sum__natinterval__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > rat] :
% 5.27/5.62 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_rat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_natinterval_diff
% 5.27/5.62 thf(fact_9298_sum__natinterval__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > int] :
% 5.27/5.62 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_int ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_natinterval_diff
% 5.27/5.62 thf(fact_9299_sum__natinterval__diff,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > real] :
% 5.27/5.62 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( plus_plus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = zero_zero_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_natinterval_diff
% 5.27/5.62 thf(fact_9300_sum__telescope_H_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_rat @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.27/5.62 = ( minus_minus_rat @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_telescope''
% 5.27/5.62 thf(fact_9301_sum__telescope_H_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_int @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.27/5.62 = ( minus_minus_int @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_telescope''
% 5.27/5.62 thf(fact_9302_sum__telescope_H_H,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,F: nat > real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [K3: nat] : ( minus_minus_real @ ( F @ K3 ) @ ( F @ ( minus_minus_nat @ K3 @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.27/5.62 = ( minus_minus_real @ ( F @ N2 ) @ ( F @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_telescope''
% 5.27/5.62 thf(fact_9303_sum__power__shift,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: complex] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_power_shift
% 5.27/5.62 thf(fact_9304_sum__power__shift,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( times_times_int @ ( power_power_int @ X4 @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_power_shift
% 5.27/5.62 thf(fact_9305_sum__power__shift,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_ord_atMost_nat @ ( minus_minus_nat @ N2 @ M ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_power_shift
% 5.27/5.62 thf(fact_9306_summable__partial__sum__bound,axiom,
% 5.27/5.62 ! [F: nat > complex,E2: real] :
% 5.27/5.62 ( ( summable_complex @ F )
% 5.27/5.62 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.62 => ~ ! [N8: nat] :
% 5.27/5.62 ~ ! [M2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N8 @ M2 )
% 5.27/5.62 => ! [N6: nat] : ( ord_less_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % summable_partial_sum_bound
% 5.27/5.62 thf(fact_9307_summable__partial__sum__bound,axiom,
% 5.27/5.62 ! [F: nat > real,E2: real] :
% 5.27/5.62 ( ( summable_real @ F )
% 5.27/5.62 => ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.27/5.62 => ~ ! [N8: nat] :
% 5.27/5.62 ~ ! [M2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N8 @ M2 )
% 5.27/5.62 => ! [N6: nat] : ( ord_less_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ M2 @ N6 ) ) ) @ E2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % summable_partial_sum_bound
% 5.27/5.62 thf(fact_9308_sum__gp__multiplied,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X4 ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( minus_minus_rat @ ( power_power_rat @ X4 @ M ) @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_multiplied
% 5.27/5.62 thf(fact_9309_sum__gp__multiplied,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: complex] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X4 ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( minus_minus_complex @ ( power_power_complex @ X4 @ M ) @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_multiplied
% 5.27/5.62 thf(fact_9310_sum__gp__multiplied,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X4 ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( minus_minus_int @ ( power_power_int @ X4 @ M ) @ ( power_power_int @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_multiplied
% 5.27/5.62 thf(fact_9311_sum__gp__multiplied,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.62 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X4 ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( minus_minus_real @ ( power_power_real @ X4 @ M ) @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_multiplied
% 5.27/5.62 thf(fact_9312_sum_Oin__pairs,axiom,
% 5.27/5.62 ! [G: nat > rat,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.62 = ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [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 ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.in_pairs
% 5.27/5.62 thf(fact_9313_sum_Oin__pairs,axiom,
% 5.27/5.62 ! [G: nat > int,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.62 = ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [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 ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.in_pairs
% 5.27/5.62 thf(fact_9314_sum_Oin__pairs,axiom,
% 5.27/5.62 ! [G: nat > nat,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.62 = ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [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 ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.in_pairs
% 5.27/5.62 thf(fact_9315_sum_Oin__pairs,axiom,
% 5.27/5.62 ! [G: nat > real,M: nat,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.27/5.62 = ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [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 ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum.in_pairs
% 5.27/5.62 thf(fact_9316_polyfun__eq__const,axiom,
% 5.27/5.62 ! [C: nat > complex,N2: nat,K: complex] :
% 5.27/5.62 ( ( ! [X: complex] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( C @ I3 ) @ ( power_power_complex @ X @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = K ) )
% 5.27/5.62 = ( ( ( C @ zero_zero_nat )
% 5.27/5.62 = K )
% 5.27/5.62 & ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.27/5.62 => ( ( C @ X )
% 5.27/5.62 = zero_zero_complex ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_eq_const
% 5.27/5.62 thf(fact_9317_polyfun__eq__const,axiom,
% 5.27/5.62 ! [C: nat > real,N2: nat,K: real] :
% 5.27/5.62 ( ( ! [X: real] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( C @ I3 ) @ ( power_power_real @ X @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 = K ) )
% 5.27/5.62 = ( ( ( C @ zero_zero_nat )
% 5.27/5.62 = K )
% 5.27/5.62 & ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) )
% 5.27/5.62 => ( ( C @ X )
% 5.27/5.62 = zero_zero_real ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_eq_const
% 5.27/5.62 thf(fact_9318_gbinomial__sum__up__index,axiom,
% 5.27/5.62 ! [K: nat,N2: nat] :
% 5.27/5.62 ( ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [J3: nat] : ( gbinomial_complex @ ( semiri8010041392384452111omplex @ J3 ) @ K )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( gbinomial_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gbinomial_sum_up_index
% 5.27/5.62 thf(fact_9319_gbinomial__sum__up__index,axiom,
% 5.27/5.62 ! [K: nat,N2: nat] :
% 5.27/5.62 ( ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [J3: nat] : ( gbinomial_rat @ ( semiri681578069525770553at_rat @ J3 ) @ K )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( gbinomial_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gbinomial_sum_up_index
% 5.27/5.62 thf(fact_9320_gbinomial__sum__up__index,axiom,
% 5.27/5.62 ! [K: nat,N2: nat] :
% 5.27/5.62 ( ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [J3: nat] : ( gbinomial_real @ ( semiri5074537144036343181t_real @ J3 ) @ K )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( gbinomial_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gbinomial_sum_up_index
% 5.27/5.62 thf(fact_9321_gauss__sum__nat,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [X: nat] : X
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum_nat
% 5.27/5.62 thf(fact_9322_double__arith__series,axiom,
% 5.27/5.62 ! [A: rat,D: rat,N2: nat] :
% 5.27/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9323_double__arith__series,axiom,
% 5.27/5.62 ! [A: extended_enat,D: extended_enat,N2: nat] :
% 5.27/5.62 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups7108830773950497114d_enat
% 5.27/5.62 @ ^ [I3: nat] : ( plus_p3455044024723400733d_enat @ A @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_7803423173614009249d_enat @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) @ ( plus_p3455044024723400733d_enat @ ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ A ) @ ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9324_double__arith__series,axiom,
% 5.27/5.62 ! [A: complex,D: complex,N2: nat] :
% 5.27/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9325_double__arith__series,axiom,
% 5.27/5.62 ! [A: int,D: int,N2: nat] :
% 5.27/5.62 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9326_double__arith__series,axiom,
% 5.27/5.62 ! [A: nat,D: nat,N2: nat] :
% 5.27/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9327_double__arith__series,axiom,
% 5.27/5.62 ! [A: real,D: real,N2: nat] :
% 5.27/5.62 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ D ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_arith_series
% 5.27/5.62 thf(fact_9328_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9329_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9330_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9331_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9332_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9333_double__gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum
% 5.27/5.62 thf(fact_9334_arith__series__nat,axiom,
% 5.27/5.62 ! [A: nat,D: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I3 @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N2 @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arith_series_nat
% 5.27/5.62 thf(fact_9335_Sum__Icc__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [X: nat] : X
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( plus_plus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Sum_Icc_nat
% 5.27/5.62 thf(fact_9336_arith__series,axiom,
% 5.27/5.62 ! [A: code_integer,D: code_integer,N2: nat] :
% 5.27/5.62 ( ( groups7501900531339628137nteger
% 5.27/5.62 @ ^ [I3: nat] : ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ D ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arith_series
% 5.27/5.62 thf(fact_9337_arith__series,axiom,
% 5.27/5.62 ! [A: int,D: int,N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arith_series
% 5.27/5.62 thf(fact_9338_arith__series,axiom,
% 5.27/5.62 ! [A: nat,D: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I3 ) @ D ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arith_series
% 5.27/5.62 thf(fact_9339_gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups7501900531339628137nteger @ semiri4939895301339042750nteger @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ N2 ) @ ( plus_p5714425477246183910nteger @ ( semiri4939895301339042750nteger @ N2 ) @ one_one_Code_integer ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum
% 5.27/5.62 thf(fact_9340_gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum
% 5.27/5.62 thf(fact_9341_gauss__sum,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % gauss_sum
% 5.27/5.62 thf(fact_9342_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N2 ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9343_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_7803423173614009249d_enat @ ( numera1916890842035813515d_enat @ ( bit0 @ one ) ) @ ( groups7108830773950497114d_enat @ semiri4216267220026989637d_enat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_7803423173614009249d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ ( plus_p3455044024723400733d_enat @ ( semiri4216267220026989637d_enat @ N2 ) @ one_on7984719198319812577d_enat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9344_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N2 ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9345_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( semiri1314217659103216013at_int @ N2 ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N2 ) @ one_one_int ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9346_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N2 ) @ one_one_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9347_double__gauss__sum__from__Suc__0,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % double_gauss_sum_from_Suc_0
% 5.27/5.62 thf(fact_9348_sum__gp__offset,axiom,
% 5.27/5.62 ! [X4: rat,M: nat,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N2 ) @ one_one_rat ) ) )
% 5.27/5.62 & ( ( X4 != one_one_rat )
% 5.27/5.62 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X4 @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_offset
% 5.27/5.62 thf(fact_9349_sum__gp__offset,axiom,
% 5.27/5.62 ! [X4: complex,M: nat,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N2 ) @ one_one_complex ) ) )
% 5.27/5.62 & ( ( X4 != one_one_complex )
% 5.27/5.62 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X4 @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_offset
% 5.27/5.62 thf(fact_9350_sum__gp__offset,axiom,
% 5.27/5.62 ! [X4: real,M: nat,N2: nat] :
% 5.27/5.62 ( ( ( X4 = one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) ) )
% 5.27/5.62 & ( ( X4 != one_one_real )
% 5.27/5.62 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X4 ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N2 ) ) )
% 5.27/5.62 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X4 @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( suc @ N2 ) ) ) ) @ ( minus_minus_real @ one_one_real @ X4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_gp_offset
% 5.27/5.62 thf(fact_9351_polyfun__diff,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > rat,X4: rat,Y: rat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_rat
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( minus_minus_rat @ X4 @ Y )
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( times_times_rat
% 5.27/5.62 @ ( groups2906978787729119204at_rat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_rat @ ( A @ I3 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( power_power_rat @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff
% 5.27/5.62 thf(fact_9352_polyfun__diff,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > complex,X4: complex,Y: complex] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_complex
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( minus_minus_complex @ X4 @ Y )
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( times_times_complex
% 5.27/5.62 @ ( groups2073611262835488442omplex
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_complex @ ( A @ I3 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( power_power_complex @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff
% 5.27/5.62 thf(fact_9353_polyfun__diff,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > int,X4: int,Y: int] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_int
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( minus_minus_int @ X4 @ Y )
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( times_times_int
% 5.27/5.62 @ ( groups3539618377306564664at_int
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_int @ ( A @ I3 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( power_power_int @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff
% 5.27/5.62 thf(fact_9354_polyfun__diff,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > real,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_eq_nat @ one_one_nat @ N2 )
% 5.27/5.62 => ( ( minus_minus_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ X4 @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ I3 ) )
% 5.27/5.62 @ ( set_ord_atMost_nat @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( minus_minus_real @ X4 @ Y )
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [J3: nat] :
% 5.27/5.62 ( times_times_real
% 5.27/5.62 @ ( groups6591440286371151544t_real
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_real @ ( A @ I3 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ ( minus_minus_nat @ I3 @ J3 ) @ one_one_nat ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ J3 ) @ N2 ) )
% 5.27/5.62 @ ( power_power_real @ X4 @ J3 ) )
% 5.27/5.62 @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % polyfun_diff
% 5.27/5.62 thf(fact_9355_pochhammer__times__pochhammer__half,axiom,
% 5.27/5.62 ! [Z: rat,N2: nat] :
% 5.27/5.62 ( ( times_times_rat @ ( comm_s4028243227959126397er_rat @ Z @ ( suc @ N2 ) ) @ ( comm_s4028243227959126397er_rat @ ( plus_plus_rat @ Z @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( groups73079841787564623at_rat
% 5.27/5.62 @ ^ [K3: nat] : ( plus_plus_rat @ Z @ ( divide_divide_rat @ ( semiri681578069525770553at_rat @ K3 ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % pochhammer_times_pochhammer_half
% 5.27/5.62 thf(fact_9356_pochhammer__times__pochhammer__half,axiom,
% 5.27/5.62 ! [Z: complex,N2: nat] :
% 5.27/5.62 ( ( times_times_complex @ ( comm_s2602460028002588243omplex @ Z @ ( suc @ N2 ) ) @ ( comm_s2602460028002588243omplex @ ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ one_one_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( groups6464643781859351333omplex
% 5.27/5.62 @ ^ [K3: nat] : ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ ( semiri8010041392384452111omplex @ K3 ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % pochhammer_times_pochhammer_half
% 5.27/5.62 thf(fact_9357_pochhammer__times__pochhammer__half,axiom,
% 5.27/5.62 ! [Z: real,N2: nat] :
% 5.27/5.62 ( ( times_times_real @ ( comm_s7457072308508201937r_real @ Z @ ( suc @ N2 ) ) @ ( comm_s7457072308508201937r_real @ ( plus_plus_real @ Z @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( groups129246275422532515t_real
% 5.27/5.62 @ ^ [K3: nat] : ( plus_plus_real @ Z @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ K3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % pochhammer_times_pochhammer_half
% 5.27/5.62 thf(fact_9358_vebt__buildup_Opelims,axiom,
% 5.27/5.62 ! [X4: nat,Y: vEBT_VEBT] :
% 5.27/5.62 ( ( ( vEBT_vebt_buildup @ X4 )
% 5.27/5.62 = Y )
% 5.27/5.62 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X4 )
% 5.27/5.62 => ( ( ( X4 = zero_zero_nat )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( vEBT_Leaf @ $false @ $false ) )
% 5.27/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.27/5.62 => ( ( ( X4
% 5.27/5.62 = ( suc @ zero_zero_nat ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( vEBT_Leaf @ $false @ $false ) )
% 5.27/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.27/5.62 => ~ ! [Va2: nat] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.62 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( 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 ) ) ) ) ) ) )
% 5.27/5.62 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( 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 ) ) ) ) ) ) ) ) )
% 5.27/5.62 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % vebt_buildup.pelims
% 5.27/5.62 thf(fact_9359_divmod__algorithm__code_I6_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc4245557441103728435nt_int
% 5.27/5.62 @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.27/5.62 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(6)
% 5.27/5.62 thf(fact_9360_divmod__algorithm__code_I6_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc2626176000494625587at_nat
% 5.27/5.62 @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.27/5.62 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(6)
% 5.27/5.62 thf(fact_9361_divmod__algorithm__code_I6_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc6916734918728496179nteger
% 5.27/5.62 @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.27/5.62 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(6)
% 5.27/5.62 thf(fact_9362_arctan__def,axiom,
% 5.27/5.62 ( arctan
% 5.27/5.62 = ( ^ [Y5: real] :
% 5.27/5.62 ( the_real
% 5.27/5.62 @ ^ [X: real] :
% 5.27/5.62 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.27/5.62 & ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.62 & ( ( tan_real @ X )
% 5.27/5.62 = Y5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arctan_def
% 5.27/5.62 thf(fact_9363_prod_Oneutral__const,axiom,
% 5.27/5.62 ! [A2: set_nat] :
% 5.27/5.62 ( ( groups708209901874060359at_nat
% 5.27/5.62 @ ^ [Uu3: nat] : one_one_nat
% 5.27/5.62 @ A2 )
% 5.27/5.62 = one_one_nat ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral_const
% 5.27/5.62 thf(fact_9364_prod_Oneutral__const,axiom,
% 5.27/5.62 ! [A2: set_nat] :
% 5.27/5.62 ( ( groups705719431365010083at_int
% 5.27/5.62 @ ^ [Uu3: nat] : one_one_int
% 5.27/5.62 @ A2 )
% 5.27/5.62 = one_one_int ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral_const
% 5.27/5.62 thf(fact_9365_prod_Oneutral__const,axiom,
% 5.27/5.62 ! [A2: set_int] :
% 5.27/5.62 ( ( groups1705073143266064639nt_int
% 5.27/5.62 @ ^ [Uu3: int] : one_one_int
% 5.27/5.62 @ A2 )
% 5.27/5.62 = one_one_int ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral_const
% 5.27/5.62 thf(fact_9366_prod_OlessThan__Suc,axiom,
% 5.27/5.62 ! [G: nat > complex,N2: nat] :
% 5.27/5.62 ( ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.lessThan_Suc
% 5.27/5.62 thf(fact_9367_prod_OlessThan__Suc,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.lessThan_Suc
% 5.27/5.62 thf(fact_9368_prod_OlessThan__Suc,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.lessThan_Suc
% 5.27/5.62 thf(fact_9369_prod_OlessThan__Suc,axiom,
% 5.27/5.62 ! [G: nat > int,N2: nat] :
% 5.27/5.62 ( ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_lessThan_nat @ N2 ) ) @ ( G @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.lessThan_Suc
% 5.27/5.62 thf(fact_9370_prod_OatMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > complex,N2: nat] :
% 5.27/5.62 ( ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.atMost_Suc
% 5.27/5.62 thf(fact_9371_prod_OatMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > real,N2: nat] :
% 5.27/5.62 ( ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.atMost_Suc
% 5.27/5.62 thf(fact_9372_prod_OatMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > nat,N2: nat] :
% 5.27/5.62 ( ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.atMost_Suc
% 5.27/5.62 thf(fact_9373_prod_OatMost__Suc,axiom,
% 5.27/5.62 ! [G: nat > int,N2: nat] :
% 5.27/5.62 ( ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_ord_atMost_nat @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.atMost_Suc
% 5.27/5.62 thf(fact_9374_prod_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > rat] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = one_one_rat ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_rat @ ( groups73079841787564623at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.cl_ivl_Suc
% 5.27/5.62 thf(fact_9375_prod_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > complex] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = one_one_complex ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_complex @ ( groups6464643781859351333omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.cl_ivl_Suc
% 5.27/5.62 thf(fact_9376_prod_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > real] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = one_one_real ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_real @ ( groups129246275422532515t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.cl_ivl_Suc
% 5.27/5.62 thf(fact_9377_prod_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > nat] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = one_one_nat ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_nat @ ( groups708209901874060359at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.cl_ivl_Suc
% 5.27/5.62 thf(fact_9378_prod_Ocl__ivl__Suc,axiom,
% 5.27/5.62 ! [N2: nat,M: nat,G: nat > int] :
% 5.27/5.62 ( ( ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = one_one_int ) )
% 5.27/5.62 & ( ~ ( ord_less_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 => ( ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) ) )
% 5.27/5.62 = ( times_times_int @ ( groups705719431365010083at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) @ ( G @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.cl_ivl_Suc
% 5.27/5.62 thf(fact_9379_divmod__algorithm__code_I5_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc4245557441103728435nt_int
% 5.27/5.62 @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.27/5.62 @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(5)
% 5.27/5.62 thf(fact_9380_divmod__algorithm__code_I5_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc2626176000494625587at_nat
% 5.27/5.62 @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.27/5.62 @ ( unique5055182867167087721od_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(5)
% 5.27/5.62 thf(fact_9381_divmod__algorithm__code_I5_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.62 = ( produc6916734918728496179nteger
% 5.27/5.62 @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.27/5.62 @ ( unique3479559517661332726nteger @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_algorithm_code(5)
% 5.27/5.62 thf(fact_9382_mod__prod__eq,axiom,
% 5.27/5.62 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.27/5.62 ( ( modulo_modulo_nat
% 5.27/5.62 @ ( groups708209901874060359at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( modulo_modulo_nat @ ( F @ I3 ) @ A )
% 5.27/5.62 @ A2 )
% 5.27/5.62 @ A )
% 5.27/5.62 = ( modulo_modulo_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ A ) ) ).
% 5.27/5.62
% 5.27/5.62 % mod_prod_eq
% 5.27/5.62 thf(fact_9383_mod__prod__eq,axiom,
% 5.27/5.62 ! [F: nat > int,A: int,A2: set_nat] :
% 5.27/5.62 ( ( modulo_modulo_int
% 5.27/5.62 @ ( groups705719431365010083at_int
% 5.27/5.62 @ ^ [I3: nat] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.27/5.62 @ A2 )
% 5.27/5.62 @ A )
% 5.27/5.62 = ( modulo_modulo_int @ ( groups705719431365010083at_int @ F @ A2 ) @ A ) ) ).
% 5.27/5.62
% 5.27/5.62 % mod_prod_eq
% 5.27/5.62 thf(fact_9384_mod__prod__eq,axiom,
% 5.27/5.62 ! [F: int > int,A: int,A2: set_int] :
% 5.27/5.62 ( ( modulo_modulo_int
% 5.27/5.62 @ ( groups1705073143266064639nt_int
% 5.27/5.62 @ ^ [I3: int] : ( modulo_modulo_int @ ( F @ I3 ) @ A )
% 5.27/5.62 @ A2 )
% 5.27/5.62 @ A )
% 5.27/5.62 = ( modulo_modulo_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ A ) ) ).
% 5.27/5.62
% 5.27/5.62 % mod_prod_eq
% 5.27/5.62 thf(fact_9385_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: real > complex,A2: set_real] :
% 5.27/5.62 ( ( ( groups713298508707869441omplex @ G @ A2 )
% 5.27/5.62 != one_one_complex )
% 5.27/5.62 => ~ ! [A5: real] :
% 5.27/5.62 ( ( member_real @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9386_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: nat > complex,A2: set_nat] :
% 5.27/5.62 ( ( ( groups6464643781859351333omplex @ G @ A2 )
% 5.27/5.62 != one_one_complex )
% 5.27/5.62 => ~ ! [A5: nat] :
% 5.27/5.62 ( ( member_nat @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9387_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: complex > complex,A2: set_complex] :
% 5.27/5.62 ( ( ( groups3708469109370488835omplex @ G @ A2 )
% 5.27/5.62 != one_one_complex )
% 5.27/5.62 => ~ ! [A5: complex] :
% 5.27/5.62 ( ( member_complex @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9388_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: int > complex,A2: set_int] :
% 5.27/5.62 ( ( ( groups7440179247065528705omplex @ G @ A2 )
% 5.27/5.62 != one_one_complex )
% 5.27/5.62 => ~ ! [A5: int] :
% 5.27/5.62 ( ( member_int @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_complex ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9389_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: real > real,A2: set_real] :
% 5.27/5.62 ( ( ( groups1681761925125756287l_real @ G @ A2 )
% 5.27/5.62 != one_one_real )
% 5.27/5.62 => ~ ! [A5: real] :
% 5.27/5.62 ( ( member_real @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9390_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: nat > real,A2: set_nat] :
% 5.27/5.62 ( ( ( groups129246275422532515t_real @ G @ A2 )
% 5.27/5.62 != one_one_real )
% 5.27/5.62 => ~ ! [A5: nat] :
% 5.27/5.62 ( ( member_nat @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9391_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: complex > real,A2: set_complex] :
% 5.27/5.62 ( ( ( groups766887009212190081x_real @ G @ A2 )
% 5.27/5.62 != one_one_real )
% 5.27/5.62 => ~ ! [A5: complex] :
% 5.27/5.62 ( ( member_complex @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9392_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: int > real,A2: set_int] :
% 5.27/5.62 ( ( ( groups2316167850115554303t_real @ G @ A2 )
% 5.27/5.62 != one_one_real )
% 5.27/5.62 => ~ ! [A5: int] :
% 5.27/5.62 ( ( member_int @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9393_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: real > rat,A2: set_real] :
% 5.27/5.62 ( ( ( groups4061424788464935467al_rat @ G @ A2 )
% 5.27/5.62 != one_one_rat )
% 5.27/5.62 => ~ ! [A5: real] :
% 5.27/5.62 ( ( member_real @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_rat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9394_prod_Onot__neutral__contains__not__neutral,axiom,
% 5.27/5.62 ! [G: nat > rat,A2: set_nat] :
% 5.27/5.62 ( ( ( groups73079841787564623at_rat @ G @ A2 )
% 5.27/5.62 != one_one_rat )
% 5.27/5.62 => ~ ! [A5: nat] :
% 5.27/5.62 ( ( member_nat @ A5 @ A2 )
% 5.27/5.62 => ( ( G @ A5 )
% 5.27/5.62 = one_one_rat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.not_neutral_contains_not_neutral
% 5.27/5.62 thf(fact_9395_prod_Oneutral,axiom,
% 5.27/5.62 ! [A2: set_nat,G: nat > nat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ( G @ X5 )
% 5.27/5.62 = one_one_nat ) )
% 5.27/5.62 => ( ( groups708209901874060359at_nat @ G @ A2 )
% 5.27/5.62 = one_one_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral
% 5.27/5.62 thf(fact_9396_prod_Oneutral,axiom,
% 5.27/5.62 ! [A2: set_nat,G: nat > int] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ( G @ X5 )
% 5.27/5.62 = one_one_int ) )
% 5.27/5.62 => ( ( groups705719431365010083at_int @ G @ A2 )
% 5.27/5.62 = one_one_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral
% 5.27/5.62 thf(fact_9397_prod_Oneutral,axiom,
% 5.27/5.62 ! [A2: set_int,G: int > int] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ( G @ X5 )
% 5.27/5.62 = one_one_int ) )
% 5.27/5.62 => ( ( groups1705073143266064639nt_int @ G @ A2 )
% 5.27/5.62 = one_one_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod.neutral
% 5.27/5.62 thf(fact_9398_prod__power__distrib,axiom,
% 5.27/5.62 ! [F: nat > nat,A2: set_nat,N2: nat] :
% 5.27/5.62 ( ( power_power_nat @ ( groups708209901874060359at_nat @ F @ A2 ) @ N2 )
% 5.27/5.62 = ( groups708209901874060359at_nat
% 5.27/5.62 @ ^ [X: nat] : ( power_power_nat @ ( F @ X ) @ N2 )
% 5.27/5.62 @ A2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_power_distrib
% 5.27/5.62 thf(fact_9399_prod__power__distrib,axiom,
% 5.27/5.62 ! [F: nat > int,A2: set_nat,N2: nat] :
% 5.27/5.62 ( ( power_power_int @ ( groups705719431365010083at_int @ F @ A2 ) @ N2 )
% 5.27/5.62 = ( groups705719431365010083at_int
% 5.27/5.62 @ ^ [X: nat] : ( power_power_int @ ( F @ X ) @ N2 )
% 5.27/5.62 @ A2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_power_distrib
% 5.27/5.62 thf(fact_9400_prod__power__distrib,axiom,
% 5.27/5.62 ! [F: int > int,A2: set_int,N2: nat] :
% 5.27/5.62 ( ( power_power_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ N2 )
% 5.27/5.62 = ( groups1705073143266064639nt_int
% 5.27/5.62 @ ^ [X: int] : ( power_power_int @ ( F @ X ) @ N2 )
% 5.27/5.62 @ A2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_power_distrib
% 5.27/5.62 thf(fact_9401_prod__nonneg,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > nat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups708209901874060359at_nat @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_nonneg
% 5.27/5.62 thf(fact_9402_prod__nonneg,axiom,
% 5.27/5.62 ! [A2: set_nat,F: nat > int] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( groups705719431365010083at_int @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_nonneg
% 5.27/5.62 thf(fact_9403_prod__nonneg,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > int] :
% 5.27/5.62 ( ! [X5: int] :
% 5.27/5.62 ( ( member_int @ X5 @ A2 )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X5 ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( groups1705073143266064639nt_int @ F @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_nonneg
% 5.27/5.62 thf(fact_9404_prod__mono,axiom,
% 5.27/5.62 ! [A2: set_int,F: int > int,G: int > int] :
% 5.27/5.62 ( ! [I4: int] :
% 5.27/5.62 ( ( member_int @ I4 @ A2 )
% 5.27/5.62 => ( ( ord_less_eq_int @ zero_zero_int @ ( F @ I4 ) )
% 5.27/5.62 & ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) ) )
% 5.27/5.62 => ( ord_less_eq_int @ ( groups1705073143266064639nt_int @ F @ A2 ) @ ( groups1705073143266064639nt_int @ G @ A2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_mono
% 5.27/5.62 thf(fact_9405_ln__neg__is__const,axiom,
% 5.27/5.62 ! [X4: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ X4 @ zero_zero_real )
% 5.27/5.62 => ( ( ln_ln_real @ X4 )
% 5.27/5.62 = ( the_real
% 5.27/5.62 @ ^ [X: real] : $false ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % ln_neg_is_const
% 5.27/5.62 thf(fact_9406_periodic__finite__ex,axiom,
% 5.27/5.62 ! [D: int,P: int > $o] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D )
% 5.27/5.62 => ( ! [X5: int,K2: int] :
% 5.27/5.62 ( ( P @ X5 )
% 5.27/5.62 = ( P @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D ) ) ) )
% 5.27/5.62 => ( ( ? [X3: int] : ( P @ X3 ) )
% 5.27/5.62 = ( ? [X: int] :
% 5.27/5.62 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.27/5.62 & ( P @ X ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % periodic_finite_ex
% 5.27/5.62 thf(fact_9407_bset_I3_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,B3: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( X2 = T2 )
% 5.27/5.62 => ( ( minus_minus_int @ X2 @ D4 )
% 5.27/5.62 = T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(3)
% 5.27/5.62 thf(fact_9408_bset_I4_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,B3: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ T2 @ B3 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( X2 != T2 )
% 5.27/5.62 => ( ( minus_minus_int @ X2 @ D4 )
% 5.27/5.62 != T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(4)
% 5.27/5.62 thf(fact_9409_bset_I5_J,axiom,
% 5.27/5.62 ! [D4: int,B3: set_int,T2: int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_int @ X2 @ T2 )
% 5.27/5.62 => ( ord_less_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(5)
% 5.27/5.62 thf(fact_9410_bset_I7_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,B3: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ T2 @ B3 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_int @ T2 @ X2 )
% 5.27/5.62 => ( ord_less_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(7)
% 5.27/5.62 thf(fact_9411_aset_I3_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,A2: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( X2 = T2 )
% 5.27/5.62 => ( ( plus_plus_int @ X2 @ D4 )
% 5.27/5.62 = T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(3)
% 5.27/5.62 thf(fact_9412_aset_I4_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,A2: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ T2 @ A2 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( X2 != T2 )
% 5.27/5.62 => ( ( plus_plus_int @ X2 @ D4 )
% 5.27/5.62 != T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(4)
% 5.27/5.62 thf(fact_9413_aset_I5_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,A2: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ T2 @ A2 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_int @ X2 @ T2 )
% 5.27/5.62 => ( ord_less_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(5)
% 5.27/5.62 thf(fact_9414_aset_I7_J,axiom,
% 5.27/5.62 ! [D4: int,A2: set_int,T2: int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_int @ T2 @ X2 )
% 5.27/5.62 => ( ord_less_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(7)
% 5.27/5.62 thf(fact_9415_fact__eq__fact__times,axiom,
% 5.27/5.62 ! [N2: nat,M: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.62 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.27/5.62 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N2 )
% 5.27/5.62 @ ( groups708209901874060359at_nat
% 5.27/5.62 @ ^ [X: nat] : X
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( suc @ N2 ) @ M ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % fact_eq_fact_times
% 5.27/5.62 thf(fact_9416_bset_I6_J,axiom,
% 5.27/5.62 ! [D4: int,B3: set_int,T2: int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_eq_int @ X2 @ T2 )
% 5.27/5.62 => ( ord_less_eq_int @ ( minus_minus_int @ X2 @ D4 ) @ T2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(6)
% 5.27/5.62 thf(fact_9417_bset_I8_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,B3: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ ( minus_minus_int @ T2 @ one_one_int ) @ B3 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ B3 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( plus_plus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_eq_int @ T2 @ X2 )
% 5.27/5.62 => ( ord_less_eq_int @ T2 @ ( minus_minus_int @ X2 @ D4 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bset(8)
% 5.27/5.62 thf(fact_9418_aset_I6_J,axiom,
% 5.27/5.62 ! [D4: int,T2: int,A2: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ( member_int @ ( plus_plus_int @ T2 @ one_one_int ) @ A2 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_eq_int @ X2 @ T2 )
% 5.27/5.62 => ( ord_less_eq_int @ ( plus_plus_int @ X2 @ D4 ) @ T2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(6)
% 5.27/5.62 thf(fact_9419_aset_I8_J,axiom,
% 5.27/5.62 ! [D4: int,A2: set_int,T2: int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ! [X2: int] :
% 5.27/5.62 ( ! [Xa2: int] :
% 5.27/5.62 ( ( member_int @ Xa2 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb2: int] :
% 5.27/5.62 ( ( member_int @ Xb2 @ A2 )
% 5.27/5.62 => ( X2
% 5.27/5.62 != ( minus_minus_int @ Xb2 @ Xa2 ) ) ) )
% 5.27/5.62 => ( ( ord_less_eq_int @ T2 @ X2 )
% 5.27/5.62 => ( ord_less_eq_int @ T2 @ ( plus_plus_int @ X2 @ D4 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % aset(8)
% 5.27/5.62 thf(fact_9420_cppi,axiom,
% 5.27/5.62 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ? [Z3: int] :
% 5.27/5.62 ! [X5: int] :
% 5.27/5.62 ( ( ord_less_int @ Z3 @ X5 )
% 5.27/5.62 => ( ( P @ X5 )
% 5.27/5.62 = ( P6 @ X5 ) ) )
% 5.27/5.62 => ( ! [X5: int] :
% 5.27/5.62 ( ! [Xa3: int] :
% 5.27/5.62 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb3: int] :
% 5.27/5.62 ( ( member_int @ Xb3 @ A2 )
% 5.27/5.62 => ( X5
% 5.27/5.62 != ( minus_minus_int @ Xb3 @ Xa3 ) ) ) )
% 5.27/5.62 => ( ( P @ X5 )
% 5.27/5.62 => ( P @ ( plus_plus_int @ X5 @ D4 ) ) ) )
% 5.27/5.62 => ( ! [X5: int,K2: int] :
% 5.27/5.62 ( ( P6 @ X5 )
% 5.27/5.62 = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.27/5.62 => ( ( ? [X3: int] : ( P @ X3 ) )
% 5.27/5.62 = ( ? [X: int] :
% 5.27/5.62 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 & ( P6 @ X ) )
% 5.27/5.62 | ? [X: int] :
% 5.27/5.62 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 & ? [Y5: int] :
% 5.27/5.62 ( ( member_int @ Y5 @ A2 )
% 5.27/5.62 & ( P @ ( minus_minus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % cppi
% 5.27/5.62 thf(fact_9421_cpmi,axiom,
% 5.27/5.62 ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.27/5.62 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.27/5.62 => ( ? [Z3: int] :
% 5.27/5.62 ! [X5: int] :
% 5.27/5.62 ( ( ord_less_int @ X5 @ Z3 )
% 5.27/5.62 => ( ( P @ X5 )
% 5.27/5.62 = ( P6 @ X5 ) ) )
% 5.27/5.62 => ( ! [X5: int] :
% 5.27/5.62 ( ! [Xa3: int] :
% 5.27/5.62 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 => ! [Xb3: int] :
% 5.27/5.62 ( ( member_int @ Xb3 @ B3 )
% 5.27/5.62 => ( X5
% 5.27/5.62 != ( plus_plus_int @ Xb3 @ Xa3 ) ) ) )
% 5.27/5.62 => ( ( P @ X5 )
% 5.27/5.62 => ( P @ ( minus_minus_int @ X5 @ D4 ) ) ) )
% 5.27/5.62 => ( ! [X5: int,K2: int] :
% 5.27/5.62 ( ( P6 @ X5 )
% 5.27/5.62 = ( P6 @ ( minus_minus_int @ X5 @ ( times_times_int @ K2 @ D4 ) ) ) )
% 5.27/5.62 => ( ( ? [X3: int] : ( P @ X3 ) )
% 5.27/5.62 = ( ? [X: int] :
% 5.27/5.62 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 & ( P6 @ X ) )
% 5.27/5.62 | ? [X: int] :
% 5.27/5.62 ( ( member_int @ X @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.27/5.62 & ? [Y5: int] :
% 5.27/5.62 ( ( member_int @ Y5 @ B3 )
% 5.27/5.62 & ( P @ ( plus_plus_int @ Y5 @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % cpmi
% 5.27/5.62 thf(fact_9422_arccos__def,axiom,
% 5.27/5.62 ( arccos
% 5.27/5.62 = ( ^ [Y5: real] :
% 5.27/5.62 ( the_real
% 5.27/5.62 @ ^ [X: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.27/5.62 & ( ord_less_eq_real @ X @ pi )
% 5.27/5.62 & ( ( cos_real @ X )
% 5.27/5.62 = Y5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arccos_def
% 5.27/5.62 thf(fact_9423_fact__div__fact,axiom,
% 5.27/5.62 ! [N2: nat,M: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.62 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N2 ) )
% 5.27/5.62 = ( groups708209901874060359at_nat
% 5.27/5.62 @ ^ [X: nat] : X
% 5.27/5.62 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N2 @ one_one_nat ) @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % fact_div_fact
% 5.27/5.62 thf(fact_9424_divmod__step__nat__def,axiom,
% 5.27/5.62 ( unique5026877609467782581ep_nat
% 5.27/5.62 = ( ^ [L2: num] :
% 5.27/5.62 ( produc2626176000494625587at_nat
% 5.27/5.62 @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L2 ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_step_nat_def
% 5.27/5.62 thf(fact_9425_divmod__step__int__def,axiom,
% 5.27/5.62 ( unique5024387138958732305ep_int
% 5.27/5.62 = ( ^ [L2: num] :
% 5.27/5.62 ( produc4245557441103728435nt_int
% 5.27/5.62 @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L2 ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_step_int_def
% 5.27/5.62 thf(fact_9426_pi__half,axiom,
% 5.27/5.62 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.62 = ( the_real
% 5.27/5.62 @ ^ [X: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.27/5.62 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.62 & ( ( cos_real @ X )
% 5.27/5.62 = zero_zero_real ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % pi_half
% 5.27/5.62 thf(fact_9427_pi__def,axiom,
% 5.27/5.62 ( pi
% 5.27/5.62 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.27/5.62 @ ( the_real
% 5.27/5.62 @ ^ [X: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.27/5.62 & ( ord_less_eq_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.27/5.62 & ( ( cos_real @ X )
% 5.27/5.62 = zero_zero_real ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % pi_def
% 5.27/5.62 thf(fact_9428_Sum__Icc__int,axiom,
% 5.27/5.62 ! [M: int,N2: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ M @ N2 )
% 5.27/5.62 => ( ( groups4538972089207619220nt_int
% 5.27/5.62 @ ^ [X: int] : X
% 5.27/5.62 @ ( set_or1266510415728281911st_int @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N2 @ ( plus_plus_int @ N2 @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Sum_Icc_int
% 5.27/5.62 thf(fact_9429_arcsin__def,axiom,
% 5.27/5.62 ( arcsin
% 5.27/5.62 = ( ^ [Y5: real] :
% 5.27/5.62 ( the_real
% 5.27/5.62 @ ^ [X: real] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.27/5.62 & ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.62 & ( ( sin_real @ X )
% 5.27/5.62 = Y5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % arcsin_def
% 5.27/5.62 thf(fact_9430_divmod__nat__if,axiom,
% 5.27/5.62 ( divmod_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] :
% 5.27/5.62 ( if_Pro6206227464963214023at_nat
% 5.27/5.62 @ ( ( N = zero_zero_nat )
% 5.27/5.62 | ( ord_less_nat @ M6 @ N ) )
% 5.27/5.62 @ ( product_Pair_nat_nat @ zero_zero_nat @ M6 )
% 5.27/5.62 @ ( produc2626176000494625587at_nat
% 5.27/5.62 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 5.27/5.62 @ ( divmod_nat @ ( minus_minus_nat @ M6 @ N ) @ N ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_nat_if
% 5.27/5.62 thf(fact_9431_complex__mult__cnj,axiom,
% 5.27/5.62 ! [Z: complex] :
% 5.27/5.62 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.27/5.62 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_mult_cnj
% 5.27/5.62 thf(fact_9432_prod__int__eq,axiom,
% 5.27/5.62 ! [I2: nat,J: nat] :
% 5.27/5.62 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.27/5.62 = ( groups1705073143266064639nt_int
% 5.27/5.62 @ ^ [X: int] : X
% 5.27/5.62 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_int_eq
% 5.27/5.62 thf(fact_9433_prod__int__plus__eq,axiom,
% 5.27/5.62 ! [I2: nat,J: nat] :
% 5.27/5.62 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I2 @ ( plus_plus_nat @ I2 @ J ) ) )
% 5.27/5.62 = ( groups1705073143266064639nt_int
% 5.27/5.62 @ ^ [X: int] : X
% 5.27/5.62 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I2 ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I2 @ J ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_int_plus_eq
% 5.27/5.62 thf(fact_9434_Re__complex__div__gt__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Re_complex_div_gt_0
% 5.27/5.62 thf(fact_9435_Re__complex__div__lt__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % Re_complex_div_lt_0
% 5.27/5.62 thf(fact_9436_Re__complex__div__ge__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Re_complex_div_ge_0
% 5.27/5.62 thf(fact_9437_Re__complex__div__le__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % Re_complex_div_le_0
% 5.27/5.62 thf(fact_9438_Im__complex__div__gt__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Im_complex_div_gt_0
% 5.27/5.62 thf(fact_9439_Im__complex__div__lt__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % Im_complex_div_lt_0
% 5.27/5.62 thf(fact_9440_Im__complex__div__ge__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Im_complex_div_ge_0
% 5.27/5.62 thf(fact_9441_Im__complex__div__le__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % Im_complex_div_le_0
% 5.27/5.62 thf(fact_9442_complex__mod__mult__cnj,axiom,
% 5.27/5.62 ! [Z: complex] :
% 5.27/5.62 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.27/5.62 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_mod_mult_cnj
% 5.27/5.62 thf(fact_9443_complex__div__gt__0,axiom,
% 5.27/5.62 ! [A: complex,B: complex] :
% 5.27/5.62 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.27/5.62 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.27/5.62 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_div_gt_0
% 5.27/5.62 thf(fact_9444_complex__norm__square,axiom,
% 5.27/5.62 ! [Z: complex] :
% 5.27/5.62 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.27/5.62 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_norm_square
% 5.27/5.62 thf(fact_9445_divmod__nat__def,axiom,
% 5.27/5.62 ( divmod_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M6 @ N ) @ ( modulo_modulo_nat @ M6 @ N ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_nat_def
% 5.27/5.62 thf(fact_9446_complex__add__cnj,axiom,
% 5.27/5.62 ! [Z: complex] :
% 5.27/5.62 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.27/5.62 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_add_cnj
% 5.27/5.62 thf(fact_9447_complex__diff__cnj,axiom,
% 5.27/5.62 ! [Z: complex] :
% 5.27/5.62 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.27/5.62 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_diff_cnj
% 5.27/5.62 thf(fact_9448_complex__div__cnj,axiom,
% 5.27/5.62 ( divide1717551699836669952omplex
% 5.27/5.62 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % complex_div_cnj
% 5.27/5.62 thf(fact_9449_cnj__add__mult__eq__Re,axiom,
% 5.27/5.62 ! [Z: complex,W: complex] :
% 5.27/5.62 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.27/5.62 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % cnj_add_mult_eq_Re
% 5.27/5.62 thf(fact_9450_set__encode__def,axiom,
% 5.27/5.62 ( nat_set_encode
% 5.27/5.62 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % set_encode_def
% 5.27/5.62 thf(fact_9451_VEBT_Osize_I3_J,axiom,
% 5.27/5.62 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.27/5.62 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.27/5.62 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % VEBT.size(3)
% 5.27/5.62 thf(fact_9452_VEBT_Osize__gen_I1_J,axiom,
% 5.27/5.62 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.27/5.62 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.27/5.62 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % VEBT.size_gen(1)
% 5.27/5.62 thf(fact_9453_Sum__Ico__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [X: nat] : X
% 5.27/5.62 @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N2 @ ( minus_minus_nat @ N2 @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Sum_Ico_nat
% 5.27/5.62 thf(fact_9454_ex__nat__less__eq,axiom,
% 5.27/5.62 ! [N2: nat,P: nat > $o] :
% 5.27/5.62 ( ( ? [M6: nat] :
% 5.27/5.62 ( ( ord_less_nat @ M6 @ N2 )
% 5.27/5.62 & ( P @ M6 ) ) )
% 5.27/5.62 = ( ? [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 & ( P @ X ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % ex_nat_less_eq
% 5.27/5.62 thf(fact_9455_all__nat__less__eq,axiom,
% 5.27/5.62 ! [N2: nat,P: nat > $o] :
% 5.27/5.62 ( ( ! [M6: nat] :
% 5.27/5.62 ( ( ord_less_nat @ M6 @ N2 )
% 5.27/5.62 => ( P @ M6 ) ) )
% 5.27/5.62 = ( ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 => ( P @ X ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % all_nat_less_eq
% 5.27/5.62 thf(fact_9456_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.27/5.62 ! [L: nat,U: nat] :
% 5.27/5.62 ( ( set_or4665077453230672383an_nat @ L @ ( suc @ U ) )
% 5.27/5.62 = ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastLessThanSuc_atLeastAtMost
% 5.27/5.62 thf(fact_9457_lessThan__atLeast0,axiom,
% 5.27/5.62 ( set_ord_lessThan_nat
% 5.27/5.62 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % lessThan_atLeast0
% 5.27/5.62 thf(fact_9458_prod__Suc__fact,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_Suc_fact
% 5.27/5.62 thf(fact_9459_prod__Suc__Suc__fact,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 ) )
% 5.27/5.62 = ( semiri1408675320244567234ct_nat @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_Suc_Suc_fact
% 5.27/5.62 thf(fact_9460_VEBT_Osize__gen_I2_J,axiom,
% 5.27/5.62 ! [X21: $o,X222: $o] :
% 5.27/5.62 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.27/5.62 = zero_zero_nat ) ).
% 5.27/5.62
% 5.27/5.62 % VEBT.size_gen(2)
% 5.27/5.62 thf(fact_9461_sum__power2,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.27/5.62 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % sum_power2
% 5.27/5.62 thf(fact_9462_Chebyshev__sum__upper__nat,axiom,
% 5.27/5.62 ! [N2: nat,A: nat > nat,B: nat > nat] :
% 5.27/5.62 ( ! [I4: nat,J2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.27/5.62 => ( ( ord_less_nat @ J2 @ N2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 5.27/5.62 => ( ! [I4: nat,J2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.27/5.62 => ( ( ord_less_nat @ J2 @ N2 )
% 5.27/5.62 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 5.27/5.62 => ( ord_less_eq_nat
% 5.27/5.62 @ ( times_times_nat @ N2
% 5.27/5.62 @ ( groups3542108847815614940at_nat
% 5.27/5.62 @ ^ [I3: nat] : ( times_times_nat @ ( A @ I3 ) @ ( B @ I3 ) )
% 5.27/5.62 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.27/5.62 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Chebyshev_sum_upper_nat
% 5.27/5.62 thf(fact_9463_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.27/5.62 ! [L: int,U: int] :
% 5.27/5.62 ( ( set_or4662586982721622107an_int @ L @ ( plus_plus_int @ U @ one_one_int ) )
% 5.27/5.62 = ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.27/5.62 thf(fact_9464_int__ge__less__than2__def,axiom,
% 5.27/5.62 ( int_ge_less_than2
% 5.27/5.62 = ( ^ [D5: int] :
% 5.27/5.62 ( collec213857154873943460nt_int
% 5.27/5.62 @ ( produc4947309494688390418_int_o
% 5.27/5.62 @ ^ [Z7: int,Z5: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ D5 @ Z5 )
% 5.27/5.62 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % int_ge_less_than2_def
% 5.27/5.62 thf(fact_9465_int__ge__less__than__def,axiom,
% 5.27/5.62 ( int_ge_less_than
% 5.27/5.62 = ( ^ [D5: int] :
% 5.27/5.62 ( collec213857154873943460nt_int
% 5.27/5.62 @ ( produc4947309494688390418_int_o
% 5.27/5.62 @ ^ [Z7: int,Z5: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ D5 @ Z7 )
% 5.27/5.62 & ( ord_less_int @ Z7 @ Z5 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % int_ge_less_than_def
% 5.27/5.62 thf(fact_9466_upto_Opinduct,axiom,
% 5.27/5.62 ! [A0: int,A12: int,P: int > int > $o] :
% 5.27/5.62 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.27/5.62 => ( ! [I4: int,J2: int] :
% 5.27/5.62 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 5.27/5.62 => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 5.27/5.62 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 5.27/5.62 => ( P @ I4 @ J2 ) ) )
% 5.27/5.62 => ( P @ A0 @ A12 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % upto.pinduct
% 5.27/5.62 thf(fact_9467_divmod__step__integer__def,axiom,
% 5.27/5.62 ( unique4921790084139445826nteger
% 5.27/5.62 = ( ^ [L2: num] :
% 5.27/5.62 ( produc6916734918728496179nteger
% 5.27/5.62 @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L2 ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_step_integer_def
% 5.27/5.62 thf(fact_9468_or__int__rec,axiom,
% 5.27/5.62 ( bit_se1409905431419307370or_int
% 5.27/5.62 = ( ^ [K3: int,L2: int] :
% 5.27/5.62 ( plus_plus_int
% 5.27/5.62 @ ( zero_n2684676970156552555ol_int
% 5.27/5.62 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.27/5.62 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.27/5.62 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_int_rec
% 5.27/5.62 thf(fact_9469_or__nonnegative__int__iff,axiom,
% 5.27/5.62 ! [K: int,L: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L ) )
% 5.27/5.62 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.27/5.62 & ( ord_less_eq_int @ zero_zero_int @ L ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nonnegative_int_iff
% 5.27/5.62 thf(fact_9470_or__negative__int__iff,axiom,
% 5.27/5.62 ! [K: int,L: int] :
% 5.27/5.62 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ zero_zero_int )
% 5.27/5.62 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.27/5.62 | ( ord_less_int @ L @ zero_zero_int ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_negative_int_iff
% 5.27/5.62 thf(fact_9471_or__minus__numerals_I6_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ one_one_int )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(6)
% 5.27/5.62 thf(fact_9472_or__minus__numerals_I2_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(2)
% 5.27/5.62 thf(fact_9473_or__minus__minus__numerals,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_minus_numerals
% 5.27/5.62 thf(fact_9474_and__minus__minus__numerals,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N2 ) @ one_one_int ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % and_minus_minus_numerals
% 5.27/5.62 thf(fact_9475_divmod__integer_H__def,axiom,
% 5.27/5.62 ( unique3479559517661332726nteger
% 5.27/5.62 = ( ^ [M6: num,N: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M6 ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_integer'_def
% 5.27/5.62 thf(fact_9476_bit__or__int__iff,axiom,
% 5.27/5.62 ! [K: int,L: int,N2: nat] :
% 5.27/5.62 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L ) @ N2 )
% 5.27/5.62 = ( ( bit_se1146084159140164899it_int @ K @ N2 )
% 5.27/5.62 | ( bit_se1146084159140164899it_int @ L @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bit_or_int_iff
% 5.27/5.62 thf(fact_9477_sgn__integer__code,axiom,
% 5.27/5.62 ( sgn_sgn_Code_integer
% 5.27/5.62 = ( ^ [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 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sgn_integer_code
% 5.27/5.62 thf(fact_9478_less__eq__integer__code_I1_J,axiom,
% 5.27/5.62 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.27/5.62
% 5.27/5.62 % less_eq_integer_code(1)
% 5.27/5.62 thf(fact_9479_OR__lower,axiom,
% 5.27/5.62 ! [X4: int,Y: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.62 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.62 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % OR_lower
% 5.27/5.62 thf(fact_9480_or__greater__eq,axiom,
% 5.27/5.62 ! [L: int,K: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ zero_zero_int @ L )
% 5.27/5.62 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_greater_eq
% 5.27/5.62 thf(fact_9481_plus__and__or,axiom,
% 5.27/5.62 ! [X4: int,Y: int] :
% 5.27/5.62 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X4 @ Y ) @ ( bit_se1409905431419307370or_int @ X4 @ Y ) )
% 5.27/5.62 = ( plus_plus_int @ X4 @ Y ) ) ).
% 5.27/5.62
% 5.27/5.62 % plus_and_or
% 5.27/5.62 thf(fact_9482_nat_Odisc__eq__case_I1_J,axiom,
% 5.27/5.62 ! [Nat: nat] :
% 5.27/5.62 ( ( Nat = zero_zero_nat )
% 5.27/5.62 = ( case_nat_o @ $true
% 5.27/5.62 @ ^ [Uu3: nat] : $false
% 5.27/5.62 @ Nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat.disc_eq_case(1)
% 5.27/5.62 thf(fact_9483_nat_Odisc__eq__case_I2_J,axiom,
% 5.27/5.62 ! [Nat: nat] :
% 5.27/5.62 ( ( Nat != zero_zero_nat )
% 5.27/5.62 = ( case_nat_o @ $false
% 5.27/5.62 @ ^ [Uu3: nat] : $true
% 5.27/5.62 @ Nat ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat.disc_eq_case(2)
% 5.27/5.62 thf(fact_9484_or__int__def,axiom,
% 5.27/5.62 ( bit_se1409905431419307370or_int
% 5.27/5.62 = ( ^ [K3: int,L2: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ ( bit_ri7919022796975470100ot_int @ L2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_int_def
% 5.27/5.62 thf(fact_9485_or__not__numerals_I1_J,axiom,
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(1)
% 5.27/5.62 thf(fact_9486_xor__int__def,axiom,
% 5.27/5.62 ( bit_se6526347334894502574or_int
% 5.27/5.62 = ( ^ [K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K3 @ ( bit_ri7919022796975470100ot_int @ L2 ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K3 ) @ L2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % xor_int_def
% 5.27/5.62 thf(fact_9487_concat__bit__def,axiom,
% 5.27/5.62 ( bit_concat_bit
% 5.27/5.62 = ( ^ [N: nat,K3: int,L2: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N @ K3 ) @ ( bit_se545348938243370406it_int @ N @ L2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % concat_bit_def
% 5.27/5.62 thf(fact_9488_set__bit__int__def,axiom,
% 5.27/5.62 ( bit_se7879613467334960850it_int
% 5.27/5.62 = ( ^ [N: nat,K3: int] : ( bit_se1409905431419307370or_int @ K3 @ ( bit_se545348938243370406it_int @ N @ one_one_int ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % set_bit_int_def
% 5.27/5.62 thf(fact_9489_one__natural_Orsp,axiom,
% 5.27/5.62 one_one_nat = one_one_nat ).
% 5.27/5.62
% 5.27/5.62 % one_natural.rsp
% 5.27/5.62 thf(fact_9490_less__eq__nat_Osimps_I2_J,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ ( suc @ M ) @ N2 )
% 5.27/5.62 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % less_eq_nat.simps(2)
% 5.27/5.62 thf(fact_9491_or__not__numerals_I4_J,axiom,
% 5.27/5.62 ! [M: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(4)
% 5.27/5.62 thf(fact_9492_or__not__numerals_I2_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(2)
% 5.27/5.62 thf(fact_9493_diff__Suc,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( minus_minus_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 = ( case_nat_nat @ zero_zero_nat
% 5.27/5.62 @ ^ [K3: nat] : K3
% 5.27/5.62 @ ( minus_minus_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % diff_Suc
% 5.27/5.62 thf(fact_9494_or__not__numerals_I3_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(3)
% 5.27/5.62 thf(fact_9495_or__not__numerals_I7_J,axiom,
% 5.27/5.62 ! [M: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.27/5.62 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(7)
% 5.27/5.62 thf(fact_9496_or__not__numerals_I6_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.62 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(6)
% 5.27/5.62 thf(fact_9497_OR__upper,axiom,
% 5.27/5.62 ! [X4: int,N2: nat,Y: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.62 => ( ( ord_less_int @ X4 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.62 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) )
% 5.27/5.62 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X4 @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % OR_upper
% 5.27/5.62 thf(fact_9498_or__not__numerals_I5_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.62 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(5)
% 5.27/5.62 thf(fact_9499_or__not__numerals_I9_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.62 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(9)
% 5.27/5.62 thf(fact_9500_or__not__numerals_I8_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.62 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_numerals(8)
% 5.27/5.62 thf(fact_9501_integer__of__int__code,axiom,
% 5.27/5.62 ( code_integer_of_int
% 5.27/5.62 = ( ^ [K3: int] :
% 5.27/5.62 ( if_Code_integer @ ( ord_less_int @ K3 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K3 ) ) )
% 5.27/5.62 @ ( if_Code_integer @ ( K3 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.27/5.62 @ ( if_Code_integer
% 5.27/5.62 @ ( ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.27/5.62 = zero_zero_int )
% 5.27/5.62 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.62 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % integer_of_int_code
% 5.27/5.62 thf(fact_9502_or__minus__numerals_I1_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(1)
% 5.27/5.62 thf(fact_9503_or__minus__numerals_I5_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ one_one_int )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(5)
% 5.27/5.62 thf(fact_9504_or__nat__numerals_I4_J,axiom,
% 5.27/5.62 ! [X4: num] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.62 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_numerals(4)
% 5.27/5.62 thf(fact_9505_or__nat__numerals_I2_J,axiom,
% 5.27/5.62 ! [Y: num] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.27/5.62 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_numerals(2)
% 5.27/5.62 thf(fact_9506_or__nat__numerals_I3_J,axiom,
% 5.27/5.62 ! [X4: num] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X4 ) ) @ ( suc @ zero_zero_nat ) )
% 5.27/5.62 = ( numeral_numeral_nat @ ( bit1 @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_numerals(3)
% 5.27/5.62 thf(fact_9507_or__nat__numerals_I1_J,axiom,
% 5.27/5.62 ! [Y: num] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.27/5.62 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_numerals(1)
% 5.27/5.62 thf(fact_9508_or__minus__numerals_I8_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(8)
% 5.27/5.62 thf(fact_9509_or__minus__numerals_I4_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(4)
% 5.27/5.62 thf(fact_9510_or__minus__numerals_I3_J,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(3)
% 5.27/5.62 thf(fact_9511_or__minus__numerals_I7_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_minus_numerals(7)
% 5.27/5.62 thf(fact_9512_modulo__integer_Oabs__eq,axiom,
% 5.27/5.62 ! [Xa: int,X4: int] :
% 5.27/5.62 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.27/5.62 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % modulo_integer.abs_eq
% 5.27/5.62 thf(fact_9513_abs__integer__code,axiom,
% 5.27/5.62 ( abs_abs_Code_integer
% 5.27/5.62 = ( ^ [K3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K3 ) @ K3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % abs_integer_code
% 5.27/5.62 thf(fact_9514_less__integer__code_I1_J,axiom,
% 5.27/5.62 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.27/5.62
% 5.27/5.62 % less_integer_code(1)
% 5.27/5.62 thf(fact_9515_less__integer_Oabs__eq,axiom,
% 5.27/5.62 ! [Xa: int,X4: int] :
% 5.27/5.62 ( ( ord_le6747313008572928689nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.27/5.62 = ( ord_less_int @ Xa @ X4 ) ) ).
% 5.27/5.62
% 5.27/5.62 % less_integer.abs_eq
% 5.27/5.62 thf(fact_9516_or__not__num__neg_Osimps_I1_J,axiom,
% 5.27/5.62 ( ( bit_or_not_num_neg @ one @ one )
% 5.27/5.62 = one ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(1)
% 5.27/5.62 thf(fact_9517_less__eq__integer_Oabs__eq,axiom,
% 5.27/5.62 ! [Xa: int,X4: int] :
% 5.27/5.62 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa ) @ ( code_integer_of_int @ X4 ) )
% 5.27/5.62 = ( ord_less_eq_int @ Xa @ X4 ) ) ).
% 5.27/5.62
% 5.27/5.62 % less_eq_integer.abs_eq
% 5.27/5.62 thf(fact_9518_set__bit__nat__def,axiom,
% 5.27/5.62 ( bit_se7882103937844011126it_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] : ( bit_se1412395901928357646or_nat @ N @ ( bit_se547839408752420682it_nat @ M6 @ one_one_nat ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % set_bit_nat_def
% 5.27/5.62 thf(fact_9519_or__not__num__neg_Osimps_I4_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ one )
% 5.27/5.62 = ( bit0 @ one ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(4)
% 5.27/5.62 thf(fact_9520_or__not__num__neg_Osimps_I6_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit1 @ M ) )
% 5.27/5.62 = ( bit0 @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(6)
% 5.27/5.62 thf(fact_9521_or__not__num__neg_Osimps_I3_J,axiom,
% 5.27/5.62 ! [M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.27/5.62 = ( bit1 @ M ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(3)
% 5.27/5.62 thf(fact_9522_or__not__num__neg_Osimps_I7_J,axiom,
% 5.27/5.62 ! [N2: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ one )
% 5.27/5.62 = one ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(7)
% 5.27/5.62 thf(fact_9523_or__not__num__neg_Osimps_I5_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit0 @ N2 ) @ ( bit0 @ M ) )
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(5)
% 5.27/5.62 thf(fact_9524_or__not__num__neg_Osimps_I9_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit1 @ M ) )
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(9)
% 5.27/5.62 thf(fact_9525_or__nat__def,axiom,
% 5.27/5.62 ( bit_se1412395901928357646or_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M6 ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_def
% 5.27/5.62 thf(fact_9526_or__not__num__neg_Osimps_I2_J,axiom,
% 5.27/5.62 ! [M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.27/5.62 = ( bit1 @ M ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(2)
% 5.27/5.62 thf(fact_9527_or__not__num__neg_Osimps_I8_J,axiom,
% 5.27/5.62 ! [N2: num,M: num] :
% 5.27/5.62 ( ( bit_or_not_num_neg @ ( bit1 @ N2 ) @ ( bit0 @ M ) )
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.simps(8)
% 5.27/5.62 thf(fact_9528_or__not__num__neg_Oelims,axiom,
% 5.27/5.62 ! [X4: num,Xa: num,Y: num] :
% 5.27/5.62 ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 5.27/5.62 = Y )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( Y != one ) ) )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bit1 @ M5 ) ) ) )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bit1 @ M5 ) ) ) )
% 5.27/5.62 => ( ( ? [N3: num] :
% 5.27/5.62 ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bit0 @ one ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.27/5.62 => ( ( ? [N3: num] :
% 5.27/5.62 ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( Y != one ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) )
% 5.27/5.62 => ~ ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( Y
% 5.27/5.62 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.elims
% 5.27/5.62 thf(fact_9529_numeral__or__not__num__eq,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % numeral_or_not_num_eq
% 5.27/5.62 thf(fact_9530_int__numeral__not__or__num__neg,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N2 @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % int_numeral_not_or_num_neg
% 5.27/5.62 thf(fact_9531_int__numeral__or__not__num__neg,axiom,
% 5.27/5.62 ! [M: num,N2: num] :
% 5.27/5.62 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.62 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % int_numeral_or_not_num_neg
% 5.27/5.62 thf(fact_9532_floor__real__def,axiom,
% 5.27/5.62 ( archim6058952711729229775r_real
% 5.27/5.62 = ( ^ [X: real] :
% 5.27/5.62 ( the_int
% 5.27/5.62 @ ^ [Z5: int] :
% 5.27/5.62 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 5.27/5.62 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % floor_real_def
% 5.27/5.62 thf(fact_9533_or__Suc__0__eq,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.62 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_Suc_0_eq
% 5.27/5.62 thf(fact_9534_Suc__0__or__eq,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.62 = ( plus_plus_nat @ N2 @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Suc_0_or_eq
% 5.27/5.62 thf(fact_9535_or__nat__rec,axiom,
% 5.27/5.62 ( bit_se1412395901928357646or_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] :
% 5.27/5.62 ( plus_plus_nat
% 5.27/5.62 @ ( zero_n2687167440665602831ol_nat
% 5.27/5.62 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M6 )
% 5.27/5.62 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.62 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_rec
% 5.27/5.62 thf(fact_9536_or__not__num__neg_Opelims,axiom,
% 5.27/5.62 ! [X4: num,Xa: num,Y: num] :
% 5.27/5.62 ( ( ( bit_or_not_num_neg @ X4 @ Xa )
% 5.27/5.62 = Y )
% 5.27/5.62 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( ( Y = one )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M5 ) ) ) ) ) )
% 5.27/5.62 => ( ( ( X4 = one )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M5 ) ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bit0 @ one ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit0 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ( ( Xa = one )
% 5.27/5.62 => ( ( Y = one )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.27/5.62 => ( ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit0 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M5 ) ) ) ) ) )
% 5.27/5.62 => ~ ! [N3: num] :
% 5.27/5.62 ( ( X4
% 5.27/5.62 = ( bit1 @ N3 ) )
% 5.27/5.62 => ! [M5: num] :
% 5.27/5.62 ( ( Xa
% 5.27/5.62 = ( bit1 @ M5 ) )
% 5.27/5.62 => ( ( Y
% 5.27/5.62 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M5 ) ) )
% 5.27/5.62 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_not_num_neg.pelims
% 5.27/5.62 thf(fact_9537_or__int__unfold,axiom,
% 5.27/5.62 ( bit_se1409905431419307370or_int
% 5.27/5.62 = ( ^ [K3: int,L2: int] :
% 5.27/5.62 ( if_int
% 5.27/5.62 @ ( ( K3
% 5.27/5.62 = ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.62 | ( L2
% 5.27/5.62 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.27/5.62 @ ( uminus_uminus_int @ one_one_int )
% 5.27/5.62 @ ( if_int @ ( K3 = zero_zero_int ) @ L2 @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_int_unfold
% 5.27/5.62 thf(fact_9538_max__enat__simps_I2_J,axiom,
% 5.27/5.62 ! [Q3: extended_enat] :
% 5.27/5.62 ( ( ord_ma741700101516333627d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.27/5.62 = Q3 ) ).
% 5.27/5.62
% 5.27/5.62 % max_enat_simps(2)
% 5.27/5.62 thf(fact_9539_max__enat__simps_I3_J,axiom,
% 5.27/5.62 ! [Q3: extended_enat] :
% 5.27/5.62 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.27/5.62 = Q3 ) ).
% 5.27/5.62
% 5.27/5.62 % max_enat_simps(3)
% 5.27/5.62 thf(fact_9540_max__Suc__Suc,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.27/5.62 = ( suc @ ( ord_max_nat @ M @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_Suc_Suc
% 5.27/5.62 thf(fact_9541_max__0R,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( ord_max_nat @ N2 @ zero_zero_nat )
% 5.27/5.62 = N2 ) ).
% 5.27/5.62
% 5.27/5.62 % max_0R
% 5.27/5.62 thf(fact_9542_max__0L,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( ord_max_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 = N2 ) ).
% 5.27/5.62
% 5.27/5.62 % max_0L
% 5.27/5.62 thf(fact_9543_max__nat_Oright__neutral,axiom,
% 5.27/5.62 ! [A: nat] :
% 5.27/5.62 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.27/5.62 = A ) ).
% 5.27/5.62
% 5.27/5.62 % max_nat.right_neutral
% 5.27/5.62 thf(fact_9544_max__nat_Oneutr__eq__iff,axiom,
% 5.27/5.62 ! [A: nat,B: nat] :
% 5.27/5.62 ( ( zero_zero_nat
% 5.27/5.62 = ( ord_max_nat @ A @ B ) )
% 5.27/5.62 = ( ( A = zero_zero_nat )
% 5.27/5.62 & ( B = zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_nat.neutr_eq_iff
% 5.27/5.62 thf(fact_9545_max__nat_Oleft__neutral,axiom,
% 5.27/5.62 ! [A: nat] :
% 5.27/5.62 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.27/5.62 = A ) ).
% 5.27/5.62
% 5.27/5.62 % max_nat.left_neutral
% 5.27/5.62 thf(fact_9546_max__nat_Oeq__neutr__iff,axiom,
% 5.27/5.62 ! [A: nat,B: nat] :
% 5.27/5.62 ( ( ( ord_max_nat @ A @ B )
% 5.27/5.62 = zero_zero_nat )
% 5.27/5.62 = ( ( A = zero_zero_nat )
% 5.27/5.62 & ( B = zero_zero_nat ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_nat.eq_neutr_iff
% 5.27/5.62 thf(fact_9547_max__Suc__numeral,axiom,
% 5.27/5.62 ! [N2: nat,K: num] :
% 5.27/5.62 ( ( ord_max_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.62 = ( suc @ ( ord_max_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_Suc_numeral
% 5.27/5.62 thf(fact_9548_max__numeral__Suc,axiom,
% 5.27/5.62 ! [K: num,N2: nat] :
% 5.27/5.62 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.27/5.62 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_numeral_Suc
% 5.27/5.62 thf(fact_9549_nat__add__max__left,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.62 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 5.27/5.62 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q3 ) @ ( plus_plus_nat @ N2 @ Q3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat_add_max_left
% 5.27/5.62 thf(fact_9550_nat__add__max__right,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.62 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 5.27/5.62 = ( ord_max_nat @ ( plus_plus_nat @ M @ N2 ) @ ( plus_plus_nat @ M @ Q3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat_add_max_right
% 5.27/5.62 thf(fact_9551_nat__mult__max__right,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.62 ( ( times_times_nat @ M @ ( ord_max_nat @ N2 @ Q3 ) )
% 5.27/5.62 = ( ord_max_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat_mult_max_right
% 5.27/5.62 thf(fact_9552_nat__mult__max__left,axiom,
% 5.27/5.62 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.62 ( ( times_times_nat @ ( ord_max_nat @ M @ N2 ) @ Q3 )
% 5.27/5.62 = ( ord_max_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat_mult_max_left
% 5.27/5.62 thf(fact_9553_nat__minus__add__max,axiom,
% 5.27/5.62 ! [N2: nat,M: nat] :
% 5.27/5.62 ( ( plus_plus_nat @ ( minus_minus_nat @ N2 @ M ) @ M )
% 5.27/5.62 = ( ord_max_nat @ N2 @ M ) ) ).
% 5.27/5.62
% 5.27/5.62 % nat_minus_add_max
% 5.27/5.62 thf(fact_9554_max__Suc2,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( ord_max_nat @ M @ ( suc @ N2 ) )
% 5.27/5.62 = ( case_nat_nat @ ( suc @ N2 )
% 5.27/5.62 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ M3 @ N2 ) )
% 5.27/5.62 @ M ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_Suc2
% 5.27/5.62 thf(fact_9555_max__Suc1,axiom,
% 5.27/5.62 ! [N2: nat,M: nat] :
% 5.27/5.62 ( ( ord_max_nat @ ( suc @ N2 ) @ M )
% 5.27/5.62 = ( case_nat_nat @ ( suc @ N2 )
% 5.27/5.62 @ ^ [M3: nat] : ( suc @ ( ord_max_nat @ N2 @ M3 ) )
% 5.27/5.62 @ M ) ) ).
% 5.27/5.62
% 5.27/5.62 % max_Suc1
% 5.27/5.62 thf(fact_9556_or__nat__unfold,axiom,
% 5.27/5.62 ( bit_se1412395901928357646or_nat
% 5.27/5.62 = ( ^ [M6: nat,N: nat] : ( if_nat @ ( M6 = zero_zero_nat ) @ N @ ( if_nat @ ( N = zero_zero_nat ) @ M6 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % or_nat_unfold
% 5.27/5.62 thf(fact_9557_floor__rat__def,axiom,
% 5.27/5.62 ( archim3151403230148437115or_rat
% 5.27/5.62 = ( ^ [X: rat] :
% 5.27/5.62 ( the_int
% 5.27/5.62 @ ^ [Z5: int] :
% 5.27/5.62 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 5.27/5.62 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % floor_rat_def
% 5.27/5.62 thf(fact_9558_bit__cut__integer__def,axiom,
% 5.27/5.62 ( code_bit_cut_integer
% 5.27/5.62 = ( ^ [K3: code_integer] :
% 5.27/5.62 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.27/5.62 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bit_cut_integer_def
% 5.27/5.62 thf(fact_9559_divmod__integer__def,axiom,
% 5.27/5.62 ( code_divmod_integer
% 5.27/5.62 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K3 @ L2 ) @ ( modulo364778990260209775nteger @ K3 @ L2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_integer_def
% 5.27/5.62 thf(fact_9560_sgn__rat__def,axiom,
% 5.27/5.62 ( sgn_sgn_rat
% 5.27/5.62 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % sgn_rat_def
% 5.27/5.62 thf(fact_9561_obtain__pos__sum,axiom,
% 5.27/5.62 ! [R3: rat] :
% 5.27/5.62 ( ( ord_less_rat @ zero_zero_rat @ R3 )
% 5.27/5.62 => ~ ! [S3: rat] :
% 5.27/5.62 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.27/5.62 => ! [T3: rat] :
% 5.27/5.62 ( ( ord_less_rat @ zero_zero_rat @ T3 )
% 5.27/5.62 => ( R3
% 5.27/5.62 != ( plus_plus_rat @ S3 @ T3 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % obtain_pos_sum
% 5.27/5.62 thf(fact_9562_less__eq__rat__def,axiom,
% 5.27/5.62 ( ord_less_eq_rat
% 5.27/5.62 = ( ^ [X: rat,Y5: rat] :
% 5.27/5.62 ( ( ord_less_rat @ X @ Y5 )
% 5.27/5.62 | ( X = Y5 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % less_eq_rat_def
% 5.27/5.62 thf(fact_9563_abs__rat__def,axiom,
% 5.27/5.62 ( abs_abs_rat
% 5.27/5.62 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % abs_rat_def
% 5.27/5.62 thf(fact_9564_pred__def,axiom,
% 5.27/5.62 ( pred
% 5.27/5.62 = ( case_nat_nat @ zero_zero_nat
% 5.27/5.62 @ ^ [X24: nat] : X24 ) ) ).
% 5.27/5.62
% 5.27/5.62 % pred_def
% 5.27/5.62 thf(fact_9565_bit__cut__integer__code,axiom,
% 5.27/5.62 ( code_bit_cut_integer
% 5.27/5.62 = ( ^ [K3: code_integer] :
% 5.27/5.62 ( if_Pro5737122678794959658eger_o @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.27/5.62 @ ( produc9125791028180074456eger_o
% 5.27/5.62 @ ^ [R5: code_integer,S4: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S4 ) ) @ ( S4 = one_one_Code_integer ) )
% 5.27/5.62 @ ( code_divmod_abs @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bit_cut_integer_code
% 5.27/5.62 thf(fact_9566_normalize__negative,axiom,
% 5.27/5.62 ! [Q3: int,P2: int] :
% 5.27/5.62 ( ( ord_less_int @ Q3 @ zero_zero_int )
% 5.27/5.62 => ( ( normalize @ ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.27/5.62 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P2 ) @ ( uminus_uminus_int @ Q3 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % normalize_negative
% 5.27/5.62 thf(fact_9567_divmod__abs__def,axiom,
% 5.27/5.62 ( code_divmod_abs
% 5.27/5.62 = ( ^ [K3: code_integer,L2: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_abs_def
% 5.27/5.62 thf(fact_9568_prod__decode__aux_Oelims,axiom,
% 5.27/5.62 ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.27/5.62 ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 5.27/5.62 = Y )
% 5.27/5.62 => ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_decode_aux.elims
% 5.27/5.62 thf(fact_9569_normalize__denom__pos,axiom,
% 5.27/5.62 ! [R3: product_prod_int_int,P2: int,Q3: int] :
% 5.27/5.62 ( ( ( normalize @ R3 )
% 5.27/5.62 = ( product_Pair_int_int @ P2 @ Q3 ) )
% 5.27/5.62 => ( ord_less_int @ zero_zero_int @ Q3 ) ) ).
% 5.27/5.62
% 5.27/5.62 % normalize_denom_pos
% 5.27/5.62 thf(fact_9570_prod__decode__aux_Osimps,axiom,
% 5.27/5.62 ( nat_prod_decode_aux
% 5.27/5.62 = ( ^ [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 ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_decode_aux.simps
% 5.27/5.62 thf(fact_9571_prod__decode__aux_Opelims,axiom,
% 5.27/5.62 ! [X4: nat,Xa: nat,Y: product_prod_nat_nat] :
% 5.27/5.62 ( ( ( nat_prod_decode_aux @ X4 @ Xa )
% 5.27/5.62 = Y )
% 5.27/5.62 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.27/5.62 => ~ ( ( ( ( ord_less_eq_nat @ Xa @ X4 )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( product_Pair_nat_nat @ Xa @ ( minus_minus_nat @ X4 @ Xa ) ) ) )
% 5.27/5.62 & ( ~ ( ord_less_eq_nat @ Xa @ X4 )
% 5.27/5.62 => ( Y
% 5.27/5.62 = ( nat_prod_decode_aux @ ( suc @ X4 ) @ ( minus_minus_nat @ Xa @ ( suc @ X4 ) ) ) ) ) )
% 5.27/5.62 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % prod_decode_aux.pelims
% 5.27/5.62 thf(fact_9572_divmod__integer__code,axiom,
% 5.27/5.62 ( code_divmod_integer
% 5.27/5.62 = ( ^ [K3: code_integer,L2: code_integer] :
% 5.27/5.62 ( if_Pro6119634080678213985nteger @ ( K3 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.27/5.62 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.27/5.62 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K3 ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.27/5.62 @ ( produc6916734918728496179nteger
% 5.27/5.62 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L2 @ S4 ) ) )
% 5.27/5.62 @ ( code_divmod_abs @ K3 @ L2 ) ) )
% 5.27/5.62 @ ( if_Pro6119634080678213985nteger @ ( L2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K3 )
% 5.27/5.62 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.27/5.62 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K3 @ L2 )
% 5.27/5.62 @ ( produc6916734918728496179nteger
% 5.27/5.62 @ ^ [R5: code_integer,S4: code_integer] : ( if_Pro6119634080678213985nteger @ ( S4 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L2 ) @ S4 ) ) )
% 5.27/5.62 @ ( code_divmod_abs @ K3 @ L2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % divmod_integer_code
% 5.27/5.62 thf(fact_9573_Suc__0__div__numeral,axiom,
% 5.27/5.62 ! [K: num] :
% 5.27/5.62 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.62 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % Suc_0_div_numeral
% 5.27/5.62 thf(fact_9574_finite__atLeastAtMost,axiom,
% 5.27/5.62 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atLeastAtMost
% 5.27/5.62 thf(fact_9575_finite__atLeastLessThan,axiom,
% 5.27/5.62 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atLeastLessThan
% 5.27/5.62 thf(fact_9576_finite__lessThan,axiom,
% 5.27/5.62 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_lessThan
% 5.27/5.62 thf(fact_9577_finite__atMost,axiom,
% 5.27/5.62 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atMost
% 5.27/5.62 thf(fact_9578_fst__divmod__nat,axiom,
% 5.27/5.62 ! [M: nat,N2: nat] :
% 5.27/5.62 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.27/5.62 = ( divide_divide_nat @ M @ N2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % fst_divmod_nat
% 5.27/5.62 thf(fact_9579_finite__nat__set__iff__bounded__le,axiom,
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 = ( ^ [N9: set_nat] :
% 5.27/5.62 ? [M6: nat] :
% 5.27/5.62 ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ N9 )
% 5.27/5.62 => ( ord_less_eq_nat @ X @ M6 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nat_set_iff_bounded_le
% 5.27/5.62 thf(fact_9580_finite__less__ub,axiom,
% 5.27/5.62 ! [F: nat > nat,U: nat] :
% 5.27/5.62 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.27/5.62 => ( finite_finite_nat
% 5.27/5.62 @ ( collect_nat
% 5.27/5.62 @ ^ [N: nat] : ( ord_less_eq_nat @ ( F @ N ) @ U ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_less_ub
% 5.27/5.62 thf(fact_9581_finite__M__bounded__by__nat,axiom,
% 5.27/5.62 ! [P: nat > $o,I2: nat] :
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 @ ( collect_nat
% 5.27/5.62 @ ^ [K3: nat] :
% 5.27/5.62 ( ( P @ K3 )
% 5.27/5.62 & ( ord_less_nat @ K3 @ I2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_M_bounded_by_nat
% 5.27/5.62 thf(fact_9582_bounded__nat__set__is__finite,axiom,
% 5.27/5.62 ! [N4: set_nat,N2: nat] :
% 5.27/5.62 ( ! [X5: nat] :
% 5.27/5.62 ( ( member_nat @ X5 @ N4 )
% 5.27/5.62 => ( ord_less_nat @ X5 @ N2 ) )
% 5.27/5.62 => ( finite_finite_nat @ N4 ) ) ).
% 5.27/5.62
% 5.27/5.62 % bounded_nat_set_is_finite
% 5.27/5.62 thf(fact_9583_finite__nat__set__iff__bounded,axiom,
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 = ( ^ [N9: set_nat] :
% 5.27/5.62 ? [M6: nat] :
% 5.27/5.62 ! [X: nat] :
% 5.27/5.62 ( ( member_nat @ X @ N9 )
% 5.27/5.62 => ( ord_less_nat @ X @ M6 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nat_set_iff_bounded
% 5.27/5.62 thf(fact_9584_finite__divisors__nat,axiom,
% 5.27/5.62 ! [M: nat] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.62 => ( finite_finite_nat
% 5.27/5.62 @ ( collect_nat
% 5.27/5.62 @ ^ [D5: nat] : ( dvd_dvd_nat @ D5 @ M ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_divisors_nat
% 5.27/5.62 thf(fact_9585_subset__eq__atLeast0__atMost__finite,axiom,
% 5.27/5.62 ! [N4: set_nat,N2: nat] :
% 5.27/5.62 ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 => ( finite_finite_nat @ N4 ) ) ).
% 5.27/5.62
% 5.27/5.62 % subset_eq_atLeast0_atMost_finite
% 5.27/5.62 thf(fact_9586_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.27/5.62 ! [N4: set_nat,N2: nat] :
% 5.27/5.62 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.62 => ( finite_finite_nat @ N4 ) ) ).
% 5.27/5.62
% 5.27/5.62 % subset_eq_atLeast0_lessThan_finite
% 5.27/5.62 thf(fact_9587_even__set__encode__iff,axiom,
% 5.27/5.62 ! [A2: set_nat] :
% 5.27/5.62 ( ( finite_finite_nat @ A2 )
% 5.27/5.62 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.27/5.62 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % even_set_encode_iff
% 5.27/5.62 thf(fact_9588_finite__Collect__le__nat,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 @ ( collect_nat
% 5.27/5.62 @ ^ [N: nat] : ( ord_less_eq_nat @ N @ K ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_Collect_le_nat
% 5.27/5.62 thf(fact_9589_finite__Collect__less__nat,axiom,
% 5.27/5.62 ! [K: nat] :
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 @ ( collect_nat
% 5.27/5.62 @ ^ [N: nat] : ( ord_less_nat @ N @ K ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_Collect_less_nat
% 5.27/5.62 thf(fact_9590_finite__atLeastAtMost__int,axiom,
% 5.27/5.62 ! [L: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atLeastAtMost_int
% 5.27/5.62 thf(fact_9591_finite__atLeastLessThan__int,axiom,
% 5.27/5.62 ! [L: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atLeastLessThan_int
% 5.27/5.62 thf(fact_9592_finite__interval__int1,axiom,
% 5.27/5.62 ! [A: int,B: int] :
% 5.27/5.62 ( finite_finite_int
% 5.27/5.62 @ ( collect_int
% 5.27/5.62 @ ^ [I3: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ A @ I3 )
% 5.27/5.62 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_interval_int1
% 5.27/5.62 thf(fact_9593_finite__interval__int4,axiom,
% 5.27/5.62 ! [A: int,B: int] :
% 5.27/5.62 ( finite_finite_int
% 5.27/5.62 @ ( collect_int
% 5.27/5.62 @ ^ [I3: int] :
% 5.27/5.62 ( ( ord_less_int @ A @ I3 )
% 5.27/5.62 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_interval_int4
% 5.27/5.62 thf(fact_9594_finite__interval__int2,axiom,
% 5.27/5.62 ! [A: int,B: int] :
% 5.27/5.62 ( finite_finite_int
% 5.27/5.62 @ ( collect_int
% 5.27/5.62 @ ^ [I3: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ A @ I3 )
% 5.27/5.62 & ( ord_less_int @ I3 @ B ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_interval_int2
% 5.27/5.62 thf(fact_9595_finite__interval__int3,axiom,
% 5.27/5.62 ! [A: int,B: int] :
% 5.27/5.62 ( finite_finite_int
% 5.27/5.62 @ ( collect_int
% 5.27/5.62 @ ^ [I3: int] :
% 5.27/5.62 ( ( ord_less_int @ A @ I3 )
% 5.27/5.62 & ( ord_less_eq_int @ I3 @ B ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_interval_int3
% 5.27/5.62 thf(fact_9596_finite__nth__roots,axiom,
% 5.27/5.62 ! [N2: nat,C: complex] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( finite3207457112153483333omplex
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = C ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nth_roots
% 5.27/5.62 thf(fact_9597_finite__atLeastZeroLessThan__int,axiom,
% 5.27/5.62 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_atLeastZeroLessThan_int
% 5.27/5.62 thf(fact_9598_finite__nat__iff__bounded__le,axiom,
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 = ( ^ [S5: set_nat] :
% 5.27/5.62 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_atMost_nat @ K3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nat_iff_bounded_le
% 5.27/5.62 thf(fact_9599_finite__nat__iff__bounded,axiom,
% 5.27/5.62 ( finite_finite_nat
% 5.27/5.62 = ( ^ [S5: set_nat] :
% 5.27/5.62 ? [K3: nat] : ( ord_less_eq_set_nat @ S5 @ ( set_ord_lessThan_nat @ K3 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nat_iff_bounded
% 5.27/5.62 thf(fact_9600_finite__nat__bounded,axiom,
% 5.27/5.62 ! [S2: set_nat] :
% 5.27/5.62 ( ( finite_finite_nat @ S2 )
% 5.27/5.62 => ? [K2: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K2 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % finite_nat_bounded
% 5.27/5.62 thf(fact_9601_infinite__int__iff__unbounded__le,axiom,
% 5.27/5.62 ! [S2: set_int] :
% 5.27/5.62 ( ( ~ ( finite_finite_int @ S2 ) )
% 5.27/5.62 = ( ! [M6: int] :
% 5.27/5.62 ? [N: int] :
% 5.27/5.62 ( ( ord_less_eq_int @ M6 @ ( abs_abs_int @ N ) )
% 5.27/5.62 & ( member_int @ N @ S2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % infinite_int_iff_unbounded_le
% 5.27/5.62 thf(fact_9602_infinite__int__iff__unbounded,axiom,
% 5.27/5.62 ! [S2: set_int] :
% 5.27/5.62 ( ( ~ ( finite_finite_int @ S2 ) )
% 5.27/5.62 = ( ! [M6: int] :
% 5.27/5.62 ? [N: int] :
% 5.27/5.62 ( ( ord_less_int @ M6 @ ( abs_abs_int @ N ) )
% 5.27/5.62 & ( member_int @ N @ S2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % infinite_int_iff_unbounded
% 5.27/5.62 thf(fact_9603_unbounded__k__infinite,axiom,
% 5.27/5.62 ! [K: nat,S2: set_nat] :
% 5.27/5.62 ( ! [M5: nat] :
% 5.27/5.62 ( ( ord_less_nat @ K @ M5 )
% 5.27/5.62 => ? [N6: nat] :
% 5.27/5.62 ( ( ord_less_nat @ M5 @ N6 )
% 5.27/5.62 & ( member_nat @ N6 @ S2 ) ) )
% 5.27/5.62 => ~ ( finite_finite_nat @ S2 ) ) ).
% 5.27/5.62
% 5.27/5.62 % unbounded_k_infinite
% 5.27/5.62 thf(fact_9604_infinite__nat__iff__unbounded,axiom,
% 5.27/5.62 ! [S2: set_nat] :
% 5.27/5.62 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.27/5.62 = ( ! [M6: nat] :
% 5.27/5.62 ? [N: nat] :
% 5.27/5.62 ( ( ord_less_nat @ M6 @ N )
% 5.27/5.62 & ( member_nat @ N @ S2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % infinite_nat_iff_unbounded
% 5.27/5.62 thf(fact_9605_infinite__nat__iff__unbounded__le,axiom,
% 5.27/5.62 ! [S2: set_nat] :
% 5.27/5.62 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.27/5.62 = ( ! [M6: nat] :
% 5.27/5.62 ? [N: nat] :
% 5.27/5.62 ( ( ord_less_eq_nat @ M6 @ N )
% 5.27/5.62 & ( member_nat @ N @ S2 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % infinite_nat_iff_unbounded_le
% 5.27/5.62 thf(fact_9606_bij__betw__nth__root__unity,axiom,
% 5.27/5.62 ! [C: complex,N2: nat] :
% 5.27/5.62 ( ( C != zero_zero_complex )
% 5.27/5.62 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N2 @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) )
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = one_one_complex ) )
% 5.27/5.62 @ ( collect_complex
% 5.27/5.62 @ ^ [Z5: complex] :
% 5.27/5.62 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.62 = C ) ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % bij_betw_nth_root_unity
% 5.27/5.62 thf(fact_9607_real__root__Suc__0,axiom,
% 5.27/5.62 ! [X4: real] :
% 5.27/5.62 ( ( root @ ( suc @ zero_zero_nat ) @ X4 )
% 5.27/5.62 = X4 ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_Suc_0
% 5.27/5.62 thf(fact_9608_real__root__eq__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ( root @ N2 @ X4 )
% 5.27/5.62 = ( root @ N2 @ Y ) )
% 5.27/5.62 = ( X4 = Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_eq_iff
% 5.27/5.62 thf(fact_9609_real__root__eq__0__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ( root @ N2 @ X4 )
% 5.27/5.62 = zero_zero_real )
% 5.27/5.62 = ( X4 = zero_zero_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_eq_0_iff
% 5.27/5.62 thf(fact_9610_real__root__less__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_real @ X4 @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_less_iff
% 5.27/5.62 thf(fact_9611_real__root__le__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_eq_real @ X4 @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_le_iff
% 5.27/5.62 thf(fact_9612_real__root__one,axiom,
% 5.27/5.62 ! [N2: nat] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( root @ N2 @ one_one_real )
% 5.27/5.62 = one_one_real ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_one
% 5.27/5.62 thf(fact_9613_real__root__eq__1__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ( root @ N2 @ X4 )
% 5.27/5.62 = one_one_real )
% 5.27/5.62 = ( X4 = one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_eq_1_iff
% 5.27/5.62 thf(fact_9614_real__root__gt__0__iff,axiom,
% 5.27/5.62 ! [N2: nat,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_gt_0_iff
% 5.27/5.62 thf(fact_9615_real__root__lt__0__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_real @ X4 @ zero_zero_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_lt_0_iff
% 5.27/5.62 thf(fact_9616_real__root__ge__0__iff,axiom,
% 5.27/5.62 ! [N2: nat,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_ge_0_iff
% 5.27/5.62 thf(fact_9617_real__root__le__0__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ zero_zero_real )
% 5.27/5.62 = ( ord_less_eq_real @ X4 @ zero_zero_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_le_0_iff
% 5.27/5.62 thf(fact_9618_real__root__gt__1__iff,axiom,
% 5.27/5.62 ! [N2: nat,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_gt_1_iff
% 5.27/5.62 thf(fact_9619_real__root__lt__1__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 5.27/5.62 = ( ord_less_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_lt_1_iff
% 5.27/5.62 thf(fact_9620_real__root__ge__1__iff,axiom,
% 5.27/5.62 ! [N2: nat,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N2 @ Y ) )
% 5.27/5.62 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_ge_1_iff
% 5.27/5.62 thf(fact_9621_real__root__le__1__iff,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ one_one_real )
% 5.27/5.62 = ( ord_less_eq_real @ X4 @ one_one_real ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_le_1_iff
% 5.27/5.62 thf(fact_9622_real__root__pow__pos2,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.62 => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 5.27/5.62 = X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_pow_pos2
% 5.27/5.62 thf(fact_9623_real__root__pos__pos__le,axiom,
% 5.27/5.62 ! [X4: real,N2: nat] :
% 5.27/5.62 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.62 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_pos_pos_le
% 5.27/5.62 thf(fact_9624_real__root__less__mono,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_real @ X4 @ Y )
% 5.27/5.62 => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_less_mono
% 5.27/5.62 thf(fact_9625_real__root__le__mono,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,Y: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( ord_less_eq_real @ X4 @ Y )
% 5.27/5.62 => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N2 @ Y ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_le_mono
% 5.27/5.62 thf(fact_9626_real__root__power,axiom,
% 5.27/5.62 ! [N2: nat,X4: real,K: nat] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( root @ N2 @ ( power_power_real @ X4 @ K ) )
% 5.27/5.62 = ( power_power_real @ ( root @ N2 @ X4 ) @ K ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_power
% 5.27/5.62 thf(fact_9627_real__root__abs,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.62 => ( ( root @ N2 @ ( abs_abs_real @ X4 ) )
% 5.27/5.62 = ( abs_abs_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 5.27/5.62
% 5.27/5.62 % real_root_abs
% 5.27/5.62 thf(fact_9628_sgn__root,axiom,
% 5.27/5.62 ! [N2: nat,X4: real] :
% 5.27/5.62 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( sgn_sgn_real @ ( root @ N2 @ X4 ) )
% 5.27/5.63 = ( sgn_sgn_real @ X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sgn_root
% 5.27/5.63 thf(fact_9629_real__root__gt__zero,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ord_less_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_gt_zero
% 5.27/5.63 thf(fact_9630_real__root__strict__decreasing,axiom,
% 5.27/5.63 ! [N2: nat,N4: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_nat @ N2 @ N4 )
% 5.27/5.63 => ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.63 => ( ord_less_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_strict_decreasing
% 5.27/5.63 thf(fact_9631_sqrt__def,axiom,
% 5.27/5.63 ( sqrt
% 5.27/5.63 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sqrt_def
% 5.27/5.63 thf(fact_9632_root__abs__power,axiom,
% 5.27/5.63 ! [N2: nat,Y: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( abs_abs_real @ ( root @ N2 @ ( power_power_real @ Y @ N2 ) ) )
% 5.27/5.63 = ( abs_abs_real @ Y ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % root_abs_power
% 5.27/5.63 thf(fact_9633_real__root__pos__pos,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N2 @ X4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_pos_pos
% 5.27/5.63 thf(fact_9634_real__root__strict__increasing,axiom,
% 5.27/5.63 ! [N2: nat,N4: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_nat @ N2 @ N4 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( ord_less_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_strict_increasing
% 5.27/5.63 thf(fact_9635_real__root__decreasing,axiom,
% 5.27/5.63 ! [N2: nat,N4: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ one_one_real @ X4 )
% 5.27/5.63 => ( ord_less_eq_real @ ( root @ N4 @ X4 ) @ ( root @ N2 @ X4 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_decreasing
% 5.27/5.63 thf(fact_9636_real__root__pow__pos,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 5.27/5.63 = X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_pow_pos
% 5.27/5.63 thf(fact_9637_real__root__pos__unique,axiom,
% 5.27/5.63 ! [N2: nat,Y: real,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.27/5.63 => ( ( ( power_power_real @ Y @ N2 )
% 5.27/5.63 = X4 )
% 5.27/5.63 => ( ( root @ N2 @ X4 )
% 5.27/5.63 = Y ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_pos_unique
% 5.27/5.63 thf(fact_9638_real__root__power__cancel,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.63 = X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_power_cancel
% 5.27/5.63 thf(fact_9639_odd__real__root__power__cancel,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( root @ N2 @ ( power_power_real @ X4 @ N2 ) )
% 5.27/5.63 = X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % odd_real_root_power_cancel
% 5.27/5.63 thf(fact_9640_odd__real__root__unique,axiom,
% 5.27/5.63 ! [N2: nat,Y: real,X4: real] :
% 5.27/5.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( ( power_power_real @ Y @ N2 )
% 5.27/5.63 = X4 )
% 5.27/5.63 => ( ( root @ N2 @ X4 )
% 5.27/5.63 = Y ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % odd_real_root_unique
% 5.27/5.63 thf(fact_9641_odd__real__root__pow,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( power_power_real @ ( root @ N2 @ X4 ) @ N2 )
% 5.27/5.63 = X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % odd_real_root_pow
% 5.27/5.63 thf(fact_9642_real__root__increasing,axiom,
% 5.27/5.63 ! [N2: nat,N4: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_eq_nat @ N2 @ N4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.63 => ( ord_less_eq_real @ ( root @ N2 @ X4 ) @ ( root @ N4 @ X4 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % real_root_increasing
% 5.27/5.63 thf(fact_9643_root__sgn__power,axiom,
% 5.27/5.63 ! [N2: nat,Y: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( root @ N2 @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N2 ) ) )
% 5.27/5.63 = Y ) ) ).
% 5.27/5.63
% 5.27/5.63 % root_sgn_power
% 5.27/5.63 thf(fact_9644_sgn__power__root,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N2 @ X4 ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N2 @ X4 ) ) @ N2 ) )
% 5.27/5.63 = X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % sgn_power_root
% 5.27/5.63 thf(fact_9645_ln__root,axiom,
% 5.27/5.63 ! [N2: nat,B: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.63 => ( ( ln_ln_real @ ( root @ N2 @ B ) )
% 5.27/5.63 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % ln_root
% 5.27/5.63 thf(fact_9646_log__root,axiom,
% 5.27/5.63 ! [N2: nat,A: real,B: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.27/5.63 => ( ( log @ B @ ( root @ N2 @ A ) )
% 5.27/5.63 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % log_root
% 5.27/5.63 thf(fact_9647_log__base__root,axiom,
% 5.27/5.63 ! [N2: nat,B: real,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.27/5.63 => ( ( log @ ( root @ N2 @ B ) @ X4 )
% 5.27/5.63 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( log @ B @ X4 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % log_base_root
% 5.27/5.63 thf(fact_9648_split__root,axiom,
% 5.27/5.63 ! [P: real > $o,N2: nat,X4: real] :
% 5.27/5.63 ( ( P @ ( root @ N2 @ X4 ) )
% 5.27/5.63 = ( ( ( N2 = zero_zero_nat )
% 5.27/5.63 => ( P @ zero_zero_real ) )
% 5.27/5.63 & ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ! [Y5: real] :
% 5.27/5.63 ( ( ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 5.27/5.63 = X4 )
% 5.27/5.63 => ( P @ Y5 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % split_root
% 5.27/5.63 thf(fact_9649_root__powr__inverse,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( root @ N2 @ X4 )
% 5.27/5.63 = ( powr_real @ X4 @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % root_powr_inverse
% 5.27/5.63 thf(fact_9650_set__encode__insert,axiom,
% 5.27/5.63 ! [A2: set_nat,N2: nat] :
% 5.27/5.63 ( ( finite_finite_nat @ A2 )
% 5.27/5.63 => ( ~ ( member_nat @ N2 @ A2 )
% 5.27/5.63 => ( ( nat_set_encode @ ( insert_nat @ N2 @ A2 ) )
% 5.27/5.63 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % set_encode_insert
% 5.27/5.63 thf(fact_9651_Suc__0__mod__numeral,axiom,
% 5.27/5.63 ! [K: num] :
% 5.27/5.63 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Suc_0_mod_numeral
% 5.27/5.63 thf(fact_9652_card__lessThan,axiom,
% 5.27/5.63 ! [U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.27/5.63 = U ) ).
% 5.27/5.63
% 5.27/5.63 % card_lessThan
% 5.27/5.63 thf(fact_9653_card__Collect__less__nat,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [I3: nat] : ( ord_less_nat @ I3 @ N2 ) ) )
% 5.27/5.63 = N2 ) ).
% 5.27/5.63
% 5.27/5.63 % card_Collect_less_nat
% 5.27/5.63 thf(fact_9654_card__atMost,axiom,
% 5.27/5.63 ! [U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.27/5.63 = ( suc @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atMost
% 5.27/5.63 thf(fact_9655_card__atLeastLessThan,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L @ U ) )
% 5.27/5.63 = ( minus_minus_nat @ U @ L ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atLeastLessThan
% 5.27/5.63 thf(fact_9656_card__Collect__le__nat,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [I3: nat] : ( ord_less_eq_nat @ I3 @ N2 ) ) )
% 5.27/5.63 = ( suc @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_Collect_le_nat
% 5.27/5.63 thf(fact_9657_card__atLeastAtMost,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L @ U ) )
% 5.27/5.63 = ( minus_minus_nat @ ( suc @ U ) @ L ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atLeastAtMost
% 5.27/5.63 thf(fact_9658_card__atLeastLessThan__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L @ U ) )
% 5.27/5.63 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atLeastLessThan_int
% 5.27/5.63 thf(fact_9659_snd__divmod__nat,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N2 ) )
% 5.27/5.63 = ( modulo_modulo_nat @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % snd_divmod_nat
% 5.27/5.63 thf(fact_9660_card__atLeastAtMost__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L @ U ) )
% 5.27/5.63 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L ) @ one_one_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atLeastAtMost_int
% 5.27/5.63 thf(fact_9661_lessThan__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.27/5.63 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % lessThan_Suc
% 5.27/5.63 thf(fact_9662_atMost__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.27/5.63 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atMost_Suc
% 5.27/5.63 thf(fact_9663_atLeast0__atMost__Suc,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast0_atMost_Suc
% 5.27/5.63 thf(fact_9664_atLeast0__lessThan__Suc,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast0_lessThan_Suc
% 5.27/5.63 thf(fact_9665_Icc__eq__insert__lb__nat,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( set_or1269000886237332187st_nat @ M @ N2 )
% 5.27/5.63 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Icc_eq_insert_lb_nat
% 5.27/5.63 thf(fact_9666_atLeastAtMostSuc__conv,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ M @ ( suc @ N2 ) )
% 5.27/5.63 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ ( suc @ N2 ) @ ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastAtMostSuc_conv
% 5.27/5.63 thf(fact_9667_atLeastAtMost__insertL,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N2 ) )
% 5.27/5.63 = ( set_or1269000886237332187st_nat @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastAtMost_insertL
% 5.27/5.63 thf(fact_9668_lessThan__nat__numeral,axiom,
% 5.27/5.63 ! [K: num] :
% 5.27/5.63 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % lessThan_nat_numeral
% 5.27/5.63 thf(fact_9669_card__less,axiom,
% 5.27/5.63 ! [M7: set_nat,I2: nat] :
% 5.27/5.63 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.27/5.63 => ( ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] :
% 5.27/5.63 ( ( member_nat @ K3 @ M7 )
% 5.27/5.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) )
% 5.27/5.63 != zero_zero_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_less
% 5.27/5.63 thf(fact_9670_card__less__Suc,axiom,
% 5.27/5.63 ! [M7: set_nat,I2: nat] :
% 5.27/5.63 ( ( member_nat @ zero_zero_nat @ M7 )
% 5.27/5.63 => ( ( suc
% 5.27/5.63 @ ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] :
% 5.27/5.63 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.27/5.63 & ( ord_less_nat @ K3 @ I2 ) ) ) ) )
% 5.27/5.63 = ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] :
% 5.27/5.63 ( ( member_nat @ K3 @ M7 )
% 5.27/5.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_less_Suc
% 5.27/5.63 thf(fact_9671_card__less__Suc2,axiom,
% 5.27/5.63 ! [M7: set_nat,I2: nat] :
% 5.27/5.63 ( ~ ( member_nat @ zero_zero_nat @ M7 )
% 5.27/5.63 => ( ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] :
% 5.27/5.63 ( ( member_nat @ ( suc @ K3 ) @ M7 )
% 5.27/5.63 & ( ord_less_nat @ K3 @ I2 ) ) ) )
% 5.27/5.63 = ( finite_card_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] :
% 5.27/5.63 ( ( member_nat @ K3 @ M7 )
% 5.27/5.63 & ( ord_less_nat @ K3 @ ( suc @ I2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_less_Suc2
% 5.27/5.63 thf(fact_9672_atMost__nat__numeral,axiom,
% 5.27/5.63 ! [K: num] :
% 5.27/5.63 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atMost_nat_numeral
% 5.27/5.63 thf(fact_9673_card__atLeastZeroLessThan__int,axiom,
% 5.27/5.63 ! [U: int] :
% 5.27/5.63 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.27/5.63 = ( nat2 @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_atLeastZeroLessThan_int
% 5.27/5.63 thf(fact_9674_subset__card__intvl__is__intvl,axiom,
% 5.27/5.63 ! [A2: set_nat,K: nat] :
% 5.27/5.63 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.27/5.63 => ( A2
% 5.27/5.63 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % subset_card_intvl_is_intvl
% 5.27/5.63 thf(fact_9675_subset__eq__atLeast0__lessThan__card,axiom,
% 5.27/5.63 ! [N4: set_nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) )
% 5.27/5.63 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % subset_eq_atLeast0_lessThan_card
% 5.27/5.63 thf(fact_9676_card__sum__le__nat__sum,axiom,
% 5.27/5.63 ! [S2: set_nat] :
% 5.27/5.63 ( ord_less_eq_nat
% 5.27/5.63 @ ( groups3542108847815614940at_nat
% 5.27/5.63 @ ^ [X: nat] : X
% 5.27/5.63 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 5.27/5.63 @ ( groups3542108847815614940at_nat
% 5.27/5.63 @ ^ [X: nat] : X
% 5.27/5.63 @ S2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_sum_le_nat_sum
% 5.27/5.63 thf(fact_9677_card__nth__roots,axiom,
% 5.27/5.63 ! [C: complex,N2: nat] :
% 5.27/5.63 ( ( C != zero_zero_complex )
% 5.27/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( finite_card_complex
% 5.27/5.63 @ ( collect_complex
% 5.27/5.63 @ ^ [Z5: complex] :
% 5.27/5.63 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.63 = C ) ) )
% 5.27/5.63 = N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_nth_roots
% 5.27/5.63 thf(fact_9678_card__roots__unity__eq,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( finite_card_complex
% 5.27/5.63 @ ( collect_complex
% 5.27/5.63 @ ^ [Z5: complex] :
% 5.27/5.63 ( ( power_power_complex @ Z5 @ N2 )
% 5.27/5.63 = one_one_complex ) ) )
% 5.27/5.63 = N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_roots_unity_eq
% 5.27/5.63 thf(fact_9679_set__decode__plus__power__2,axiom,
% 5.27/5.63 ! [N2: nat,Z: nat] :
% 5.27/5.63 ( ~ ( member_nat @ N2 @ ( nat_set_decode @ Z ) )
% 5.27/5.63 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ Z ) )
% 5.27/5.63 = ( insert_nat @ N2 @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % set_decode_plus_power_2
% 5.27/5.63 thf(fact_9680_snd__divmod__integer,axiom,
% 5.27/5.63 ! [K: code_integer,L: code_integer] :
% 5.27/5.63 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L ) )
% 5.27/5.63 = ( modulo364778990260209775nteger @ K @ L ) ) ).
% 5.27/5.63
% 5.27/5.63 % snd_divmod_integer
% 5.27/5.63 thf(fact_9681_snd__divmod__abs,axiom,
% 5.27/5.63 ! [K: code_integer,L: code_integer] :
% 5.27/5.63 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L ) )
% 5.27/5.63 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % snd_divmod_abs
% 5.27/5.63 thf(fact_9682_atLeastAtMostPlus1__int__conv,axiom,
% 5.27/5.63 ! [M: int,N2: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.27/5.63 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N2 ) )
% 5.27/5.63 = ( insert_int @ ( plus_plus_int @ one_one_int @ N2 ) @ ( set_or1266510415728281911st_int @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastAtMostPlus1_int_conv
% 5.27/5.63 thf(fact_9683_minus__one__mod__numeral,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % minus_one_mod_numeral
% 5.27/5.63 thf(fact_9684_one__mod__minus__numeral,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % one_mod_minus_numeral
% 5.27/5.63 thf(fact_9685_minus__numeral__mod__numeral,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % minus_numeral_mod_numeral
% 5.27/5.63 thf(fact_9686_numeral__mod__minus__numeral,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N2 ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % numeral_mod_minus_numeral
% 5.27/5.63 thf(fact_9687_Divides_Oadjust__mod__def,axiom,
% 5.27/5.63 ( adjust_mod
% 5.27/5.63 = ( ^ [L2: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L2 @ R5 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Divides.adjust_mod_def
% 5.27/5.63 thf(fact_9688_and__int_Oelims,axiom,
% 5.27/5.63 ! [X4: int,Xa: int,Y: int] :
% 5.27/5.63 ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( uminus_uminus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.27/5.63 & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( plus_plus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.27/5.63 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_int.elims
% 5.27/5.63 thf(fact_9689_and__int_Osimps,axiom,
% 5.27/5.63 ( bit_se725231765392027082nd_int
% 5.27/5.63 = ( ^ [K3: int,L2: int] :
% 5.27/5.63 ( if_int
% 5.27/5.63 @ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 @ ( uminus_uminus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) )
% 5.27/5.63 @ ( plus_plus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K3 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.27/5.63 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_int.simps
% 5.27/5.63 thf(fact_9690_bezw_Oelims,axiom,
% 5.27/5.63 ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 5.27/5.63 ( ( ( bezw @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( Xa = zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.27/5.63 & ( ( Xa != zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezw.elims
% 5.27/5.63 thf(fact_9691_simp__from__to,axiom,
% 5.27/5.63 ( set_or1266510415728281911st_int
% 5.27/5.63 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % simp_from_to
% 5.27/5.63 thf(fact_9692_bezw__non__0,axiom,
% 5.27/5.63 ! [Y: nat,X4: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.27/5.63 => ( ( bezw @ X4 @ Y )
% 5.27/5.63 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Y ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezw_non_0
% 5.27/5.63 thf(fact_9693_bezw_Osimps,axiom,
% 5.27/5.63 ( bezw
% 5.27/5.63 = ( ^ [X: nat,Y5: nat] : ( if_Pro3027730157355071871nt_int @ ( Y5 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y5 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezw.simps
% 5.27/5.63 thf(fact_9694_bezw_Opelims,axiom,
% 5.27/5.63 ! [X4: nat,Xa: nat,Y: product_prod_int_int] :
% 5.27/5.63 ( ( ( bezw @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.27/5.63 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.27/5.63 & ( ( Xa != zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X4 @ Xa ) ) ) ) ) ) ) )
% 5.27/5.63 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezw.pelims
% 5.27/5.63 thf(fact_9695_and__int_Opsimps,axiom,
% 5.27/5.63 ! [K: int,L: int] :
% 5.27/5.63 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L ) )
% 5.27/5.63 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.27/5.63 = ( uminus_uminus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) ) ) )
% 5.27/5.63 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( ( bit_se725231765392027082nd_int @ K @ L )
% 5.27/5.63 = ( plus_plus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.27/5.63 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_int.psimps
% 5.27/5.63 thf(fact_9696_and__int_Opelims,axiom,
% 5.27/5.63 ! [X4: int,Xa: int,Y: int] :
% 5.27/5.63 ( ( ( bit_se725231765392027082nd_int @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 5.27/5.63 => ~ ( ( ( ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( uminus_uminus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) ) ) ) )
% 5.27/5.63 & ( ~ ( ( member_int @ X4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ Xa @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( plus_plus_int
% 5.27/5.63 @ ( zero_n2684676970156552555ol_int
% 5.27/5.63 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X4 )
% 5.27/5.63 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa ) ) )
% 5.27/5.63 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.27/5.63 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_int.pelims
% 5.27/5.63 thf(fact_9697_lessThan__0,axiom,
% 5.27/5.63 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.27/5.63 = bot_bot_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % lessThan_0
% 5.27/5.63 thf(fact_9698_atLeastLessThan__singleton,axiom,
% 5.27/5.63 ! [M: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.27/5.63 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan_singleton
% 5.27/5.63 thf(fact_9699_atMost__0,axiom,
% 5.27/5.63 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % atMost_0
% 5.27/5.63 thf(fact_9700_bot__enat__def,axiom,
% 5.27/5.63 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.27/5.63
% 5.27/5.63 % bot_enat_def
% 5.27/5.63 thf(fact_9701_bot__nat__def,axiom,
% 5.27/5.63 bot_bot_nat = zero_zero_nat ).
% 5.27/5.63
% 5.27/5.63 % bot_nat_def
% 5.27/5.63 thf(fact_9702_atLeastLessThan0,axiom,
% 5.27/5.63 ! [M: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.27/5.63 = bot_bot_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan0
% 5.27/5.63 thf(fact_9703_lessThan__empty__iff,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ( set_ord_lessThan_nat @ N2 )
% 5.27/5.63 = bot_bot_set_nat )
% 5.27/5.63 = ( N2 = zero_zero_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % lessThan_empty_iff
% 5.27/5.63 thf(fact_9704_atLeastLessThanSuc,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ N2 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N2 ) )
% 5.27/5.63 = bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThanSuc
% 5.27/5.63 thf(fact_9705_atLeast1__lessThan__eq__remove0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.63 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast1_lessThan_eq_remove0
% 5.27/5.63 thf(fact_9706_atLeast1__atMost__eq__remove0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N2 )
% 5.27/5.63 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N2 ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast1_atMost_eq_remove0
% 5.27/5.63 thf(fact_9707_atLeastLessThan__nat__numeral,axiom,
% 5.27/5.63 ! [M: nat,K: num] :
% 5.27/5.63 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.27/5.63 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.27/5.63 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan_nat_numeral
% 5.27/5.63 thf(fact_9708_and__int_Opinduct,axiom,
% 5.27/5.63 ! [A0: int,A12: int,P: int > int > $o] :
% 5.27/5.63 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.27/5.63 => ( ! [K2: int,L4: int] :
% 5.27/5.63 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K2 @ L4 ) )
% 5.27/5.63 => ( ( ~ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.27/5.63 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.27/5.63 => ( P @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 => ( P @ K2 @ L4 ) ) )
% 5.27/5.63 => ( P @ A0 @ A12 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_int.pinduct
% 5.27/5.63 thf(fact_9709_normalize__def,axiom,
% 5.27/5.63 ( normalize
% 5.27/5.63 = ( ^ [P5: product_prod_int_int] :
% 5.27/5.63 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P5 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) )
% 5.27/5.63 @ ( if_Pro3027730157355071871nt_int
% 5.27/5.63 @ ( ( product_snd_int_int @ P5 )
% 5.27/5.63 = zero_zero_int )
% 5.27/5.63 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.27/5.63 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P5 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P5 ) @ ( product_snd_int_int @ P5 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % normalize_def
% 5.27/5.63 thf(fact_9710_gcd__pos__int,axiom,
% 5.27/5.63 ! [M: int,N2: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N2 ) )
% 5.27/5.63 = ( ( M != zero_zero_int )
% 5.27/5.63 | ( N2 != zero_zero_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_pos_int
% 5.27/5.63 thf(fact_9711_gcd__red__int,axiom,
% 5.27/5.63 ( gcd_gcd_int
% 5.27/5.63 = ( ^ [X: int,Y5: int] : ( gcd_gcd_int @ Y5 @ ( modulo_modulo_int @ X @ Y5 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_red_int
% 5.27/5.63 thf(fact_9712_gcd__ge__0__int,axiom,
% 5.27/5.63 ! [X4: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X4 @ Y ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_ge_0_int
% 5.27/5.63 thf(fact_9713_gcd__le1__int,axiom,
% 5.27/5.63 ! [A: int,B: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ A )
% 5.27/5.63 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_le1_int
% 5.27/5.63 thf(fact_9714_gcd__le2__int,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_le2_int
% 5.27/5.63 thf(fact_9715_gcd__cases__int,axiom,
% 5.27/5.63 ! [X4: int,Y: int,P: int > $o] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.63 => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) )
% 5.27/5.63 => ( ( ( ord_less_eq_int @ zero_zero_int @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.27/5.63 => ( P @ ( gcd_gcd_int @ X4 @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.27/5.63 => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 5.27/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.27/5.63 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ Y ) ) ) )
% 5.27/5.63 => ( ( ( ord_less_eq_int @ X4 @ zero_zero_int )
% 5.27/5.63 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.27/5.63 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X4 ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.27/5.63 => ( P @ ( gcd_gcd_int @ X4 @ Y ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_cases_int
% 5.27/5.63 thf(fact_9716_gcd__unique__int,axiom,
% 5.27/5.63 ! [D: int,A: int,B: int] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.27/5.63 & ( dvd_dvd_int @ D @ A )
% 5.27/5.63 & ( dvd_dvd_int @ D @ B )
% 5.27/5.63 & ! [E3: int] :
% 5.27/5.63 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.27/5.63 & ( dvd_dvd_int @ E3 @ B ) )
% 5.27/5.63 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.27/5.63 = ( D
% 5.27/5.63 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_unique_int
% 5.27/5.63 thf(fact_9717_gcd__non__0__int,axiom,
% 5.27/5.63 ! [Y: int,X4: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.27/5.63 => ( ( gcd_gcd_int @ X4 @ Y )
% 5.27/5.63 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X4 @ Y ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_non_0_int
% 5.27/5.63 thf(fact_9718_gcd__code__int,axiom,
% 5.27/5.63 ( gcd_gcd_int
% 5.27/5.63 = ( ^ [K3: int,L2: int] : ( abs_abs_int @ ( if_int @ ( L2 = zero_zero_int ) @ K3 @ ( gcd_gcd_int @ L2 @ ( modulo_modulo_int @ ( abs_abs_int @ K3 ) @ ( abs_abs_int @ L2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_code_int
% 5.27/5.63 thf(fact_9719_gcd__1__nat,axiom,
% 5.27/5.63 ! [M: nat] :
% 5.27/5.63 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.27/5.63 = one_one_nat ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_1_nat
% 5.27/5.63 thf(fact_9720_gcd__Suc__0,axiom,
% 5.27/5.63 ! [M: nat] :
% 5.27/5.63 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.27/5.63 = ( suc @ zero_zero_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_Suc_0
% 5.27/5.63 thf(fact_9721_gcd__pos__nat,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N2 ) )
% 5.27/5.63 = ( ( M != zero_zero_nat )
% 5.27/5.63 | ( N2 != zero_zero_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_pos_nat
% 5.27/5.63 thf(fact_9722_gcd__red__nat,axiom,
% 5.27/5.63 ( gcd_gcd_nat
% 5.27/5.63 = ( ^ [X: nat,Y5: nat] : ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_red_nat
% 5.27/5.63 thf(fact_9723_gcd__le1__nat,axiom,
% 5.27/5.63 ! [A: nat,B: nat] :
% 5.27/5.63 ( ( A != zero_zero_nat )
% 5.27/5.63 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_le1_nat
% 5.27/5.63 thf(fact_9724_gcd__le2__nat,axiom,
% 5.27/5.63 ! [B: nat,A: nat] :
% 5.27/5.63 ( ( B != zero_zero_nat )
% 5.27/5.63 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_le2_nat
% 5.27/5.63 thf(fact_9725_gcd__diff1__nat,axiom,
% 5.27/5.63 ! [N2: nat,M: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ N2 @ M )
% 5.27/5.63 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N2 ) @ N2 )
% 5.27/5.63 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_diff1_nat
% 5.27/5.63 thf(fact_9726_gcd__diff2__nat,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N2 @ M ) @ N2 )
% 5.27/5.63 = ( gcd_gcd_nat @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_diff2_nat
% 5.27/5.63 thf(fact_9727_gcd__non__0__nat,axiom,
% 5.27/5.63 ! [Y: nat,X4: nat] :
% 5.27/5.63 ( ( Y != zero_zero_nat )
% 5.27/5.63 => ( ( gcd_gcd_nat @ X4 @ Y )
% 5.27/5.63 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X4 @ Y ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_non_0_nat
% 5.27/5.63 thf(fact_9728_gcd__nat_Osimps,axiom,
% 5.27/5.63 ( gcd_gcd_nat
% 5.27/5.63 = ( ^ [X: nat,Y5: nat] : ( if_nat @ ( Y5 = zero_zero_nat ) @ X @ ( gcd_gcd_nat @ Y5 @ ( modulo_modulo_nat @ X @ Y5 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_nat.simps
% 5.27/5.63 thf(fact_9729_gcd__nat_Oelims,axiom,
% 5.27/5.63 ! [X4: nat,Xa: nat,Y: nat] :
% 5.27/5.63 ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( Xa = zero_zero_nat )
% 5.27/5.63 => ( Y = X4 ) )
% 5.27/5.63 & ( ( Xa != zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_nat.elims
% 5.27/5.63 thf(fact_9730_bezout__nat,axiom,
% 5.27/5.63 ! [A: nat,B: nat] :
% 5.27/5.63 ( ( A != zero_zero_nat )
% 5.27/5.63 => ? [X5: nat,Y3: nat] :
% 5.27/5.63 ( ( times_times_nat @ A @ X5 )
% 5.27/5.63 = ( plus_plus_nat @ ( times_times_nat @ B @ Y3 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezout_nat
% 5.27/5.63 thf(fact_9731_bezout__gcd__nat_H,axiom,
% 5.27/5.63 ! [B: nat,A: nat] :
% 5.27/5.63 ? [X5: nat,Y3: nat] :
% 5.27/5.63 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y3 ) @ ( times_times_nat @ A @ X5 ) )
% 5.27/5.63 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X5 ) @ ( times_times_nat @ B @ Y3 ) )
% 5.27/5.63 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.27/5.63 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y3 ) @ ( times_times_nat @ B @ X5 ) )
% 5.27/5.63 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X5 ) @ ( times_times_nat @ A @ Y3 ) )
% 5.27/5.63 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % bezout_gcd_nat'
% 5.27/5.63 thf(fact_9732_gcd__code__integer,axiom,
% 5.27/5.63 ( gcd_gcd_Code_integer
% 5.27/5.63 = ( ^ [K3: code_integer,L2: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L2 = zero_z3403309356797280102nteger ) @ K3 @ ( gcd_gcd_Code_integer @ L2 @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K3 ) @ ( abs_abs_Code_integer @ L2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_code_integer
% 5.27/5.63 thf(fact_9733_nat__descend__induct,axiom,
% 5.27/5.63 ! [N2: nat,P: nat > $o,M: nat] :
% 5.27/5.63 ( ! [K2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ N2 @ K2 )
% 5.27/5.63 => ( P @ K2 ) )
% 5.27/5.63 => ( ! [K2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ K2 @ N2 )
% 5.27/5.63 => ( ! [I: nat] :
% 5.27/5.63 ( ( ord_less_nat @ K2 @ I )
% 5.27/5.63 => ( P @ I ) )
% 5.27/5.63 => ( P @ K2 ) ) )
% 5.27/5.63 => ( P @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_descend_induct
% 5.27/5.63 thf(fact_9734_gcd__nat_Opelims,axiom,
% 5.27/5.63 ! [X4: nat,Xa: nat,Y: nat] :
% 5.27/5.63 ( ( ( gcd_gcd_nat @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) )
% 5.27/5.63 => ~ ( ( ( ( Xa = zero_zero_nat )
% 5.27/5.63 => ( Y = X4 ) )
% 5.27/5.63 & ( ( Xa != zero_zero_nat )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( gcd_gcd_nat @ Xa @ ( modulo_modulo_nat @ X4 @ Xa ) ) ) ) )
% 5.27/5.63 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X4 @ Xa ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_nat.pelims
% 5.27/5.63 thf(fact_9735_drop__bit__numeral__minus__bit1,axiom,
% 5.27/5.63 ! [L: num,K: num] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.63 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_numeral_minus_bit1
% 5.27/5.63 thf(fact_9736_finite__enumerate,axiom,
% 5.27/5.63 ! [S2: set_nat] :
% 5.27/5.63 ( ( finite_finite_nat @ S2 )
% 5.27/5.63 => ? [R2: nat > nat] :
% 5.27/5.63 ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 5.27/5.63 & ! [N6: nat] :
% 5.27/5.63 ( ( ord_less_nat @ N6 @ ( finite_card_nat @ S2 ) )
% 5.27/5.63 => ( member_nat @ ( R2 @ N6 ) @ S2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_enumerate
% 5.27/5.63 thf(fact_9737_drop__bit__nonnegative__int__iff,axiom,
% 5.27/5.63 ! [N2: nat,K: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) )
% 5.27/5.63 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_nonnegative_int_iff
% 5.27/5.63 thf(fact_9738_drop__bit__negative__int__iff,axiom,
% 5.27/5.63 ! [N2: nat,K: int] :
% 5.27/5.63 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N2 @ K ) @ zero_zero_int )
% 5.27/5.63 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_negative_int_iff
% 5.27/5.63 thf(fact_9739_drop__bit__minus__one,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ one_one_int ) )
% 5.27/5.63 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_minus_one
% 5.27/5.63 thf(fact_9740_drop__bit__Suc__minus__bit0,axiom,
% 5.27/5.63 ! [N2: nat,K: num] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.63 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_Suc_minus_bit0
% 5.27/5.63 thf(fact_9741_drop__bit__numeral__minus__bit0,axiom,
% 5.27/5.63 ! [L: num,K: num] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.27/5.63 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_numeral_minus_bit0
% 5.27/5.63 thf(fact_9742_drop__bit__Suc__minus__bit1,axiom,
% 5.27/5.63 ! [N2: nat,K: num] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ ( suc @ N2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.27/5.63 = ( bit_se8568078237143864401it_int @ N2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_Suc_minus_bit1
% 5.27/5.63 thf(fact_9743_drop__bit__push__bit__int,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,K: int] :
% 5.27/5.63 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N2 @ K ) )
% 5.27/5.63 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N2 ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N2 @ M ) @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_push_bit_int
% 5.27/5.63 thf(fact_9744_drop__bit__int__def,axiom,
% 5.27/5.63 ( bit_se8568078237143864401it_int
% 5.27/5.63 = ( ^ [N: nat,K3: int] : ( divide_divide_int @ K3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_int_def
% 5.27/5.63 thf(fact_9745_drop__bit__of__Suc__0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( bit_se8570568707652914677it_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.27/5.63 = ( zero_n2687167440665602831ol_nat @ ( N2 = zero_zero_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_of_Suc_0
% 5.27/5.63 thf(fact_9746_drop__bit__nat__eq,axiom,
% 5.27/5.63 ! [N2: nat,K: int] :
% 5.27/5.63 ( ( bit_se8570568707652914677it_nat @ N2 @ ( nat2 @ K ) )
% 5.27/5.63 = ( nat2 @ ( bit_se8568078237143864401it_int @ N2 @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_nat_eq
% 5.27/5.63 thf(fact_9747_drop__bit__nat__def,axiom,
% 5.27/5.63 ( bit_se8570568707652914677it_nat
% 5.27/5.63 = ( ^ [N: nat,M6: nat] : ( divide_divide_nat @ M6 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_bit_nat_def
% 5.27/5.63 thf(fact_9748_card__greaterThanLessThan__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L @ U ) )
% 5.27/5.63 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L @ one_one_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_greaterThanLessThan_int
% 5.27/5.63 thf(fact_9749_finite__greaterThanLessThan__int,axiom,
% 5.27/5.63 ! [L: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_greaterThanLessThan_int
% 5.27/5.63 thf(fact_9750_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.27/5.63 = ( set_or5832277885323065728an_int @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.27/5.63 thf(fact_9751_xor__minus__numerals_I1_J,axiom,
% 5.27/5.63 ! [N2: num,K: int] :
% 5.27/5.63 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) @ K )
% 5.27/5.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N2 @ one ) @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_minus_numerals(1)
% 5.27/5.63 thf(fact_9752_xor__minus__numerals_I2_J,axiom,
% 5.27/5.63 ! [K: int,N2: num] :
% 5.27/5.63 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_minus_numerals(2)
% 5.27/5.63 thf(fact_9753_finite__greaterThanLessThan,axiom,
% 5.27/5.63 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_greaterThanLessThan
% 5.27/5.63 thf(fact_9754_card__greaterThanLessThan,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L @ U ) )
% 5.27/5.63 = ( minus_minus_nat @ U @ ( suc @ L ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_greaterThanLessThan
% 5.27/5.63 thf(fact_9755_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ ( suc @ L ) @ U )
% 5.27/5.63 = ( set_or5834768355832116004an_nat @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastSucLessThan_greaterThanLessThan
% 5.27/5.63 thf(fact_9756_tanh__real__bounds,axiom,
% 5.27/5.63 ! [X4: real] : ( member_real @ ( tanh_real @ X4 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % tanh_real_bounds
% 5.27/5.63 thf(fact_9757_sub__BitM__One__eq,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( neg_numeral_sub_int @ ( bitM @ N2 ) @ one )
% 5.27/5.63 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N2 @ one ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sub_BitM_One_eq
% 5.27/5.63 thf(fact_9758_Suc__funpow,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( compow_nat_nat @ N2 @ suc )
% 5.27/5.63 = ( plus_plus_nat @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Suc_funpow
% 5.27/5.63 thf(fact_9759_nat__of__integer__non__positive,axiom,
% 5.27/5.63 ! [K: code_integer] :
% 5.27/5.63 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.27/5.63 => ( ( code_nat_of_integer @ K )
% 5.27/5.63 = zero_zero_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_of_integer_non_positive
% 5.27/5.63 thf(fact_9760_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.27/5.63 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.27/5.63 @ ^ [X: nat,Y5: nat] : ( ord_less_eq_nat @ Y5 @ X )
% 5.27/5.63 @ ^ [X: nat,Y5: nat] : ( ord_less_nat @ Y5 @ X ) ) ).
% 5.27/5.63
% 5.27/5.63 % max_nat.semilattice_neutr_order_axioms
% 5.27/5.63 thf(fact_9761_nat__of__integer__code__post_I3_J,axiom,
% 5.27/5.63 ! [K: num] :
% 5.27/5.63 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.27/5.63 = ( numeral_numeral_nat @ K ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_of_integer_code_post(3)
% 5.27/5.63 thf(fact_9762_nat__of__integer__code__post_I2_J,axiom,
% 5.27/5.63 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.27/5.63 = one_one_nat ) ).
% 5.27/5.63
% 5.27/5.63 % nat_of_integer_code_post(2)
% 5.27/5.63 thf(fact_9763_nat__of__integer__code,axiom,
% 5.27/5.63 ( code_nat_of_integer
% 5.27/5.63 = ( ^ [K3: code_integer] :
% 5.27/5.63 ( if_nat @ ( ord_le3102999989581377725nteger @ K3 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.27/5.63 @ ( produc1555791787009142072er_nat
% 5.27/5.63 @ ^ [L2: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L2 ) @ ( code_nat_of_integer @ L2 ) ) @ one_one_nat ) )
% 5.27/5.63 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_of_integer_code
% 5.27/5.63 thf(fact_9764_int__of__integer__code,axiom,
% 5.27/5.63 ( code_int_of_integer
% 5.27/5.63 = ( ^ [K3: code_integer] :
% 5.27/5.63 ( if_int @ ( ord_le6747313008572928689nteger @ K3 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K3 ) ) )
% 5.27/5.63 @ ( if_int @ ( K3 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.27/5.63 @ ( produc1553301316500091796er_int
% 5.27/5.63 @ ^ [L2: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L2 ) ) @ one_one_int ) )
% 5.27/5.63 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % int_of_integer_code
% 5.27/5.63 thf(fact_9765_modulo__integer_Orep__eq,axiom,
% 5.27/5.63 ! [X4: code_integer,Xa: code_integer] :
% 5.27/5.63 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X4 @ Xa ) )
% 5.27/5.63 = ( modulo_modulo_int @ ( code_int_of_integer @ X4 ) @ ( code_int_of_integer @ Xa ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % modulo_integer.rep_eq
% 5.27/5.63 thf(fact_9766_integer__less__iff,axiom,
% 5.27/5.63 ( ord_le6747313008572928689nteger
% 5.27/5.63 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % integer_less_iff
% 5.27/5.63 thf(fact_9767_less__integer_Orep__eq,axiom,
% 5.27/5.63 ( ord_le6747313008572928689nteger
% 5.27/5.63 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_integer.rep_eq
% 5.27/5.63 thf(fact_9768_less__eq__integer_Orep__eq,axiom,
% 5.27/5.63 ( ord_le3102999989581377725nteger
% 5.27/5.63 = ( ^ [X: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_eq_integer.rep_eq
% 5.27/5.63 thf(fact_9769_integer__less__eq__iff,axiom,
% 5.27/5.63 ( ord_le3102999989581377725nteger
% 5.27/5.63 = ( ^ [K3: code_integer,L2: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K3 ) @ ( code_int_of_integer @ L2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % integer_less_eq_iff
% 5.27/5.63 thf(fact_9770_times__int_Oabs__eq,axiom,
% 5.27/5.63 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.27/5.63 ( ( times_times_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.27/5.63 = ( abs_Integ
% 5.27/5.63 @ ( produc27273713700761075at_nat
% 5.27/5.63 @ ^ [X: nat,Y5: nat] :
% 5.27/5.63 ( produc2626176000494625587at_nat
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X @ U2 ) @ ( times_times_nat @ Y5 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X @ V4 ) @ ( times_times_nat @ Y5 @ U2 ) ) ) )
% 5.27/5.63 @ Xa
% 5.27/5.63 @ X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % times_int.abs_eq
% 5.27/5.63 thf(fact_9771_one__int__def,axiom,
% 5.27/5.63 ( one_one_int
% 5.27/5.63 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % one_int_def
% 5.27/5.63 thf(fact_9772_less__int_Oabs__eq,axiom,
% 5.27/5.63 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.27/5.63 ( ( ord_less_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.27/5.63 = ( produc8739625826339149834_nat_o
% 5.27/5.63 @ ^ [X: nat,Y5: nat] :
% 5.27/5.63 ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 5.27/5.63 @ Xa
% 5.27/5.63 @ X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_int.abs_eq
% 5.27/5.63 thf(fact_9773_less__eq__int_Oabs__eq,axiom,
% 5.27/5.63 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.27/5.63 ( ( ord_less_eq_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.27/5.63 = ( produc8739625826339149834_nat_o
% 5.27/5.63 @ ^ [X: nat,Y5: nat] :
% 5.27/5.63 ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ U2 @ Y5 ) ) )
% 5.27/5.63 @ Xa
% 5.27/5.63 @ X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_eq_int.abs_eq
% 5.27/5.63 thf(fact_9774_plus__int_Oabs__eq,axiom,
% 5.27/5.63 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.27/5.63 ( ( plus_plus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.27/5.63 = ( abs_Integ
% 5.27/5.63 @ ( produc27273713700761075at_nat
% 5.27/5.63 @ ^ [X: nat,Y5: nat] :
% 5.27/5.63 ( produc2626176000494625587at_nat
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ U2 ) @ ( plus_plus_nat @ Y5 @ V4 ) ) )
% 5.27/5.63 @ Xa
% 5.27/5.63 @ X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % plus_int.abs_eq
% 5.27/5.63 thf(fact_9775_minus__int_Oabs__eq,axiom,
% 5.27/5.63 ! [Xa: product_prod_nat_nat,X4: product_prod_nat_nat] :
% 5.27/5.63 ( ( minus_minus_int @ ( abs_Integ @ Xa ) @ ( abs_Integ @ X4 ) )
% 5.27/5.63 = ( abs_Integ
% 5.27/5.63 @ ( produc27273713700761075at_nat
% 5.27/5.63 @ ^ [X: nat,Y5: nat] :
% 5.27/5.63 ( produc2626176000494625587at_nat
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X @ V4 ) @ ( plus_plus_nat @ Y5 @ U2 ) ) )
% 5.27/5.63 @ Xa
% 5.27/5.63 @ X4 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % minus_int.abs_eq
% 5.27/5.63 thf(fact_9776_num__of__nat_Osimps_I2_J,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( inc @ ( num_of_nat @ N2 ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( num_of_nat @ ( suc @ N2 ) )
% 5.27/5.63 = one ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat.simps(2)
% 5.27/5.63 thf(fact_9777_pred__nat__def,axiom,
% 5.27/5.63 ( pred_nat
% 5.27/5.63 = ( collec3392354462482085612at_nat
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [M6: nat,N: nat] :
% 5.27/5.63 ( N
% 5.27/5.63 = ( suc @ M6 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % pred_nat_def
% 5.27/5.63 thf(fact_9778_num__of__nat__numeral__eq,axiom,
% 5.27/5.63 ! [Q3: num] :
% 5.27/5.63 ( ( num_of_nat @ ( numeral_numeral_nat @ Q3 ) )
% 5.27/5.63 = Q3 ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat_numeral_eq
% 5.27/5.63 thf(fact_9779_num__of__nat_Osimps_I1_J,axiom,
% 5.27/5.63 ( ( num_of_nat @ zero_zero_nat )
% 5.27/5.63 = one ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat.simps(1)
% 5.27/5.63 thf(fact_9780_numeral__num__of__nat,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( numeral_numeral_nat @ ( num_of_nat @ N2 ) )
% 5.27/5.63 = N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % numeral_num_of_nat
% 5.27/5.63 thf(fact_9781_num__of__nat__One,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ N2 @ one_one_nat )
% 5.27/5.63 => ( ( num_of_nat @ N2 )
% 5.27/5.63 = one ) ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat_One
% 5.27/5.63 thf(fact_9782_num__of__nat__double,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( num_of_nat @ ( plus_plus_nat @ N2 @ N2 ) )
% 5.27/5.63 = ( bit0 @ ( num_of_nat @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat_double
% 5.27/5.63 thf(fact_9783_num__of__nat__plus__distrib,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.27/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N2 ) )
% 5.27/5.63 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N2 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_nat_plus_distrib
% 5.27/5.63 thf(fact_9784_less__eq__int_Orep__eq,axiom,
% 5.27/5.63 ( ord_less_eq_int
% 5.27/5.63 = ( ^ [X: int,Xa4: int] :
% 5.27/5.63 ( produc8739625826339149834_nat_o
% 5.27/5.63 @ ^ [Y5: nat,Z5: nat] :
% 5.27/5.63 ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.27/5.63 @ ( rep_Integ @ X )
% 5.27/5.63 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_eq_int.rep_eq
% 5.27/5.63 thf(fact_9785_less__int_Orep__eq,axiom,
% 5.27/5.63 ( ord_less_int
% 5.27/5.63 = ( ^ [X: int,Xa4: int] :
% 5.27/5.63 ( produc8739625826339149834_nat_o
% 5.27/5.63 @ ^ [Y5: nat,Z5: nat] :
% 5.27/5.63 ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y5 @ V4 ) @ ( plus_plus_nat @ U2 @ Z5 ) ) )
% 5.27/5.63 @ ( rep_Integ @ X )
% 5.27/5.63 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_int.rep_eq
% 5.27/5.63 thf(fact_9786_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.63 ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( Xa = one_one_nat ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X5: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.elims(3)
% 5.27/5.63 thf(fact_9787_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.63 ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( Xa != one_one_nat ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ~ ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X2: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.elims(2)
% 5.27/5.63 thf(fact_9788_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.63 ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( Xa != one_one_nat ) ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( ~ ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.elims(1)
% 5.27/5.63 thf(fact_9789_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.27/5.63 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.27/5.63 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 5.27/5.63 = ( ( Deg = Deg4 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.simps(2)
% 5.27/5.63 thf(fact_9790_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat,Y: $o] :
% 5.27/5.63 ( ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.63 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( Xa = one_one_nat ) )
% 5.27/5.63 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) ) ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) )
% 5.27/5.63 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.pelims(1)
% 5.27/5.63 thf(fact_9791_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.63 ( ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.63 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.27/5.63 => ( Xa != one_one_nat ) ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 5.27/5.63 => ~ ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X2: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X2 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.pelims(2)
% 5.27/5.63 thf(fact_9792_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.27/5.63 ! [X4: vEBT_VEBT,Xa: nat] :
% 5.27/5.63 ( ~ ( vEBT_VEBT_valid @ X4 @ Xa )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X4 @ Xa ) )
% 5.27/5.63 => ( ! [Uu2: $o,Uv2: $o] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa ) )
% 5.27/5.63 => ( Xa = one_one_nat ) ) )
% 5.27/5.63 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary3: vEBT_VEBT] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) )
% 5.27/5.63 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary3 ) @ Xa ) )
% 5.27/5.63 => ( ( Deg2 = Xa )
% 5.27/5.63 & ! [X5: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X5 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ( vEBT_VEBT_valid @ X5 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( vEBT_VEBT_valid @ Summary3 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.27/5.63 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 & ( case_o184042715313410164at_nat
% 5.27/5.63 @ ( ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X3 )
% 5.27/5.63 & ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 @ ( produc6081775807080527818_nat_o
% 5.27/5.63 @ ^ [Mi2: nat,Ma2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.27/5.63 & ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 & ! [I3: nat] :
% 5.27/5.63 ( ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( ( ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I3 ) @ X3 ) )
% 5.27/5.63 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I3 ) ) )
% 5.27/5.63 & ( ( Mi2 = Ma2 )
% 5.27/5.63 => ! [X: vEBT_VEBT] :
% 5.27/5.63 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.27/5.63 => ~ ? [X3: nat] : ( vEBT_V8194947554948674370ptions @ X @ X3 ) ) )
% 5.27/5.63 & ( ( Mi2 != Ma2 )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma2 )
% 5.27/5.63 & ! [X: nat] :
% 5.27/5.63 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.27/5.63 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X )
% 5.27/5.63 => ( ( ord_less_nat @ Mi2 @ X )
% 5.27/5.63 & ( ord_less_eq_nat @ X @ Ma2 ) ) ) ) ) ) ) )
% 5.27/5.63 @ Mima ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % VEBT_internal.valid'.pelims(3)
% 5.27/5.63 thf(fact_9793_Sup__int__def,axiom,
% 5.27/5.63 ( complete_Sup_Sup_int
% 5.27/5.63 = ( ^ [X3: set_int] :
% 5.27/5.63 ( the_int
% 5.27/5.63 @ ^ [X: int] :
% 5.27/5.63 ( ( member_int @ X @ X3 )
% 5.27/5.63 & ! [Y5: int] :
% 5.27/5.63 ( ( member_int @ Y5 @ X3 )
% 5.27/5.63 => ( ord_less_eq_int @ Y5 @ X ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Sup_int_def
% 5.27/5.63 thf(fact_9794_take__bit__numeral__minus__numeral__int,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int
% 5.27/5.63 @ ^ [Q5: 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 @ Q5 ) ) )
% 5.27/5.63 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_numeral_minus_numeral_int
% 5.27/5.63 thf(fact_9795_and__minus__numerals_I7_J,axiom,
% 5.27/5.63 ! [N2: num,M: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_minus_numerals(7)
% 5.27/5.63 thf(fact_9796_take__bit__num__simps_I1_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(1)
% 5.27/5.63 thf(fact_9797_take__bit__num__simps_I2_J,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( suc @ N2 ) @ one )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(2)
% 5.27/5.63 thf(fact_9798_take__bit__num__simps_I5_J,axiom,
% 5.27/5.63 ! [R3: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ one )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(5)
% 5.27/5.63 thf(fact_9799_take__bit__num__simps_I3_J,axiom,
% 5.27/5.63 ! [N2: nat,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit0 @ M ) )
% 5.27/5.63 = ( case_o6005452278849405969um_num @ none_num
% 5.27/5.63 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.27/5.63 @ ( bit_take_bit_num @ N2 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(3)
% 5.27/5.63 thf(fact_9800_take__bit__num__simps_I4_J,axiom,
% 5.27/5.63 ! [N2: nat,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( suc @ N2 ) @ ( bit1 @ M ) )
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(4)
% 5.27/5.63 thf(fact_9801_take__bit__num__simps_I6_J,axiom,
% 5.27/5.63 ! [R3: num,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit0 @ M ) )
% 5.27/5.63 = ( case_o6005452278849405969um_num @ none_num
% 5.27/5.63 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.27/5.63 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(6)
% 5.27/5.63 thf(fact_9802_take__bit__num__simps_I7_J,axiom,
% 5.27/5.63 ! [R3: num,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R3 ) @ ( bit1 @ M ) )
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R3 ) @ M ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_simps(7)
% 5.27/5.63 thf(fact_9803_and__minus__numerals_I8_J,axiom,
% 5.27/5.63 ! [N2: num,M: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_minus_numerals(8)
% 5.27/5.63 thf(fact_9804_and__minus__numerals_I4_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N2 ) ) ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_minus_numerals(4)
% 5.27/5.63 thf(fact_9805_and__minus__numerals_I3_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N2 ) ) ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_minus_numerals(3)
% 5.27/5.63 thf(fact_9806_and__not__num_Osimps_I1_J,axiom,
% 5.27/5.63 ( ( bit_and_not_num @ one @ one )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(1)
% 5.27/5.63 thf(fact_9807_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.27/5.63 ! [N2: nat,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ N2 @ ( bit0 @ M ) )
% 5.27/5.63 = ( case_nat_option_num @ none_num
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( case_o6005452278849405969um_num @ none_num
% 5.27/5.63 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.27/5.63 @ ( bit_take_bit_num @ N @ M ) )
% 5.27/5.63 @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.27/5.63 thf(fact_9808_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( bit_take_bit_num @ N2 @ one )
% 5.27/5.63 = ( case_nat_option_num @ none_num
% 5.27/5.63 @ ^ [N: nat] : ( some_num @ one )
% 5.27/5.63 @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.27/5.63 thf(fact_9809_and__not__num_Osimps_I2_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ one @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(2)
% 5.27/5.63 thf(fact_9810_and__not__num_Osimps_I4_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.27/5.63 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(4)
% 5.27/5.63 thf(fact_9811_GreatestI__ex__nat,axiom,
% 5.27/5.63 ! [P: nat > $o,B: nat] :
% 5.27/5.63 ( ? [X_1: nat] : ( P @ X_1 )
% 5.27/5.63 => ( ! [Y3: nat] :
% 5.27/5.63 ( ( P @ Y3 )
% 5.27/5.63 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.27/5.63 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % GreatestI_ex_nat
% 5.27/5.63 thf(fact_9812_Greatest__le__nat,axiom,
% 5.27/5.63 ! [P: nat > $o,K: nat,B: nat] :
% 5.27/5.63 ( ( P @ K )
% 5.27/5.63 => ( ! [Y3: nat] :
% 5.27/5.63 ( ( P @ Y3 )
% 5.27/5.63 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.27/5.63 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Greatest_le_nat
% 5.27/5.63 thf(fact_9813_GreatestI__nat,axiom,
% 5.27/5.63 ! [P: nat > $o,K: nat,B: nat] :
% 5.27/5.63 ( ( P @ K )
% 5.27/5.63 => ( ! [Y3: nat] :
% 5.27/5.63 ( ( P @ Y3 )
% 5.27/5.63 => ( ord_less_eq_nat @ Y3 @ B ) )
% 5.27/5.63 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % GreatestI_nat
% 5.27/5.63 thf(fact_9814_and__not__num_Osimps_I3_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ one @ ( bit1 @ N2 ) )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(3)
% 5.27/5.63 thf(fact_9815_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.27/5.63 ! [N2: nat,M: num] :
% 5.27/5.63 ( ( bit_take_bit_num @ N2 @ ( bit1 @ M ) )
% 5.27/5.63 = ( case_nat_option_num @ none_num
% 5.27/5.63 @ ^ [N: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) )
% 5.27/5.63 @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.27/5.63 thf(fact_9816_and__not__num_Osimps_I7_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.27/5.63 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(7)
% 5.27/5.63 thf(fact_9817_and__not__num__eq__Some__iff,axiom,
% 5.27/5.63 ! [M: num,N2: num,Q3: num] :
% 5.27/5.63 ( ( ( bit_and_not_num @ M @ N2 )
% 5.27/5.63 = ( some_num @ Q3 ) )
% 5.27/5.63 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( numeral_numeral_int @ Q3 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num_eq_Some_iff
% 5.27/5.63 thf(fact_9818_and__not__num_Osimps_I8_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(8)
% 5.27/5.63 thf(fact_9819_and__not__num__eq__None__iff,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( bit_and_not_num @ M @ N2 )
% 5.27/5.63 = none_num )
% 5.27/5.63 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = zero_zero_int ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num_eq_None_iff
% 5.27/5.63 thf(fact_9820_int__numeral__not__and__num,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N2 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % int_numeral_not_and_num
% 5.27/5.63 thf(fact_9821_int__numeral__and__not__num,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % int_numeral_and_not_num
% 5.27/5.63 thf(fact_9822_take__bit__num__def,axiom,
% 5.27/5.63 ( bit_take_bit_num
% 5.27/5.63 = ( ^ [N: nat,M6: num] :
% 5.27/5.63 ( if_option_num
% 5.27/5.63 @ ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) )
% 5.27/5.63 = zero_zero_nat )
% 5.27/5.63 @ none_num
% 5.27/5.63 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ M6 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_num_def
% 5.27/5.63 thf(fact_9823_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.27/5.63 ! [N2: nat,J: nat,I2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ ( suc @ I2 ) ) )
% 5.27/5.63 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) ) @ N2 )
% 5.27/5.63 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nth_sorted_list_of_set_greaterThanLessThan
% 5.27/5.63 thf(fact_9824_and__not__num_Oelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_and_not_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y != none_num ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ? [N3: num] :
% 5.27/5.63 ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ one ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ? [N3: num] :
% 5.27/5.63 ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y != none_num ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.elims
% 5.27/5.63 thf(fact_9825_Bit__Operations_Otake__bit__num__code,axiom,
% 5.27/5.63 ( bit_take_bit_num
% 5.27/5.63 = ( ^ [N: nat,M6: num] :
% 5.27/5.63 ( produc478579273971653890on_num
% 5.27/5.63 @ ^ [A3: nat,X: num] :
% 5.27/5.63 ( case_nat_option_num @ none_num
% 5.27/5.63 @ ^ [O: nat] :
% 5.27/5.63 ( case_num_option_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [P5: num] :
% 5.27/5.63 ( case_o6005452278849405969um_num @ none_num
% 5.27/5.63 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.27/5.63 @ ( bit_take_bit_num @ O @ P5 ) )
% 5.27/5.63 @ ^ [P5: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P5 ) ) )
% 5.27/5.63 @ X )
% 5.27/5.63 @ A3 )
% 5.27/5.63 @ ( product_Pair_nat_num @ N @ M6 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Bit_Operations.take_bit_num_code
% 5.27/5.63 thf(fact_9826_and__not__num_Osimps_I5_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(5)
% 5.27/5.63 thf(fact_9827_and__not__num_Osimps_I9_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(9)
% 5.27/5.63 thf(fact_9828_and__not__num_Osimps_I6_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_and_not_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.simps(6)
% 5.27/5.63 thf(fact_9829_and__not__num_Opelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_and_not_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y = none_num )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ one ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y = none_num )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_and_not_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_and_not_num_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_not_num.pelims
% 5.27/5.63 thf(fact_9830_and__num_Oelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ one ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ? [N3: num] :
% 5.27/5.63 ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y != none_num ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ? [N3: num] :
% 5.27/5.63 ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ one ) ) ) )
% 5.27/5.63 => ( ( ? [M5: num] :
% 5.27/5.63 ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y != none_num ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ( ? [M5: num] :
% 5.27/5.63 ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ one ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.elims
% 5.27/5.63 thf(fact_9831_xor__num_Oelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y != none_num ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit1 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit0 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit1 @ M5 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( bit0 @ M5 ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( Y
% 5.27/5.63 != ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.elims
% 5.27/5.63 thf(fact_9832_and__num_Osimps_I1_J,axiom,
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ one @ one )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(1)
% 5.27/5.63 thf(fact_9833_xor__num_Osimps_I1_J,axiom,
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ one @ one )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(1)
% 5.27/5.63 thf(fact_9834_and__num_Osimps_I5_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(5)
% 5.27/5.63 thf(fact_9835_xor__num_Osimps_I5_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(5)
% 5.27/5.63 thf(fact_9836_and__num_Osimps_I7_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ one )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(7)
% 5.27/5.63 thf(fact_9837_and__num_Osimps_I3_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ one @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( some_num @ one ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(3)
% 5.27/5.63 thf(fact_9838_and__num_Osimps_I4_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ one )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(4)
% 5.27/5.63 thf(fact_9839_and__num_Osimps_I2_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ one @ ( bit0 @ N2 ) )
% 5.27/5.63 = none_num ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(2)
% 5.27/5.63 thf(fact_9840_xor__num_Osimps_I9_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(9)
% 5.27/5.63 thf(fact_9841_and__num_Osimps_I6_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(6)
% 5.27/5.63 thf(fact_9842_and__num_Osimps_I8_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(8)
% 5.27/5.63 thf(fact_9843_xor__num_Osimps_I7_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ one )
% 5.27/5.63 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(7)
% 5.27/5.63 thf(fact_9844_xor__num_Osimps_I4_J,axiom,
% 5.27/5.63 ! [M: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ one )
% 5.27/5.63 = ( some_num @ ( bit1 @ M ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(4)
% 5.27/5.63 thf(fact_9845_xor__num_Osimps_I3_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ one @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( some_num @ ( bit0 @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(3)
% 5.27/5.63 thf(fact_9846_xor__num_Osimps_I2_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ one @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( some_num @ ( bit1 @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(2)
% 5.27/5.63 thf(fact_9847_and__num_Osimps_I9_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un7362597486090784418nd_num @ ( bit1 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_un7362597486090784418nd_num @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.simps(9)
% 5.27/5.63 thf(fact_9848_xor__num_Osimps_I8_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit1 @ M ) @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(8)
% 5.27/5.63 thf(fact_9849_xor__num_Osimps_I6_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( bit_un2480387367778600638or_num @ ( bit0 @ M ) @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.simps(6)
% 5.27/5.63 thf(fact_9850_and__num_Opelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_un7362597486090784418nd_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ one ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y = none_num )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ one ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y = none_num )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ one ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.27/5.63 @ ^ [N10: num] : ( some_num @ ( bit1 @ N10 ) )
% 5.27/5.63 @ ( bit_un7362597486090784418nd_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un4731106466462545111um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % and_num.pelims
% 5.27/5.63 thf(fact_9851_xor__num_Opelims,axiom,
% 5.27/5.63 ! [X4: num,Xa: num,Y: option_num] :
% 5.27/5.63 ( ( ( bit_un2480387367778600638or_num @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ X4 @ Xa ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y = none_num )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit1 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ( ( X4 = one )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit0 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit1 @ M5 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit0 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit0 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ( ( Xa = one )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( bit0 @ M5 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ one ) ) ) ) )
% 5.27/5.63 => ( ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit0 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit0 @ N3 ) ) ) ) ) )
% 5.27/5.63 => ~ ! [M5: num] :
% 5.27/5.63 ( ( X4
% 5.27/5.63 = ( bit1 @ M5 ) )
% 5.27/5.63 => ! [N3: num] :
% 5.27/5.63 ( ( Xa
% 5.27/5.63 = ( bit1 @ N3 ) )
% 5.27/5.63 => ( ( Y
% 5.27/5.63 = ( map_option_num_num @ bit0 @ ( bit_un2480387367778600638or_num @ M5 @ N3 ) ) )
% 5.27/5.63 => ~ ( accp_P3113834385874906142um_num @ bit_un2901131394128224187um_rel @ ( product_Pair_num_num @ ( bit1 @ M5 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % xor_num.pelims
% 5.27/5.63 thf(fact_9852_xor__num__dict,axiom,
% 5.27/5.63 bit_un2480387367778600638or_num = bit_un6178654185764691216or_num ).
% 5.27/5.63
% 5.27/5.63 % xor_num_dict
% 5.27/5.63 thf(fact_9853_and__num__rel__dict,axiom,
% 5.27/5.63 bit_un4731106466462545111um_rel = bit_un5425074673868309765um_rel ).
% 5.27/5.63
% 5.27/5.63 % and_num_rel_dict
% 5.27/5.63 thf(fact_9854_xor__num__rel__dict,axiom,
% 5.27/5.63 bit_un2901131394128224187um_rel = bit_un3595099601533988841um_rel ).
% 5.27/5.63
% 5.27/5.63 % xor_num_rel_dict
% 5.27/5.63 thf(fact_9855_and__num__dict,axiom,
% 5.27/5.63 bit_un7362597486090784418nd_num = bit_un1837492267222099188nd_num ).
% 5.27/5.63
% 5.27/5.63 % and_num_dict
% 5.27/5.63 thf(fact_9856_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.27/5.63 ! [N2: nat,J: nat,I2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ N2 @ ( minus_minus_nat @ J @ I2 ) )
% 5.27/5.63 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) ) @ N2 )
% 5.27/5.63 = ( suc @ ( plus_plus_nat @ I2 @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nth_sorted_list_of_set_greaterThanAtMost
% 5.27/5.63 thf(fact_9857_pow_Osimps_I3_J,axiom,
% 5.27/5.63 ! [X4: num,Y: num] :
% 5.27/5.63 ( ( pow @ X4 @ ( bit1 @ Y ) )
% 5.27/5.63 = ( times_times_num @ ( sqr @ ( pow @ X4 @ Y ) ) @ X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % pow.simps(3)
% 5.27/5.63 thf(fact_9858_finite__greaterThanAtMost,axiom,
% 5.27/5.63 ! [L: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_greaterThanAtMost
% 5.27/5.63 thf(fact_9859_card__greaterThanAtMost,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L @ U ) )
% 5.27/5.63 = ( minus_minus_nat @ U @ L ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_greaterThanAtMost
% 5.27/5.63 thf(fact_9860_sqr_Osimps_I2_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( sqr @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( bit0 @ ( bit0 @ ( sqr @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sqr.simps(2)
% 5.27/5.63 thf(fact_9861_sqr_Osimps_I1_J,axiom,
% 5.27/5.63 ( ( sqr @ one )
% 5.27/5.63 = one ) ).
% 5.27/5.63
% 5.27/5.63 % sqr.simps(1)
% 5.27/5.63 thf(fact_9862_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.27/5.63 ! [L: nat,U: nat] :
% 5.27/5.63 ( ( set_or1269000886237332187st_nat @ ( suc @ L ) @ U )
% 5.27/5.63 = ( set_or6659071591806873216st_nat @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastSucAtMost_greaterThanAtMost
% 5.27/5.63 thf(fact_9863_sqr__conv__mult,axiom,
% 5.27/5.63 ( sqr
% 5.27/5.63 = ( ^ [X: num] : ( times_times_num @ X @ X ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sqr_conv_mult
% 5.27/5.63 thf(fact_9864_pow_Osimps_I2_J,axiom,
% 5.27/5.63 ! [X4: num,Y: num] :
% 5.27/5.63 ( ( pow @ X4 @ ( bit0 @ Y ) )
% 5.27/5.63 = ( sqr @ ( pow @ X4 @ Y ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % pow.simps(2)
% 5.27/5.63 thf(fact_9865_sqr_Osimps_I3_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( sqr @ ( bit1 @ N2 ) )
% 5.27/5.63 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N2 ) @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sqr.simps(3)
% 5.27/5.63 thf(fact_9866_integer__of__num__triv_I2_J,axiom,
% 5.27/5.63 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.27/5.63 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % integer_of_num_triv(2)
% 5.27/5.63 thf(fact_9867_finite__greaterThanAtMost__int,axiom,
% 5.27/5.63 ! [L: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_greaterThanAtMost_int
% 5.27/5.63 thf(fact_9868_card__greaterThanAtMost__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L @ U ) )
% 5.27/5.63 = ( nat2 @ ( minus_minus_int @ U @ L ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_greaterThanAtMost_int
% 5.27/5.63 thf(fact_9869_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L @ one_one_int ) @ U )
% 5.27/5.63 = ( set_or6656581121297822940st_int @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.27/5.63 thf(fact_9870_integer__of__num__triv_I1_J,axiom,
% 5.27/5.63 ( ( code_integer_of_num @ one )
% 5.27/5.63 = one_one_Code_integer ) ).
% 5.27/5.63
% 5.27/5.63 % integer_of_num_triv(1)
% 5.27/5.63 thf(fact_9871_integer__of__num_I2_J,axiom,
% 5.27/5.63 ! [N2: num] :
% 5.27/5.63 ( ( code_integer_of_num @ ( bit0 @ N2 ) )
% 5.27/5.63 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N2 ) @ ( code_integer_of_num @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % integer_of_num(2)
% 5.27/5.63 thf(fact_9872_Rats__eq__int__div__nat,axiom,
% 5.27/5.63 ( field_5140801741446780682s_real
% 5.27/5.63 = ( collect_real
% 5.27/5.63 @ ^ [Uu3: real] :
% 5.27/5.63 ? [I3: int,N: nat] :
% 5.27/5.63 ( ( Uu3
% 5.27/5.63 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.27/5.63 & ( N != zero_zero_nat ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_eq_int_div_nat
% 5.27/5.63 thf(fact_9873_image__minus__const__atLeastLessThan__nat,axiom,
% 5.27/5.63 ! [C: nat,Y: nat,X4: nat] :
% 5.27/5.63 ( ( ( ord_less_nat @ C @ Y )
% 5.27/5.63 => ( ( image_nat_nat
% 5.27/5.63 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.27/5.63 @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 5.27/5.63 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X4 @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_nat @ C @ Y )
% 5.27/5.63 => ( ( ( ord_less_nat @ X4 @ Y )
% 5.27/5.63 => ( ( image_nat_nat
% 5.27/5.63 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.27/5.63 @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.27/5.63 & ( ~ ( ord_less_nat @ X4 @ Y )
% 5.27/5.63 => ( ( image_nat_nat
% 5.27/5.63 @ ^ [I3: nat] : ( minus_minus_nat @ I3 @ C )
% 5.27/5.63 @ ( set_or4665077453230672383an_nat @ X4 @ Y ) )
% 5.27/5.63 = bot_bot_set_nat ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_minus_const_atLeastLessThan_nat
% 5.27/5.63 thf(fact_9874_bij__betw__Suc,axiom,
% 5.27/5.63 ! [M7: set_nat,N4: set_nat] :
% 5.27/5.63 ( ( bij_betw_nat_nat @ suc @ M7 @ N4 )
% 5.27/5.63 = ( ( image_nat_nat @ suc @ M7 )
% 5.27/5.63 = N4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % bij_betw_Suc
% 5.27/5.63 thf(fact_9875_Rats__abs__iff,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( member_real @ ( abs_abs_real @ X4 ) @ field_5140801741446780682s_real )
% 5.27/5.63 = ( member_real @ X4 @ field_5140801741446780682s_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_abs_iff
% 5.27/5.63 thf(fact_9876_image__Suc__atLeastAtMost,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I2 @ J ) )
% 5.27/5.63 = ( set_or1269000886237332187st_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_Suc_atLeastAtMost
% 5.27/5.63 thf(fact_9877_image__Suc__atLeastLessThan,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I2 @ J ) )
% 5.27/5.63 = ( set_or4665077453230672383an_nat @ ( suc @ I2 ) @ ( suc @ J ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_Suc_atLeastLessThan
% 5.27/5.63 thf(fact_9878_Rats__dense__in__real,axiom,
% 5.27/5.63 ! [X4: real,Y: real] :
% 5.27/5.63 ( ( ord_less_real @ X4 @ Y )
% 5.27/5.63 => ? [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.27/5.63 & ( ord_less_real @ X4 @ X5 )
% 5.27/5.63 & ( ord_less_real @ X5 @ Y ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_dense_in_real
% 5.27/5.63 thf(fact_9879_Rats__no__bot__less,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ? [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.27/5.63 & ( ord_less_real @ X5 @ X4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_no_bot_less
% 5.27/5.63 thf(fact_9880_Rats__no__top__le,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ? [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ field_5140801741446780682s_real )
% 5.27/5.63 & ( ord_less_eq_real @ X4 @ X5 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_no_top_le
% 5.27/5.63 thf(fact_9881_zero__notin__Suc__image,axiom,
% 5.27/5.63 ! [A2: set_nat] :
% 5.27/5.63 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % zero_notin_Suc_image
% 5.27/5.63 thf(fact_9882_image__Suc__lessThan,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 = ( set_or1269000886237332187st_nat @ one_one_nat @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_Suc_lessThan
% 5.27/5.63 thf(fact_9883_image__Suc__atMost,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) )
% 5.27/5.63 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_Suc_atMost
% 5.27/5.63 thf(fact_9884_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast0_atMost_Suc_eq_insert_0
% 5.27/5.63 thf(fact_9885_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast0_lessThan_Suc_eq_insert_0
% 5.27/5.63 thf(fact_9886_lessThan__Suc__eq__insert__0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_ord_lessThan_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % lessThan_Suc_eq_insert_0
% 5.27/5.63 thf(fact_9887_atMost__Suc__eq__insert__0,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( set_ord_atMost_nat @ ( suc @ N2 ) )
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atMost_Suc_eq_insert_0
% 5.27/5.63 thf(fact_9888_Rats__eq__int__div__int,axiom,
% 5.27/5.63 ( field_5140801741446780682s_real
% 5.27/5.63 = ( collect_real
% 5.27/5.63 @ ^ [Uu3: real] :
% 5.27/5.63 ? [I3: int,J3: int] :
% 5.27/5.63 ( ( Uu3
% 5.27/5.63 = ( divide_divide_real @ ( ring_1_of_int_real @ I3 ) @ ( ring_1_of_int_real @ J3 ) ) )
% 5.27/5.63 & ( J3 != zero_zero_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rats_eq_int_div_int
% 5.27/5.63 thf(fact_9889_Inf__real__def,axiom,
% 5.27/5.63 ( comple4887499456419720421f_real
% 5.27/5.63 = ( ^ [X3: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X3 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Inf_real_def
% 5.27/5.63 thf(fact_9890_finite__int__iff__bounded__le,axiom,
% 5.27/5.63 ( finite_finite_int
% 5.27/5.63 = ( ^ [S5: set_int] :
% 5.27/5.63 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_atMost_int @ K3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_int_iff_bounded_le
% 5.27/5.63 thf(fact_9891_finite__int__iff__bounded,axiom,
% 5.27/5.63 ( finite_finite_int
% 5.27/5.63 = ( ^ [S5: set_int] :
% 5.27/5.63 ? [K3: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S5 ) @ ( set_ord_lessThan_int @ K3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % finite_int_iff_bounded
% 5.27/5.63 thf(fact_9892_image__int__atLeastAtMost,axiom,
% 5.27/5.63 ! [A: nat,B: nat] :
% 5.27/5.63 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.27/5.63 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_int_atLeastAtMost
% 5.27/5.63 thf(fact_9893_image__int__atLeastLessThan,axiom,
% 5.27/5.63 ! [A: nat,B: nat] :
% 5.27/5.63 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.27/5.63 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_int_atLeastLessThan
% 5.27/5.63 thf(fact_9894_image__add__int__atLeastLessThan,axiom,
% 5.27/5.63 ! [L: int,U: int] :
% 5.27/5.63 ( ( image_int_int
% 5.27/5.63 @ ^ [X: int] : ( plus_plus_int @ X @ L )
% 5.27/5.63 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L ) ) )
% 5.27/5.63 = ( set_or4662586982721622107an_int @ L @ U ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_add_int_atLeastLessThan
% 5.27/5.63 thf(fact_9895_image__atLeastZeroLessThan__int,axiom,
% 5.27/5.63 ! [U: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.27/5.63 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.27/5.63 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % image_atLeastZeroLessThan_int
% 5.27/5.63 thf(fact_9896_suminf__eq__SUP__real,axiom,
% 5.27/5.63 ! [X8: nat > real] :
% 5.27/5.63 ( ( summable_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 5.27/5.63 => ( ( suminf_real @ X8 )
% 5.27/5.63 = ( comple1385675409528146559p_real
% 5.27/5.63 @ ( image_nat_real
% 5.27/5.63 @ ^ [I3: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I3 ) )
% 5.27/5.63 @ top_top_set_nat ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % suminf_eq_SUP_real
% 5.27/5.63 thf(fact_9897_UN__atMost__UNIV,axiom,
% 5.27/5.63 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.27/5.63 = top_top_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % UN_atMost_UNIV
% 5.27/5.63 thf(fact_9898_UN__lessThan__UNIV,axiom,
% 5.27/5.63 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.27/5.63 = top_top_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % UN_lessThan_UNIV
% 5.27/5.63 thf(fact_9899_range__mod,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( image_nat_nat
% 5.27/5.63 @ ^ [M6: nat] : ( modulo_modulo_nat @ M6 @ N2 )
% 5.27/5.63 @ top_top_set_nat )
% 5.27/5.63 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % range_mod
% 5.27/5.63 thf(fact_9900_UNIV__nat__eq,axiom,
% 5.27/5.63 ( top_top_set_nat
% 5.27/5.63 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % UNIV_nat_eq
% 5.27/5.63 thf(fact_9901_card__UNIV__unit,axiom,
% 5.27/5.63 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.27/5.63 = one_one_nat ) ).
% 5.27/5.63
% 5.27/5.63 % card_UNIV_unit
% 5.27/5.63 thf(fact_9902_card__UNIV__bool,axiom,
% 5.27/5.63 ( ( finite_card_o @ top_top_set_o )
% 5.27/5.63 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_UNIV_bool
% 5.27/5.63 thf(fact_9903_root__def,axiom,
% 5.27/5.63 ( root
% 5.27/5.63 = ( ^ [N: nat,X: real] :
% 5.27/5.63 ( if_real @ ( N = zero_zero_nat ) @ zero_zero_real
% 5.27/5.63 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.27/5.63 @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N ) )
% 5.27/5.63 @ X ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % root_def
% 5.27/5.63 thf(fact_9904_card__UNIV__char,axiom,
% 5.27/5.63 ( ( finite_card_char @ top_top_set_char )
% 5.27/5.63 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_UNIV_char
% 5.27/5.63 thf(fact_9905_DERIV__even__real__root,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_even_real_root
% 5.27/5.63 thf(fact_9906_MVT2,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,F4: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ? [Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 & ( ord_less_real @ Z2 @ B )
% 5.27/5.63 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.27/5.63 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F4 @ Z2 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % MVT2
% 5.27/5.63 thf(fact_9907_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_eq_real @ zero_zero_real @ Y4 ) ) ) )
% 5.27/5.63 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_nonneg_imp_nondecreasing
% 5.27/5.63 thf(fact_9908_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_eq_real @ Y4 @ zero_zero_real ) ) ) )
% 5.27/5.63 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_nonpos_imp_nonincreasing
% 5.27/5.63 thf(fact_9909_DERIV__neg__imp__decreasing,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.27/5.63 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_neg_imp_decreasing
% 5.27/5.63 thf(fact_9910_DERIV__pos__imp__increasing,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.27/5.63 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pos_imp_increasing
% 5.27/5.63 thf(fact_9911_deriv__nonneg__imp__mono,axiom,
% 5.27/5.63 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.27/5.63 ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.27/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X5 ) ) )
% 5.27/5.63 => ( ( ord_less_eq_real @ A @ B )
% 5.27/5.63 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % deriv_nonneg_imp_mono
% 5.27/5.63 thf(fact_9912_DERIV__isconst3,axiom,
% 5.27/5.63 ! [A: real,B: real,X4: real,Y: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( member_real @ X4 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ( F @ X4 )
% 5.27/5.63 = ( F @ Y ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_isconst3
% 5.27/5.63 thf(fact_9913_DERIV__local__const,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,D: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.27/5.63 => ( ! [Y3: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 5.27/5.63 => ( ( F @ X4 )
% 5.27/5.63 = ( F @ Y3 ) ) )
% 5.27/5.63 => ( L = zero_zero_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_local_const
% 5.27/5.63 thf(fact_9914_DERIV__neg__dec__left,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_neg_dec_left
% 5.27/5.63 thf(fact_9915_DERIV__pos__inc__left,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pos_inc_left
% 5.27/5.63 thf(fact_9916_DERIV__neg__dec__right,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_neg_dec_right
% 5.27/5.63 thf(fact_9917_DERIV__pos__inc__right,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pos_inc_right
% 5.27/5.63 thf(fact_9918_DERIV__ln,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_ln
% 5.27/5.63 thf(fact_9919_has__real__derivative__neg__dec__right,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,S2: set_real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.27/5.63 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % has_real_derivative_neg_dec_right
% 5.27/5.63 thf(fact_9920_has__real__derivative__pos__inc__right,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,S2: set_real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( member_real @ ( plus_plus_real @ X4 @ H4 ) @ S2 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( plus_plus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % has_real_derivative_pos_inc_right
% 5.27/5.63 thf(fact_9921_has__real__derivative__pos__inc__left,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,S2: set_real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) @ ( F @ X4 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % has_real_derivative_pos_inc_left
% 5.27/5.63 thf(fact_9922_has__real__derivative__neg__dec__left,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,S2: set_real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ S2 ) )
% 5.27/5.63 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.27/5.63 => ? [D3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.27/5.63 & ! [H4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.27/5.63 => ( ( member_real @ ( minus_minus_real @ X4 @ H4 ) @ S2 )
% 5.27/5.63 => ( ( ord_less_real @ H4 @ D3 )
% 5.27/5.63 => ( ord_less_real @ ( F @ X4 ) @ ( F @ ( minus_minus_real @ X4 @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % has_real_derivative_neg_dec_left
% 5.27/5.63 thf(fact_9923_DERIV__const__average,axiom,
% 5.27/5.63 ! [A: real,B: real,V: real > real,K: real] :
% 5.27/5.63 ( ( A != B )
% 5.27/5.63 => ( ! [X5: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.27/5.63 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_const_average
% 5.27/5.63 thf(fact_9924_DERIV__local__max,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,D: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.27/5.63 => ( ! [Y3: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 5.27/5.63 => ( ord_less_eq_real @ ( F @ Y3 ) @ ( F @ X4 ) ) )
% 5.27/5.63 => ( L = zero_zero_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_local_max
% 5.27/5.63 thf(fact_9925_DERIV__local__min,axiom,
% 5.27/5.63 ! [F: real > real,L: real,X4: real,D: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ L @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.27/5.63 => ( ! [Y3: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X4 @ Y3 ) ) @ D )
% 5.27/5.63 => ( ord_less_eq_real @ ( F @ X4 ) @ ( F @ Y3 ) ) )
% 5.27/5.63 => ( L = zero_zero_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_local_min
% 5.27/5.63 thf(fact_9926_DERIV__ln__divide,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_ln_divide
% 5.27/5.63 thf(fact_9927_DERIV__fun__pow,axiom,
% 5.27/5.63 ! [G: real > real,M: real,X4: real,N2: nat] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( power_power_real @ ( G @ X ) @ N2 )
% 5.27/5.63 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( G @ X4 ) @ ( minus_minus_nat @ N2 @ one_one_nat ) ) ) @ M )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_fun_pow
% 5.27/5.63 thf(fact_9928_DERIV__pow,axiom,
% 5.27/5.63 ! [N2: nat,X4: real,S: set_real] :
% 5.27/5.63 ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( power_power_real @ X @ N2 )
% 5.27/5.63 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ X4 @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X4 @ S ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pow
% 5.27/5.63 thf(fact_9929_has__real__derivative__powr,axiom,
% 5.27/5.63 ! [Z: real,R3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [Z5: real] : ( powr_real @ Z5 @ R3 )
% 5.27/5.63 @ ( times_times_real @ R3 @ ( powr_real @ Z @ ( minus_minus_real @ R3 @ one_one_real ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % has_real_derivative_powr
% 5.27/5.63 thf(fact_9930_DERIV__log,axiom,
% 5.27/5.63 ! [X4: real,B: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X4 ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_log
% 5.27/5.63 thf(fact_9931_DERIV__fun__powr,axiom,
% 5.27/5.63 ! [G: real > real,M: real,X4: real,R3: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ R3 )
% 5.27/5.63 @ ( times_times_real @ ( times_times_real @ R3 @ ( powr_real @ ( G @ X4 ) @ ( minus_minus_real @ R3 @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_fun_powr
% 5.27/5.63 thf(fact_9932_DERIV__powr,axiom,
% 5.27/5.63 ! [G: real > real,M: real,X4: real,F: real > real,R3: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ ( G @ X4 ) )
% 5.27/5.63 => ( ( has_fi5821293074295781190e_real @ F @ R3 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( powr_real @ ( G @ X ) @ ( F @ X ) )
% 5.27/5.63 @ ( times_times_real @ ( powr_real @ ( G @ X4 ) @ ( F @ X4 ) ) @ ( plus_plus_real @ ( times_times_real @ R3 @ ( ln_ln_real @ ( G @ X4 ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X4 ) ) @ ( G @ X4 ) ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_powr
% 5.27/5.63 thf(fact_9933_DERIV__real__sqrt,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_real_sqrt
% 5.27/5.63 thf(fact_9934_DERIV__series_H,axiom,
% 5.27/5.63 ! [F: real > nat > real,F4: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.27/5.63 ( ! [N3: nat] :
% 5.27/5.63 ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( F @ X @ N3 )
% 5.27/5.63 @ ( F4 @ X0 @ N3 )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( summable_real @ ( F @ X5 ) ) )
% 5.27/5.63 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( ( summable_real @ ( F4 @ X0 ) )
% 5.27/5.63 => ( ( summable_real @ L5 )
% 5.27/5.63 => ( ! [N3: nat,X5: real,Y3: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( ( member_real @ Y3 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 => ( 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 ) ) ) ) ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] : ( suminf_real @ ( F @ X ) )
% 5.27/5.63 @ ( suminf_real @ ( F4 @ X0 ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_series'
% 5.27/5.63 thf(fact_9935_DERIV__arctan,axiom,
% 5.27/5.63 ! [X4: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_arctan
% 5.27/5.63 thf(fact_9936_DERIV__real__sqrt__generic,axiom,
% 5.27/5.63 ! [X4: real,D4: real] :
% 5.27/5.63 ( ( X4 != zero_zero_real )
% 5.27/5.63 => ( ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( D4
% 5.27/5.63 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 => ( ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.63 => ( D4
% 5.27/5.63 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X4 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_real_sqrt_generic
% 5.27/5.63 thf(fact_9937_arsinh__real__has__field__derivative,axiom,
% 5.27/5.63 ! [X4: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % arsinh_real_has_field_derivative
% 5.27/5.63 thf(fact_9938_arcosh__real__has__field__derivative,axiom,
% 5.27/5.63 ! [X4: real,A2: set_real] :
% 5.27/5.63 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % arcosh_real_has_field_derivative
% 5.27/5.63 thf(fact_9939_artanh__real__has__field__derivative,axiom,
% 5.27/5.63 ! [X4: real,A2: set_real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ A2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % artanh_real_has_field_derivative
% 5.27/5.63 thf(fact_9940_DERIV__power__series_H,axiom,
% 5.27/5.63 ! [R: real,F: nat > real,X0: real] :
% 5.27/5.63 ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.27/5.63 => ( summable_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X5 @ N ) ) ) )
% 5.27/5.63 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R ) @ R ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ R )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X: real] :
% 5.27/5.63 ( suminf_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( F @ N ) @ ( power_power_real @ X @ ( suc @ N ) ) ) )
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( times_times_real @ ( F @ N ) @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) @ ( power_power_real @ X0 @ N ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_power_series'
% 5.27/5.63 thf(fact_9941_DERIV__real__root,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_real_root
% 5.27/5.63 thf(fact_9942_DERIV__arccos,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_arccos
% 5.27/5.63 thf(fact_9943_DERIV__arcsin,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X4 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_arcsin
% 5.27/5.63 thf(fact_9944_Maclaurin__all__le__objl,axiom,
% 5.27/5.63 ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 5.27/5.63 ( ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 & ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.63 & ( ( F @ X4 )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_all_le_objl
% 5.27/5.63 thf(fact_9945_Maclaurin__all__le,axiom,
% 5.27/5.63 ! [Diff: nat > real > real,F: real > real,X4: real,N2: nat] :
% 5.27/5.63 ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.63 & ( ( F @ X4 )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_all_le
% 5.27/5.63 thf(fact_9946_DERIV__odd__real__root,axiom,
% 5.27/5.63 ! [N2: nat,X4: real] :
% 5.27/5.63 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( X4 != zero_zero_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_odd_real_root
% 5.27/5.63 thf(fact_9947_Maclaurin__minus,axiom,
% 5.27/5.63 ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ H @ zero_zero_real )
% 5.27/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ H @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ zero_zero_real ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ H @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ zero_zero_real )
% 5.27/5.63 & ( ( F @ H )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_minus
% 5.27/5.63 thf(fact_9948_Maclaurin2,axiom,
% 5.27/5.63 ! [H: real,Diff: nat > real > real,F: real > real,N2: nat] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ H ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ H )
% 5.27/5.63 & ( ( F @ H )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin2
% 5.27/5.63 thf(fact_9949_Maclaurin,axiom,
% 5.27/5.63 ! [H: real,N2: nat,Diff: nat > real > real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ H )
% 5.27/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ H ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ H )
% 5.27/5.63 & ( ( F @ H )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ H @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ H @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin
% 5.27/5.63 thf(fact_9950_Maclaurin__all__lt,axiom,
% 5.27/5.63 ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 5.27/5.63 ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( X4 != zero_zero_real )
% 5.27/5.63 => ( ! [M5: nat,X5: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T3 ) )
% 5.27/5.63 & ( ord_less_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.63 & ( ( F @ X4 )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_all_lt
% 5.27/5.63 thf(fact_9951_Maclaurin__bi__le,axiom,
% 5.27/5.63 ! [Diff: nat > real > real,F: real > real,N2: nat,X4: real] :
% 5.27/5.63 ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ T3 ) @ ( abs_abs_real @ X4 ) )
% 5.27/5.63 & ( ( F @ X4 )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ X4 @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ X4 @ N2 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_bi_le
% 5.27/5.63 thf(fact_9952_Taylor__down,axiom,
% 5.27/5.63 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ A @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ B ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ( ord_less_real @ A @ C )
% 5.27/5.63 => ( ( ord_less_eq_real @ C @ B )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ C )
% 5.27/5.63 & ( ( F @ A )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Taylor_down
% 5.27/5.63 thf(fact_9953_Taylor__up,axiom,
% 5.27/5.63 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ A @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ B ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ( ord_less_eq_real @ A @ C )
% 5.27/5.63 => ( ( ord_less_real @ C @ B )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ord_less_real @ C @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ B )
% 5.27/5.63 & ( ( F @ B )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Taylor_up
% 5.27/5.63 thf(fact_9954_Taylor,axiom,
% 5.27/5.63 ! [N2: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( ( Diff @ zero_zero_nat )
% 5.27/5.63 = F )
% 5.27/5.63 => ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ A @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ B ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ( ord_less_eq_real @ A @ C )
% 5.27/5.63 => ( ( ord_less_eq_real @ C @ B )
% 5.27/5.63 => ( ( ord_less_eq_real @ A @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X4 @ B )
% 5.27/5.63 => ( ( X4 != C )
% 5.27/5.63 => ? [T3: real] :
% 5.27/5.63 ( ( ( ord_less_real @ X4 @ C )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ C ) ) )
% 5.27/5.63 & ( ~ ( ord_less_real @ X4 @ C )
% 5.27/5.63 => ( ( ord_less_real @ C @ T3 )
% 5.27/5.63 & ( ord_less_real @ T3 @ X4 ) ) )
% 5.27/5.63 & ( ( F @ X4 )
% 5.27/5.63 = ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [M6: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M6 @ C ) @ ( semiri2265585572941072030t_real @ M6 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ M6 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ N2 ) )
% 5.27/5.63 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N2 @ T3 ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ ( power_power_real @ ( minus_minus_real @ X4 @ C ) @ N2 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Taylor
% 5.27/5.63 thf(fact_9955_Maclaurin__lemma2,axiom,
% 5.27/5.63 ! [N2: nat,H: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.27/5.63 ( ! [M5: nat,T3: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M5 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ zero_zero_real @ T3 )
% 5.27/5.63 & ( ord_less_eq_real @ T3 @ H ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( Diff @ M5 ) @ ( Diff @ ( suc @ M5 ) @ T3 ) @ ( topolo2177554685111907308n_real @ T3 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ( N2
% 5.27/5.63 = ( suc @ K ) )
% 5.27/5.63 => ! [M2: nat,T4: real] :
% 5.27/5.63 ( ( ( ord_less_nat @ M2 @ N2 )
% 5.27/5.63 & ( ord_less_eq_real @ zero_zero_real @ T4 )
% 5.27/5.63 & ( ord_less_eq_real @ T4 @ H ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [U2: real] :
% 5.27/5.63 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.27/5.63 @ ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ U2 @ P5 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ M2 ) ) )
% 5.27/5.63 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N2 @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ M2 ) ) ) ) ) )
% 5.27/5.63 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T4 )
% 5.27/5.63 @ ( plus_plus_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [P5: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P5 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P5 ) ) @ ( power_power_real @ T4 @ P5 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) )
% 5.27/5.63 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T4 @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N2 @ ( suc @ M2 ) ) ) ) ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ T4 @ top_top_set_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Maclaurin_lemma2
% 5.27/5.63 thf(fact_9956_DERIV__arctan__series,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.63 => ( has_fi5821293074295781190e_real
% 5.27/5.63 @ ^ [X9: real] :
% 5.27/5.63 ( suminf_real
% 5.27/5.63 @ ^ [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 ) ) ) ) )
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [K3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K3 ) @ ( power_power_real @ X4 @ ( times_times_nat @ K3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_arctan_series
% 5.27/5.63 thf(fact_9957_DERIV__real__root__generic,axiom,
% 5.27/5.63 ! [N2: nat,X4: real,D4: real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( X4 != zero_zero_real )
% 5.27/5.63 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( D4
% 5.27/5.63 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.27/5.63 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ zero_zero_real )
% 5.27/5.63 => ( D4
% 5.27/5.63 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.27/5.63 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( D4
% 5.27/5.63 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( power_power_real @ ( root @ N2 @ X4 ) @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ ( root @ N2 ) @ D4 @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_real_root_generic
% 5.27/5.63 thf(fact_9958_UNIV__char__of__nat,axiom,
% 5.27/5.63 ( top_top_set_char
% 5.27/5.63 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % UNIV_char_of_nat
% 5.27/5.63 thf(fact_9959_nat__of__char__less__256,axiom,
% 5.27/5.63 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_of_char_less_256
% 5.27/5.63 thf(fact_9960_range__nat__of__char,axiom,
% 5.27/5.63 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.27/5.63 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % range_nat_of_char
% 5.27/5.63 thf(fact_9961_integer__of__char__code,axiom,
% 5.27/5.63 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.27/5.63 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.27/5.63 = ( 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 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % integer_of_char_code
% 5.27/5.63 thf(fact_9962_String_Ochar__of__ascii__of,axiom,
% 5.27/5.63 ! [C: char] :
% 5.27/5.63 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.27/5.63 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % String.char_of_ascii_of
% 5.27/5.63 thf(fact_9963_sorted__list__of__set__lessThan__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.27/5.63 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_list_of_set_lessThan_Suc
% 5.27/5.63 thf(fact_9964_sorted__list__of__set__atMost__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.27/5.63 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_list_of_set_atMost_Suc
% 5.27/5.63 thf(fact_9965_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ ( suc @ I2 ) @ J )
% 5.27/5.63 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I2 @ J ) )
% 5.27/5.63 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_list_of_set_greaterThanAtMost
% 5.27/5.63 thf(fact_9966_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_nat @ ( suc @ I2 ) @ J )
% 5.27/5.63 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I2 @ J ) )
% 5.27/5.63 = ( cons_nat @ ( suc @ I2 ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I2 ) @ J ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_list_of_set_greaterThanLessThan
% 5.27/5.63 thf(fact_9967_upto__aux__rec,axiom,
% 5.27/5.63 ( upto_aux
% 5.27/5.63 = ( ^ [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 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_aux_rec
% 5.27/5.63 thf(fact_9968_upto_Opelims,axiom,
% 5.27/5.63 ! [X4: int,Xa: int,Y: list_int] :
% 5.27/5.63 ( ( ( upto @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) )
% 5.27/5.63 => ~ ( ( ( ( ord_less_eq_int @ X4 @ Xa )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 5.27/5.63 => ( Y = nil_int ) ) )
% 5.27/5.63 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X4 @ Xa ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto.pelims
% 5.27/5.63 thf(fact_9969_upto__Nil,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( ( upto @ I2 @ J )
% 5.27/5.63 = nil_int )
% 5.27/5.63 = ( ord_less_int @ J @ I2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_Nil
% 5.27/5.63 thf(fact_9970_upto__Nil2,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( nil_int
% 5.27/5.63 = ( upto @ I2 @ J ) )
% 5.27/5.63 = ( ord_less_int @ J @ I2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_Nil2
% 5.27/5.63 thf(fact_9971_upto__empty,axiom,
% 5.27/5.63 ! [J: int,I2: int] :
% 5.27/5.63 ( ( ord_less_int @ J @ I2 )
% 5.27/5.63 => ( ( upto @ I2 @ J )
% 5.27/5.63 = nil_int ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_empty
% 5.27/5.63 thf(fact_9972_upto__single,axiom,
% 5.27/5.63 ! [I2: int] :
% 5.27/5.63 ( ( upto @ I2 @ I2 )
% 5.27/5.63 = ( cons_int @ I2 @ nil_int ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_single
% 5.27/5.63 thf(fact_9973_nth__upto,axiom,
% 5.27/5.63 ! [I2: int,K: nat,J: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.27/5.63 => ( ( nth_int @ ( upto @ I2 @ J ) @ K )
% 5.27/5.63 = ( plus_plus_int @ I2 @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nth_upto
% 5.27/5.63 thf(fact_9974_length__upto,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( size_size_list_int @ ( upto @ I2 @ J ) )
% 5.27/5.63 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I2 ) @ one_one_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % length_upto
% 5.27/5.63 thf(fact_9975_upto__rec__numeral_I1_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = nil_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec_numeral(1)
% 5.27/5.63 thf(fact_9976_upto__rec__numeral_I2_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = nil_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec_numeral(2)
% 5.27/5.63 thf(fact_9977_upto__rec__numeral_I3_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N2 ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N2 ) )
% 5.27/5.63 = nil_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec_numeral(3)
% 5.27/5.63 thf(fact_9978_upto__rec__numeral_I4_J,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N2 ) ) )
% 5.27/5.63 = nil_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec_numeral(4)
% 5.27/5.63 thf(fact_9979_upto__aux__def,axiom,
% 5.27/5.63 ( upto_aux
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( append_int @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_aux_def
% 5.27/5.63 thf(fact_9980_sup__enat__def,axiom,
% 5.27/5.63 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.27/5.63
% 5.27/5.63 % sup_enat_def
% 5.27/5.63 thf(fact_9981_sup__nat__def,axiom,
% 5.27/5.63 sup_sup_nat = ord_max_nat ).
% 5.27/5.63
% 5.27/5.63 % sup_nat_def
% 5.27/5.63 thf(fact_9982_upto__code,axiom,
% 5.27/5.63 ( upto
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( upto_aux @ I3 @ J3 @ nil_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_code
% 5.27/5.63 thf(fact_9983_atLeastAtMost__upto,axiom,
% 5.27/5.63 ( set_or1266510415728281911st_int
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ J3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastAtMost_upto
% 5.27/5.63 thf(fact_9984_distinct__upto,axiom,
% 5.27/5.63 ! [I2: int,J: int] : ( distinct_int @ ( upto @ I2 @ J ) ) ).
% 5.27/5.63
% 5.27/5.63 % distinct_upto
% 5.27/5.63 thf(fact_9985_atLeastLessThan__add__Un,axiom,
% 5.27/5.63 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.63 => ( ( set_or4665077453230672383an_nat @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.27/5.63 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I2 @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan_add_Un
% 5.27/5.63 thf(fact_9986_upto__split2,axiom,
% 5.27/5.63 ! [I2: int,J: int,K: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( ord_less_eq_int @ J @ K )
% 5.27/5.63 => ( ( upto @ I2 @ K )
% 5.27/5.63 = ( append_int @ ( upto @ I2 @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_split2
% 5.27/5.63 thf(fact_9987_upto__split1,axiom,
% 5.27/5.63 ! [I2: int,J: int,K: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( ord_less_eq_int @ J @ K )
% 5.27/5.63 => ( ( upto @ I2 @ K )
% 5.27/5.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_split1
% 5.27/5.63 thf(fact_9988_atLeastLessThan__upto,axiom,
% 5.27/5.63 ( set_or4662586982721622107an_int
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ I3 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan_upto
% 5.27/5.63 thf(fact_9989_greaterThanAtMost__upto,axiom,
% 5.27/5.63 ( set_or6656581121297822940st_int
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThanAtMost_upto
% 5.27/5.63 thf(fact_9990_upto_Osimps,axiom,
% 5.27/5.63 ( upto
% 5.27/5.63 = ( ^ [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 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto.simps
% 5.27/5.63 thf(fact_9991_upto_Oelims,axiom,
% 5.27/5.63 ! [X4: int,Xa: int,Y: list_int] :
% 5.27/5.63 ( ( ( upto @ X4 @ Xa )
% 5.27/5.63 = Y )
% 5.27/5.63 => ( ( ( ord_less_eq_int @ X4 @ Xa )
% 5.27/5.63 => ( Y
% 5.27/5.63 = ( cons_int @ X4 @ ( upto @ ( plus_plus_int @ X4 @ one_one_int ) @ Xa ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ X4 @ Xa )
% 5.27/5.63 => ( Y = nil_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto.elims
% 5.27/5.63 thf(fact_9992_upto__rec1,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( upto @ I2 @ J )
% 5.27/5.63 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec1
% 5.27/5.63 thf(fact_9993_upto__rec2,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( upto @ I2 @ J )
% 5.27/5.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_rec2
% 5.27/5.63 thf(fact_9994_greaterThanLessThan__upto,axiom,
% 5.27/5.63 ( set_or5832277885323065728an_int
% 5.27/5.63 = ( ^ [I3: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I3 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThanLessThan_upto
% 5.27/5.63 thf(fact_9995_upto__split3,axiom,
% 5.27/5.63 ! [I2: int,J: int,K: int] :
% 5.27/5.63 ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( ord_less_eq_int @ J @ K )
% 5.27/5.63 => ( ( upto @ I2 @ K )
% 5.27/5.63 = ( append_int @ ( upto @ I2 @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto_split3
% 5.27/5.63 thf(fact_9996_upto_Opsimps,axiom,
% 5.27/5.63 ! [I2: int,J: int] :
% 5.27/5.63 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I2 @ J ) )
% 5.27/5.63 => ( ( ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( upto @ I2 @ J )
% 5.27/5.63 = ( cons_int @ I2 @ ( upto @ ( plus_plus_int @ I2 @ one_one_int ) @ J ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_int @ I2 @ J )
% 5.27/5.63 => ( ( upto @ I2 @ J )
% 5.27/5.63 = nil_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upto.psimps
% 5.27/5.63 thf(fact_9997_LIM__fun__gt__zero,axiom,
% 5.27/5.63 ! [F: real > real,L: real,C: real] :
% 5.27/5.63 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ L )
% 5.27/5.63 => ? [R2: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.27/5.63 & ! [X2: real] :
% 5.27/5.63 ( ( ( X2 != C )
% 5.27/5.63 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 5.27/5.63 => ( ord_less_real @ zero_zero_real @ ( F @ X2 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIM_fun_gt_zero
% 5.27/5.63 thf(fact_9998_LIM__fun__not__zero,axiom,
% 5.27/5.63 ! [F: real > real,L: real,C: real] :
% 5.27/5.63 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.27/5.63 => ( ( L != zero_zero_real )
% 5.27/5.63 => ? [R2: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.27/5.63 & ! [X2: real] :
% 5.27/5.63 ( ( ( X2 != C )
% 5.27/5.63 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 5.27/5.63 => ( ( F @ X2 )
% 5.27/5.63 != zero_zero_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIM_fun_not_zero
% 5.27/5.63 thf(fact_9999_LIM__fun__less__zero,axiom,
% 5.27/5.63 ! [F: real > real,L: real,C: real] :
% 5.27/5.63 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.27/5.63 => ( ( ord_less_real @ L @ zero_zero_real )
% 5.27/5.63 => ? [R2: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.27/5.63 & ! [X2: real] :
% 5.27/5.63 ( ( ( X2 != C )
% 5.27/5.63 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X2 ) ) @ R2 ) )
% 5.27/5.63 => ( ord_less_real @ ( F @ X2 ) @ zero_zero_real ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIM_fun_less_zero
% 5.27/5.63 thf(fact_10000_LIM__cos__div__sin,axiom,
% 5.27/5.63 ( filterlim_real_real
% 5.27/5.63 @ ^ [X: real] : ( divide_divide_real @ ( cos_real @ X ) @ ( sin_real @ X ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIM_cos_div_sin
% 5.27/5.63 thf(fact_10001_summable__Leibniz_I3_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ( topolo6980174941875973593q_real @ A )
% 5.27/5.63 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.27/5.63 => ! [N6: nat] :
% 5.27/5.63 ( member_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.27/5.63 @ ( set_or1222579329274155063t_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) )
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz(3)
% 5.27/5.63 thf(fact_10002_summable__Leibniz_I2_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ( topolo6980174941875973593q_real @ A )
% 5.27/5.63 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.27/5.63 => ! [N6: nat] :
% 5.27/5.63 ( member_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.27/5.63 @ ( set_or1222579329274155063t_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz(2)
% 5.27/5.63 thf(fact_10003_filterlim__Suc,axiom,
% 5.27/5.63 filterlim_nat_nat @ suc @ at_top_nat @ at_top_nat ).
% 5.27/5.63
% 5.27/5.63 % filterlim_Suc
% 5.27/5.63 thf(fact_10004_mult__nat__left__at__top,axiom,
% 5.27/5.63 ! [C: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.27/5.63 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % mult_nat_left_at_top
% 5.27/5.63 thf(fact_10005_mult__nat__right__at__top,axiom,
% 5.27/5.63 ! [C: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.27/5.63 => ( filterlim_nat_nat
% 5.27/5.63 @ ^ [X: nat] : ( times_times_nat @ X @ C )
% 5.27/5.63 @ at_top_nat
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % mult_nat_right_at_top
% 5.27/5.63 thf(fact_10006_monoseq__convergent,axiom,
% 5.27/5.63 ! [X8: nat > real,B3: real] :
% 5.27/5.63 ( ( topolo6980174941875973593q_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 5.27/5.63 => ~ ! [L6: real] :
% 5.27/5.63 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % monoseq_convergent
% 5.27/5.63 thf(fact_10007_LIMSEQ__root,axiom,
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( root @ N @ ( semiri5074537144036343181t_real @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_root
% 5.27/5.63 thf(fact_10008_nested__sequence__unique,axiom,
% 5.27/5.63 ! [F: nat > real,G: nat > real] :
% 5.27/5.63 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.27/5.63 => ( ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( minus_minus_real @ ( F @ N ) @ ( G @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 => ? [L4: real] :
% 5.27/5.63 ( ! [N6: nat] : ( ord_less_eq_real @ ( F @ N6 ) @ L4 )
% 5.27/5.63 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.27/5.63 & ! [N6: nat] : ( ord_less_eq_real @ L4 @ ( G @ N6 ) )
% 5.27/5.63 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nested_sequence_unique
% 5.27/5.63 thf(fact_10009_LIMSEQ__inverse__zero,axiom,
% 5.27/5.63 ! [X8: nat > real] :
% 5.27/5.63 ( ! [R2: real] :
% 5.27/5.63 ? [N7: nat] :
% 5.27/5.63 ! [N3: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ N7 @ N3 )
% 5.27/5.63 => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( inverse_inverse_real @ ( X8 @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_zero
% 5.27/5.63 thf(fact_10010_lim__inverse__n_H,axiom,
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % lim_inverse_n'
% 5.27/5.63 thf(fact_10011_LIMSEQ__root__const,axiom,
% 5.27/5.63 ! [C: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ C )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( root @ N @ C )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_root_const
% 5.27/5.63 thf(fact_10012_LIMSEQ__inverse__real__of__nat,axiom,
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_real_of_nat
% 5.27/5.63 thf(fact_10013_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.27/5.63 ! [R3: real] :
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ R3 )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_real_of_nat_add
% 5.27/5.63 thf(fact_10014_increasing__LIMSEQ,axiom,
% 5.27/5.63 ! [F: nat > real,L: real] :
% 5.27/5.63 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L )
% 5.27/5.63 => ( ! [E: real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ E )
% 5.27/5.63 => ? [N6: nat] : ( ord_less_eq_real @ L @ ( plus_plus_real @ ( F @ N6 ) @ E ) ) )
% 5.27/5.63 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L ) @ at_top_nat ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % increasing_LIMSEQ
% 5.27/5.63 thf(fact_10015_LIMSEQ__realpow__zero,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( filterlim_nat_real @ ( power_power_real @ X4 ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_realpow_zero
% 5.27/5.63 thf(fact_10016_LIMSEQ__divide__realpow__zero,axiom,
% 5.27/5.63 ! [X4: real,A: real] :
% 5.27/5.63 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( divide_divide_real @ A @ ( power_power_real @ X4 @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_divide_realpow_zero
% 5.27/5.63 thf(fact_10017_LIMSEQ__abs__realpow__zero2,axiom,
% 5.27/5.63 ! [C: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.27/5.63 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_abs_realpow_zero2
% 5.27/5.63 thf(fact_10018_LIMSEQ__abs__realpow__zero,axiom,
% 5.27/5.63 ! [C: real] :
% 5.27/5.63 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.27/5.63 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_abs_realpow_zero
% 5.27/5.63 thf(fact_10019_LIMSEQ__inverse__realpow__zero,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( inverse_inverse_real @ ( power_power_real @ X4 @ N ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_realpow_zero
% 5.27/5.63 thf(fact_10020_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.27/5.63 ! [R3: real] :
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( plus_plus_real @ R3 @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ R3 )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.27/5.63 thf(fact_10021_tendsto__exp__limit__sequentially,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % tendsto_exp_limit_sequentially
% 5.27/5.63 thf(fact_10022_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.27/5.63 ! [R3: real] :
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ R3 @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) ) ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ R3 )
% 5.27/5.63 @ at_top_nat ) ).
% 5.27/5.63
% 5.27/5.63 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.27/5.63 thf(fact_10023_summable__Leibniz_I1_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ( topolo6980174941875973593q_real @ A )
% 5.27/5.63 => ( summable_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz(1)
% 5.27/5.63 thf(fact_10024_summable,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( summable_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( A @ N ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable
% 5.27/5.63 thf(fact_10025_cos__diff__limit__1,axiom,
% 5.27/5.63 ! [Theta: nat > real,Theta2: real] :
% 5.27/5.63 ( ( filterlim_nat_real
% 5.27/5.63 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 => ~ ! [K2: nat > int] :
% 5.27/5.63 ~ ( filterlim_nat_real
% 5.27/5.63 @ ^ [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 ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % cos_diff_limit_1
% 5.27/5.63 thf(fact_10026_cos__limit__1,axiom,
% 5.27/5.63 ! [Theta: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real
% 5.27/5.63 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 => ? [K2: nat > int] :
% 5.27/5.63 ( filterlim_nat_real
% 5.27/5.63 @ ^ [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 ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % cos_limit_1
% 5.27/5.63 thf(fact_10027_summable__Leibniz_I4_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ( topolo6980174941875973593q_real @ A )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.27/5.63 @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz(4)
% 5.27/5.63 thf(fact_10028_zeroseq__arctan__series,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ X4 ) @ one_one_real )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X4 @ ( plus_plus_nat @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % zeroseq_arctan_series
% 5.27/5.63 thf(fact_10029_summable__Leibniz_H_I2_J,axiom,
% 5.27/5.63 ! [A: nat > real,N2: nat] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( ord_less_eq_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz'(2)
% 5.27/5.63 thf(fact_10030_summable__Leibniz_H_I3_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.27/5.63 @ at_top_nat ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz'(3)
% 5.27/5.63 thf(fact_10031_sums__alternating__upper__lower,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ? [L4: real] :
% 5.27/5.63 ( ! [N6: nat] :
% 5.27/5.63 ( ord_less_eq_real
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) ) )
% 5.27/5.63 @ L4 )
% 5.27/5.63 & ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ L4 )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 & ! [N6: nat] :
% 5.27/5.63 ( ord_less_eq_real @ L4
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N6 ) @ one_one_nat ) ) ) )
% 5.27/5.63 & ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ L4 )
% 5.27/5.63 @ at_top_nat ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sums_alternating_upper_lower
% 5.27/5.63 thf(fact_10032_summable__Leibniz_I5_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ( topolo6980174941875973593q_real @ A )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.27/5.63 @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz(5)
% 5.27/5.63 thf(fact_10033_summable__Leibniz_H_I5_J,axiom,
% 5.27/5.63 ! [A: nat > real] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( filterlim_nat_real
% 5.27/5.63 @ ^ [N: nat] :
% 5.27/5.63 ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) ) )
% 5.27/5.63 @ at_top_nat ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz'(5)
% 5.27/5.63 thf(fact_10034_summable__Leibniz_H_I4_J,axiom,
% 5.27/5.63 ! [A: nat > real,N2: nat] :
% 5.27/5.63 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.27/5.63 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.27/5.63 => ( ord_less_eq_real
% 5.27/5.63 @ ( suminf_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) ) )
% 5.27/5.63 @ ( groups6591440286371151544t_real
% 5.27/5.63 @ ^ [I3: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I3 ) @ ( A @ I3 ) )
% 5.27/5.63 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_Leibniz'(4)
% 5.27/5.63 thf(fact_10035_eventually__sequentially__Suc,axiom,
% 5.27/5.63 ! [P: nat > $o] :
% 5.27/5.63 ( ( eventually_nat
% 5.27/5.63 @ ^ [I3: nat] : ( P @ ( suc @ I3 ) )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_sequentially_Suc
% 5.27/5.63 thf(fact_10036_eventually__sequentially__seg,axiom,
% 5.27/5.63 ! [P: nat > $o,K: nat] :
% 5.27/5.63 ( ( eventually_nat
% 5.27/5.63 @ ^ [N: nat] : ( P @ ( plus_plus_nat @ N @ K ) )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_sequentially_seg
% 5.27/5.63 thf(fact_10037_le__sequentially,axiom,
% 5.27/5.63 ! [F5: filter_nat] :
% 5.27/5.63 ( ( ord_le2510731241096832064er_nat @ F5 @ at_top_nat )
% 5.27/5.63 = ( ! [N9: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N9 ) @ F5 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % le_sequentially
% 5.27/5.63 thf(fact_10038_eventually__sequentially,axiom,
% 5.27/5.63 ! [P: nat > $o] :
% 5.27/5.63 ( ( eventually_nat @ P @ at_top_nat )
% 5.27/5.63 = ( ? [N9: nat] :
% 5.27/5.63 ! [N: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ N9 @ N )
% 5.27/5.63 => ( P @ N ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_sequentially
% 5.27/5.63 thf(fact_10039_eventually__sequentiallyI,axiom,
% 5.27/5.63 ! [C: nat,P: nat > $o] :
% 5.27/5.63 ( ! [X5: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ C @ X5 )
% 5.27/5.63 => ( P @ X5 ) )
% 5.27/5.63 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_sequentiallyI
% 5.27/5.63 thf(fact_10040_sequentially__offset,axiom,
% 5.27/5.63 ! [P: nat > $o,K: nat] :
% 5.27/5.63 ( ( eventually_nat @ P @ at_top_nat )
% 5.27/5.63 => ( eventually_nat
% 5.27/5.63 @ ^ [I3: nat] : ( P @ ( plus_plus_nat @ I3 @ K ) )
% 5.27/5.63 @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % sequentially_offset
% 5.27/5.63 thf(fact_10041_eventually__at__left__real,axiom,
% 5.27/5.63 ! [B: real,A: real] :
% 5.27/5.63 ( ( ord_less_real @ B @ A )
% 5.27/5.63 => ( eventually_real
% 5.27/5.63 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ B @ A ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ A @ ( set_or5984915006950818249n_real @ A ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_at_left_real
% 5.27/5.63 thf(fact_10042_tanh__real__at__top,axiom,
% 5.27/5.63 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.27/5.63
% 5.27/5.63 % tanh_real_at_top
% 5.27/5.63 thf(fact_10043_artanh__real__at__left__1,axiom,
% 5.27/5.63 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % artanh_real_at_left_1
% 5.27/5.63 thf(fact_10044_tendsto__power__div__exp__0,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( filterlim_real_real
% 5.27/5.63 @ ^ [X: real] : ( divide_divide_real @ ( power_power_real @ X @ K ) @ ( exp_real @ X ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.27/5.63 @ at_top_real ) ).
% 5.27/5.63
% 5.27/5.63 % tendsto_power_div_exp_0
% 5.27/5.63 thf(fact_10045_tendsto__exp__limit__at__top,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( filterlim_real_real
% 5.27/5.63 @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X4 @ Y5 ) ) @ Y5 )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.27/5.63 @ at_top_real ) ).
% 5.27/5.63
% 5.27/5.63 % tendsto_exp_limit_at_top
% 5.27/5.63 thf(fact_10046_filterlim__tan__at__left,axiom,
% 5.27/5.63 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 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % filterlim_tan_at_left
% 5.27/5.63 thf(fact_10047_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.27/5.63 ! [B: real,F: real > real,Flim: real] :
% 5.27/5.63 ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ B @ X5 )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ Y4 @ zero_zero_real ) ) )
% 5.27/5.63 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.27/5.63 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_neg_imp_decreasing_at_top
% 5.27/5.63 thf(fact_10048_tendsto__arctan__at__top,axiom,
% 5.27/5.63 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.27/5.63
% 5.27/5.63 % tendsto_arctan_at_top
% 5.27/5.63 thf(fact_10049_at__top__le__at__infinity,axiom,
% 5.27/5.63 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.27/5.63
% 5.27/5.63 % at_top_le_at_infinity
% 5.27/5.63 thf(fact_10050_Bseq__eq__bounded,axiom,
% 5.27/5.63 ! [F: nat > real,A: real,B: real] :
% 5.27/5.63 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.27/5.63 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % Bseq_eq_bounded
% 5.27/5.63 thf(fact_10051_Bseq__realpow,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X4 @ one_one_real )
% 5.27/5.63 => ( bfun_nat_real @ ( power_power_real @ X4 ) @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Bseq_realpow
% 5.27/5.63 thf(fact_10052_filterlim__pow__at__bot__even,axiom,
% 5.27/5.63 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.27/5.63 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( filterlim_real_real
% 5.27/5.63 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 5.27/5.63 @ at_top_real
% 5.27/5.63 @ F5 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % filterlim_pow_at_bot_even
% 5.27/5.63 thf(fact_10053_at__bot__le__at__infinity,axiom,
% 5.27/5.63 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.27/5.63
% 5.27/5.63 % at_bot_le_at_infinity
% 5.27/5.63 thf(fact_10054_tanh__real__at__bot,axiom,
% 5.27/5.63 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.27/5.63
% 5.27/5.63 % tanh_real_at_bot
% 5.27/5.63 thf(fact_10055_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.27/5.63 ! [B: real,F: real > real,Flim: real] :
% 5.27/5.63 ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ zero_zero_real @ Y4 ) ) )
% 5.27/5.63 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.27/5.63 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pos_imp_increasing_at_bot
% 5.27/5.63 thf(fact_10056_filterlim__pow__at__bot__odd,axiom,
% 5.27/5.63 ! [N2: nat,F: real > real,F5: filter_real] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( filterlim_real_real @ F @ at_bot_real @ F5 )
% 5.27/5.63 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.27/5.63 => ( filterlim_real_real
% 5.27/5.63 @ ^ [X: real] : ( power_power_real @ ( F @ X ) @ N2 )
% 5.27/5.63 @ at_bot_real
% 5.27/5.63 @ F5 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % filterlim_pow_at_bot_odd
% 5.27/5.63 thf(fact_10057_tendsto__arctan__at__bot,axiom,
% 5.27/5.63 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.27/5.63
% 5.27/5.63 % tendsto_arctan_at_bot
% 5.27/5.63 thf(fact_10058_tendsto__exp__limit__at__right,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( filterlim_real_real
% 5.27/5.63 @ ^ [Y5: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X4 @ Y5 ) ) @ ( divide_divide_real @ one_one_real @ Y5 ) )
% 5.27/5.63 @ ( topolo2815343760600316023s_real @ ( exp_real @ X4 ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % tendsto_exp_limit_at_right
% 5.27/5.63 thf(fact_10059_filterlim__tan__at__right,axiom,
% 5.27/5.63 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 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % filterlim_tan_at_right
% 5.27/5.63 thf(fact_10060_eventually__at__right__real,axiom,
% 5.27/5.63 ! [A: real,B: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( eventually_real
% 5.27/5.63 @ ^ [X: real] : ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.27/5.63 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % eventually_at_right_real
% 5.27/5.63 thf(fact_10061_tendsto__arcosh__at__left__1,axiom,
% 5.27/5.63 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % tendsto_arcosh_at_left_1
% 5.27/5.63 thf(fact_10062_artanh__real__at__right__1,axiom,
% 5.27/5.63 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 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % artanh_real_at_right_1
% 5.27/5.63 thf(fact_10063_atLeast__0,axiom,
% 5.27/5.63 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.27/5.63 = top_top_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast_0
% 5.27/5.63 thf(fact_10064_atLeast__Suc__greaterThan,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.27/5.63 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast_Suc_greaterThan
% 5.27/5.63 thf(fact_10065_decseq__bounded,axiom,
% 5.27/5.63 ! [X8: nat > real,B3: real] :
% 5.27/5.63 ( ( order_9091379641038594480t_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.27/5.63 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % decseq_bounded
% 5.27/5.63 thf(fact_10066_INT__greaterThan__UNIV,axiom,
% 5.27/5.63 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.27/5.63 = bot_bot_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % INT_greaterThan_UNIV
% 5.27/5.63 thf(fact_10067_greaterThan__0,axiom,
% 5.27/5.63 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.27/5.63 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThan_0
% 5.27/5.63 thf(fact_10068_greaterThan__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.27/5.63 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThan_Suc
% 5.27/5.63 thf(fact_10069_decseq__convergent,axiom,
% 5.27/5.63 ! [X8: nat > real,B3: real] :
% 5.27/5.63 ( ( order_9091379641038594480t_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.27/5.63 => ~ ! [L6: real] :
% 5.27/5.63 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.27/5.63 => ~ ! [I: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % decseq_convergent
% 5.27/5.63 thf(fact_10070_UN__atLeast__UNIV,axiom,
% 5.27/5.63 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.27/5.63 = top_top_set_nat ) ).
% 5.27/5.63
% 5.27/5.63 % UN_atLeast_UNIV
% 5.27/5.63 thf(fact_10071_atLeast__Suc,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.27/5.63 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast_Suc
% 5.27/5.63 thf(fact_10072_isCont__Lb__Ub,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_eq_real @ X5 @ B ) )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.27/5.63 => ? [L6: real,M9: real] :
% 5.27/5.63 ( ! [X2: real] :
% 5.27/5.63 ( ( ( ord_less_eq_real @ A @ X2 )
% 5.27/5.63 & ( ord_less_eq_real @ X2 @ B ) )
% 5.27/5.63 => ( ( ord_less_eq_real @ L6 @ ( F @ X2 ) )
% 5.27/5.63 & ( ord_less_eq_real @ ( F @ X2 ) @ M9 ) ) )
% 5.27/5.63 & ! [Y4: real] :
% 5.27/5.63 ( ( ( ord_less_eq_real @ L6 @ Y4 )
% 5.27/5.63 & ( ord_less_eq_real @ Y4 @ M9 ) )
% 5.27/5.63 => ? [X5: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_eq_real @ X5 @ B )
% 5.27/5.63 & ( ( F @ X5 )
% 5.27/5.63 = Y4 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_Lb_Ub
% 5.27/5.63 thf(fact_10073_less__eq,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi6264000038957366511cl_nat @ pred_nat ) )
% 5.27/5.63 = ( ord_less_nat @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_eq
% 5.27/5.63 thf(fact_10074_isCont__inverse__function2,axiom,
% 5.27/5.63 ! [A: real,X4: real,B: real,G: real > real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ B )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.27/5.63 => ( ( G @ ( F @ Z2 ) )
% 5.27/5.63 = Z2 ) ) )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_inverse_function2
% 5.27/5.63 thf(fact_10075_isCont__arcosh,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ one_one_real @ X4 )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_arcosh
% 5.27/5.63 thf(fact_10076_DERIV__inverse__function,axiom,
% 5.27/5.63 ! [F: real > real,D4: real,G: real > real,X4: real,A: real,B: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X4 ) @ top_top_set_real ) )
% 5.27/5.63 => ( ( D4 != zero_zero_real )
% 5.27/5.63 => ( ( ord_less_real @ A @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ B )
% 5.27/5.63 => ( ! [Y3: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Y3 )
% 5.27/5.63 => ( ( ord_less_real @ Y3 @ B )
% 5.27/5.63 => ( ( F @ ( G @ Y3 ) )
% 5.27/5.63 = Y3 ) ) )
% 5.27/5.63 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ G )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_inverse_function
% 5.27/5.63 thf(fact_10077_isCont__arccos,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arccos ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_arccos
% 5.27/5.63 thf(fact_10078_isCont__arcsin,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_arcsin
% 5.27/5.63 thf(fact_10079_LIM__less__bound,axiom,
% 5.27/5.63 ! [B: real,X4: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ B @ X4 )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ ( set_or1633881224788618240n_real @ B @ X4 ) )
% 5.27/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) ) )
% 5.27/5.63 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ F )
% 5.27/5.63 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % LIM_less_bound
% 5.27/5.63 thf(fact_10080_isCont__artanh,axiom,
% 5.27/5.63 ! [X4: real] :
% 5.27/5.63 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X4 )
% 5.27/5.63 => ( ( ord_less_real @ X4 @ one_one_real )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X4 @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_artanh
% 5.27/5.63 thf(fact_10081_isCont__inverse__function,axiom,
% 5.27/5.63 ! [D: real,X4: real,G: real > real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ zero_zero_real @ D )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 5.27/5.63 => ( ( G @ ( F @ Z2 ) )
% 5.27/5.63 = Z2 ) )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z2 @ X4 ) ) @ D )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X4 ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % isCont_inverse_function
% 5.27/5.63 thf(fact_10082_GMVT_H,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F4: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ F ) ) )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_eq_real @ Z2 @ B )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) @ G ) ) )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_real @ Z2 @ B )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ( ! [Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 => ( ( ord_less_real @ Z2 @ B )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ F @ ( F4 @ Z2 ) @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ? [C3: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ C3 )
% 5.27/5.63 & ( ord_less_real @ C3 @ B )
% 5.27/5.63 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C3 ) )
% 5.27/5.63 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F4 @ C3 ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % GMVT'
% 5.27/5.63 thf(fact_10083_GMVT,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_eq_real @ X5 @ B ) )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ F ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_real @ X5 @ B ) )
% 5.27/5.63 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ( ord_less_eq_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_eq_real @ X5 @ B ) )
% 5.27/5.63 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) @ G ) )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 & ( ord_less_real @ X5 @ B ) )
% 5.27/5.63 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) )
% 5.27/5.63 => ? [G_c: real,F_c: real,C3: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.27/5.63 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C3 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ A @ C3 )
% 5.27/5.63 & ( ord_less_real @ C3 @ B )
% 5.27/5.63 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.27/5.63 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % GMVT
% 5.27/5.63 thf(fact_10084_MVT,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ? [L4: real,Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 & ( ord_less_real @ Z2 @ B )
% 5.27/5.63 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) )
% 5.27/5.63 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.27/5.63 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % MVT
% 5.27/5.63 thf(fact_10085_continuous__on__arcosh_H,axiom,
% 5.27/5.63 ! [A2: set_real,F: real > real] :
% 5.27/5.63 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ A2 )
% 5.27/5.63 => ( ord_less_eq_real @ one_one_real @ ( F @ X5 ) ) )
% 5.27/5.63 => ( topolo5044208981011980120l_real @ A2
% 5.27/5.63 @ ^ [X: real] : ( arcosh_real @ ( F @ X ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_arcosh'
% 5.27/5.63 thf(fact_10086_continuous__image__closed__interval,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ? [C3: real,D3: real] :
% 5.27/5.63 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.27/5.63 = ( set_or1222579329274155063t_real @ C3 @ D3 ) )
% 5.27/5.63 & ( ord_less_eq_real @ C3 @ D3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % continuous_image_closed_interval
% 5.27/5.63 thf(fact_10087_continuous__on__arcosh,axiom,
% 5.27/5.63 ! [A2: set_real] :
% 5.27/5.63 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.27/5.63 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_arcosh
% 5.27/5.63 thf(fact_10088_continuous__on__arccos_H,axiom,
% 5.27/5.63 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_arccos'
% 5.27/5.63 thf(fact_10089_continuous__on__arcsin_H,axiom,
% 5.27/5.63 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_arcsin'
% 5.27/5.63 thf(fact_10090_continuous__on__artanh_H,axiom,
% 5.27/5.63 ! [A2: set_real,F: real > real] :
% 5.27/5.63 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( member_real @ X5 @ A2 )
% 5.27/5.63 => ( member_real @ ( F @ X5 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.27/5.63 => ( topolo5044208981011980120l_real @ A2
% 5.27/5.63 @ ^ [X: real] : ( artanh_real @ ( F @ X ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_artanh'
% 5.27/5.63 thf(fact_10091_Rolle__deriv,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( ( F @ A )
% 5.27/5.63 = ( F @ B ) )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ? [Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 & ( ord_less_real @ Z2 @ B )
% 5.27/5.63 & ( ( F4 @ Z2 )
% 5.27/5.63 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rolle_deriv
% 5.27/5.63 thf(fact_10092_mvt,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,F4: real > real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( has_de1759254742604945161l_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ~ ! [Xi: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Xi )
% 5.27/5.63 => ( ( ord_less_real @ Xi @ B )
% 5.27/5.63 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.27/5.63 != ( F4 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % mvt
% 5.27/5.63 thf(fact_10093_DERIV__pos__imp__increasing__open,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ zero_zero_real @ Y4 ) ) ) )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_pos_imp_increasing_open
% 5.27/5.63 thf(fact_10094_DERIV__neg__imp__decreasing__open,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ? [Y4: real] :
% 5.27/5.63 ( ( has_fi5821293074295781190e_real @ F @ Y4 @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 & ( ord_less_real @ Y4 @ zero_zero_real ) ) ) )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_neg_imp_decreasing_open
% 5.27/5.63 thf(fact_10095_DERIV__isconst__end,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ( ( F @ B )
% 5.27/5.63 = ( F @ A ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_isconst_end
% 5.27/5.63 thf(fact_10096_continuous__on__artanh,axiom,
% 5.27/5.63 ! [A2: set_real] :
% 5.27/5.63 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.27/5.63 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % continuous_on_artanh
% 5.27/5.63 thf(fact_10097_DERIV__isconst2,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real,X4: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ( ( ord_less_eq_real @ A @ X4 )
% 5.27/5.63 => ( ( ord_less_eq_real @ X4 @ B )
% 5.27/5.63 => ( ( F @ X4 )
% 5.27/5.63 = ( F @ A ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % DERIV_isconst2
% 5.27/5.63 thf(fact_10098_Rolle,axiom,
% 5.27/5.63 ! [A: real,B: real,F: real > real] :
% 5.27/5.63 ( ( ord_less_real @ A @ B )
% 5.27/5.63 => ( ( ( F @ A )
% 5.27/5.63 = ( F @ B ) )
% 5.27/5.63 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.27/5.63 => ( ! [X5: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ X5 )
% 5.27/5.63 => ( ( ord_less_real @ X5 @ B )
% 5.27/5.63 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) ) ) )
% 5.27/5.63 => ? [Z2: real] :
% 5.27/5.63 ( ( ord_less_real @ A @ Z2 )
% 5.27/5.63 & ( ord_less_real @ Z2 @ B )
% 5.27/5.63 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z2 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rolle
% 5.27/5.63 thf(fact_10099_mono__Suc,axiom,
% 5.27/5.63 order_mono_nat_nat @ suc ).
% 5.27/5.63
% 5.27/5.63 % mono_Suc
% 5.27/5.63 thf(fact_10100_mono__times__nat,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( order_mono_nat_nat @ ( times_times_nat @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % mono_times_nat
% 5.27/5.63 thf(fact_10101_incseq__bounded,axiom,
% 5.27/5.63 ! [X8: nat > real,B3: real] :
% 5.27/5.63 ( ( order_mono_nat_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.27/5.63 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % incseq_bounded
% 5.27/5.63 thf(fact_10102_incseq__convergent,axiom,
% 5.27/5.63 ! [X8: nat > real,B3: real] :
% 5.27/5.63 ( ( order_mono_nat_real @ X8 )
% 5.27/5.63 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.27/5.63 => ~ ! [L6: real] :
% 5.27/5.63 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.27/5.63 => ~ ! [I: nat] : ( ord_less_eq_real @ ( X8 @ I ) @ L6 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % incseq_convergent
% 5.27/5.63 thf(fact_10103_mono__ge2__power__minus__self,axiom,
% 5.27/5.63 ! [K: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.27/5.63 => ( order_mono_nat_nat
% 5.27/5.63 @ ^ [M6: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M6 ) @ M6 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % mono_ge2_power_minus_self
% 5.27/5.63 thf(fact_10104_nonneg__incseq__Bseq__subseq__iff,axiom,
% 5.27/5.63 ! [F: nat > real,G: nat > nat] :
% 5.27/5.63 ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.27/5.63 => ( ( order_mono_nat_real @ F )
% 5.27/5.63 => ( ( order_5726023648592871131at_nat @ G )
% 5.27/5.63 => ( ( bfun_nat_real
% 5.27/5.63 @ ^ [X: nat] : ( F @ ( G @ X ) )
% 5.27/5.63 @ at_top_nat )
% 5.27/5.63 = ( bfun_nat_real @ F @ at_top_nat ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nonneg_incseq_Bseq_subseq_iff
% 5.27/5.63 thf(fact_10105_strict__mono__imp__increasing,axiom,
% 5.27/5.63 ! [F: nat > nat,N2: nat] :
% 5.27/5.63 ( ( order_5726023648592871131at_nat @ F )
% 5.27/5.63 => ( ord_less_eq_nat @ N2 @ ( F @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % strict_mono_imp_increasing
% 5.27/5.63 thf(fact_10106_inj__sgn__power,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( inj_on_real_real
% 5.27/5.63 @ ^ [Y5: real] : ( times_times_real @ ( sgn_sgn_real @ Y5 ) @ ( power_power_real @ ( abs_abs_real @ Y5 ) @ N2 ) )
% 5.27/5.63 @ top_top_set_real ) ) ).
% 5.27/5.63
% 5.27/5.63 % inj_sgn_power
% 5.27/5.63 thf(fact_10107_log__inj,axiom,
% 5.27/5.63 ! [B: real] :
% 5.27/5.63 ( ( ord_less_real @ one_one_real @ B )
% 5.27/5.63 => ( inj_on_real_real @ ( log @ B ) @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % log_inj
% 5.27/5.63 thf(fact_10108_pos__deriv__imp__strict__mono,axiom,
% 5.27/5.63 ! [F: real > real,F4: real > real] :
% 5.27/5.63 ( ! [X5: real] : ( has_fi5821293074295781190e_real @ F @ ( F4 @ X5 ) @ ( topolo2177554685111907308n_real @ X5 @ top_top_set_real ) )
% 5.27/5.63 => ( ! [X5: real] : ( ord_less_real @ zero_zero_real @ ( F4 @ X5 ) )
% 5.27/5.63 => ( order_7092887310737990675l_real @ F ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % pos_deriv_imp_strict_mono
% 5.27/5.63 thf(fact_10109_inj__on__diff__nat,axiom,
% 5.27/5.63 ! [N4: set_nat,K: nat] :
% 5.27/5.63 ( ! [N3: nat] :
% 5.27/5.63 ( ( member_nat @ N3 @ N4 )
% 5.27/5.63 => ( ord_less_eq_nat @ K @ N3 ) )
% 5.27/5.63 => ( inj_on_nat_nat
% 5.27/5.63 @ ^ [N: nat] : ( minus_minus_nat @ N @ K )
% 5.27/5.63 @ N4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % inj_on_diff_nat
% 5.27/5.63 thf(fact_10110_inj__Suc,axiom,
% 5.27/5.63 ! [N4: set_nat] : ( inj_on_nat_nat @ suc @ N4 ) ).
% 5.27/5.63
% 5.27/5.63 % inj_Suc
% 5.27/5.63 thf(fact_10111_inj__on__char__of__nat,axiom,
% 5.27/5.63 inj_on_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % inj_on_char_of_nat
% 5.27/5.63 thf(fact_10112_suminf__reindex,axiom,
% 5.27/5.63 ! [F: nat > real,G: nat > nat] :
% 5.27/5.63 ( ( summable_real @ F )
% 5.27/5.63 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.27/5.63 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.27/5.63 => ( ! [X5: nat] :
% 5.27/5.63 ( ~ ( member_nat @ X5 @ ( image_nat_nat @ G @ top_top_set_nat ) )
% 5.27/5.63 => ( ( F @ X5 )
% 5.27/5.63 = zero_zero_real ) )
% 5.27/5.63 => ( ( suminf_real @ ( comp_nat_real_nat @ F @ G ) )
% 5.27/5.63 = ( suminf_real @ F ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % suminf_reindex
% 5.27/5.63 thf(fact_10113_summable__reindex,axiom,
% 5.27/5.63 ! [F: nat > real,G: nat > nat] :
% 5.27/5.63 ( ( summable_real @ F )
% 5.27/5.63 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.27/5.63 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.27/5.63 => ( summable_real @ ( comp_nat_real_nat @ F @ G ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % summable_reindex
% 5.27/5.63 thf(fact_10114_suminf__reindex__mono,axiom,
% 5.27/5.63 ! [F: nat > real,G: nat > nat] :
% 5.27/5.63 ( ( summable_real @ F )
% 5.27/5.63 => ( ( inj_on_nat_nat @ G @ top_top_set_nat )
% 5.27/5.63 => ( ! [X5: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ X5 ) )
% 5.27/5.63 => ( ord_less_eq_real @ ( suminf_real @ ( comp_nat_real_nat @ F @ G ) ) @ ( suminf_real @ F ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % suminf_reindex_mono
% 5.27/5.63 thf(fact_10115_card_Ocomp__fun__commute__on,axiom,
% 5.27/5.63 ( ( comp_nat_nat_nat @ suc @ suc )
% 5.27/5.63 = ( comp_nat_nat_nat @ suc @ suc ) ) ).
% 5.27/5.63
% 5.27/5.63 % card.comp_fun_commute_on
% 5.27/5.63 thf(fact_10116_pred__nat__trancl__eq__le,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( member8440522571783428010at_nat @ ( product_Pair_nat_nat @ M @ N2 ) @ ( transi2905341329935302413cl_nat @ pred_nat ) )
% 5.27/5.63 = ( ord_less_eq_nat @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % pred_nat_trancl_eq_le
% 5.27/5.63 thf(fact_10117_uniformity__real__def,axiom,
% 5.27/5.63 ( topolo1511823702728130853y_real
% 5.27/5.63 = ( comple2936214249959783750l_real
% 5.27/5.63 @ ( image_2178119161166701260l_real
% 5.27/5.63 @ ^ [E3: real] :
% 5.27/5.63 ( princi6114159922880469582l_real
% 5.27/5.63 @ ( collec3799799289383736868l_real
% 5.27/5.63 @ ( produc5414030515140494994real_o
% 5.27/5.63 @ ^ [X: real,Y5: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X @ Y5 ) @ E3 ) ) ) )
% 5.27/5.63 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % uniformity_real_def
% 5.27/5.63 thf(fact_10118_uniformity__complex__def,axiom,
% 5.27/5.63 ( topolo896644834953643431omplex
% 5.27/5.63 = ( comple8358262395181532106omplex
% 5.27/5.63 @ ( image_5971271580939081552omplex
% 5.27/5.63 @ ^ [E3: real] :
% 5.27/5.63 ( princi3496590319149328850omplex
% 5.27/5.63 @ ( collec8663557070575231912omplex
% 5.27/5.63 @ ( produc6771430404735790350plex_o
% 5.27/5.63 @ ^ [X: complex,Y5: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X @ Y5 ) @ E3 ) ) ) )
% 5.27/5.63 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % uniformity_complex_def
% 5.27/5.63 thf(fact_10119_rat__floor__lemma,axiom,
% 5.27/5.63 ! [A: int,B: int] :
% 5.27/5.63 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.27/5.63 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % rat_floor_lemma
% 5.27/5.63 thf(fact_10120_less__rat,axiom,
% 5.27/5.63 ! [B: int,D: int,A: int,C: int] :
% 5.27/5.63 ( ( B != zero_zero_int )
% 5.27/5.63 => ( ( D != zero_zero_int )
% 5.27/5.63 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.27/5.63 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_rat
% 5.27/5.63 thf(fact_10121_le__rat,axiom,
% 5.27/5.63 ! [B: int,D: int,A: int,C: int] :
% 5.27/5.63 ( ( B != zero_zero_int )
% 5.27/5.63 => ( ( D != zero_zero_int )
% 5.27/5.63 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.27/5.63 = ( 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 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % le_rat
% 5.27/5.63 thf(fact_10122_Rat__induct__pos,axiom,
% 5.27/5.63 ! [P: rat > $o,Q3: rat] :
% 5.27/5.63 ( ! [A5: int,B5: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.27/5.63 => ( P @ ( fract @ A5 @ B5 ) ) )
% 5.27/5.63 => ( P @ Q3 ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rat_induct_pos
% 5.27/5.63 thf(fact_10123_Fract__less__zero__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.27/5.63 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Fract_less_zero_iff
% 5.27/5.63 thf(fact_10124_zero__less__Fract__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.27/5.63 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % zero_less_Fract_iff
% 5.27/5.63 thf(fact_10125_Fract__less__one__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.27/5.63 = ( ord_less_int @ A @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Fract_less_one_iff
% 5.27/5.63 thf(fact_10126_one__less__Fract__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.27/5.63 = ( ord_less_int @ B @ A ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % one_less_Fract_iff
% 5.27/5.63 thf(fact_10127_Fract__le__zero__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.27/5.63 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Fract_le_zero_iff
% 5.27/5.63 thf(fact_10128_zero__le__Fract__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.27/5.63 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % zero_le_Fract_iff
% 5.27/5.63 thf(fact_10129_Fract__le__one__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.27/5.63 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Fract_le_one_iff
% 5.27/5.63 thf(fact_10130_one__le__Fract__iff,axiom,
% 5.27/5.63 ! [B: int,A: int] :
% 5.27/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.27/5.63 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.27/5.63 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % one_le_Fract_iff
% 5.27/5.63 thf(fact_10131_positive__rat,axiom,
% 5.27/5.63 ! [A: int,B: int] :
% 5.27/5.63 ( ( positive @ ( fract @ A @ B ) )
% 5.27/5.63 = ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % positive_rat
% 5.27/5.63 thf(fact_10132_less__rat__def,axiom,
% 5.27/5.63 ( ord_less_rat
% 5.27/5.63 = ( ^ [X: rat,Y5: rat] : ( positive @ ( minus_minus_rat @ Y5 @ X ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % less_rat_def
% 5.27/5.63 thf(fact_10133_Rat_Opositive_Orep__eq,axiom,
% 5.27/5.63 ( positive
% 5.27/5.63 = ( ^ [X: rat] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ ( rep_Rat @ X ) ) @ ( product_snd_int_int @ ( rep_Rat @ X ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Rat.positive.rep_eq
% 5.27/5.63 thf(fact_10134_min__Suc__Suc,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ ( suc @ M ) @ ( suc @ N2 ) )
% 5.27/5.63 = ( suc @ ( ord_min_nat @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_Suc_Suc
% 5.27/5.63 thf(fact_10135_min__0R,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ N2 @ zero_zero_nat )
% 5.27/5.63 = zero_zero_nat ) ).
% 5.27/5.63
% 5.27/5.63 % min_0R
% 5.27/5.63 thf(fact_10136_min__0L,axiom,
% 5.27/5.63 ! [N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 = zero_zero_nat ) ).
% 5.27/5.63
% 5.27/5.63 % min_0L
% 5.27/5.63 thf(fact_10137_min__Suc__numeral,axiom,
% 5.27/5.63 ! [N2: nat,K: num] :
% 5.27/5.63 ( ( ord_min_nat @ ( suc @ N2 ) @ ( numeral_numeral_nat @ K ) )
% 5.27/5.63 = ( suc @ ( ord_min_nat @ N2 @ ( pred_numeral @ K ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_Suc_numeral
% 5.27/5.63 thf(fact_10138_min__numeral__Suc,axiom,
% 5.27/5.63 ! [K: num,N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N2 ) )
% 5.27/5.63 = ( suc @ ( ord_min_nat @ ( pred_numeral @ K ) @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_numeral_Suc
% 5.27/5.63 thf(fact_10139_inf__nat__def,axiom,
% 5.27/5.63 inf_inf_nat = ord_min_nat ).
% 5.27/5.63
% 5.27/5.63 % inf_nat_def
% 5.27/5.63 thf(fact_10140_nat__mult__min__left,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.63 ( ( times_times_nat @ ( ord_min_nat @ M @ N2 ) @ Q3 )
% 5.27/5.63 = ( ord_min_nat @ ( times_times_nat @ M @ Q3 ) @ ( times_times_nat @ N2 @ Q3 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_mult_min_left
% 5.27/5.63 thf(fact_10141_nat__mult__min__right,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,Q3: nat] :
% 5.27/5.63 ( ( times_times_nat @ M @ ( ord_min_nat @ N2 @ Q3 ) )
% 5.27/5.63 = ( ord_min_nat @ ( times_times_nat @ M @ N2 ) @ ( times_times_nat @ M @ Q3 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nat_mult_min_right
% 5.27/5.63 thf(fact_10142_min__diff,axiom,
% 5.27/5.63 ! [M: nat,I2: nat,N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ ( minus_minus_nat @ M @ I2 ) @ ( minus_minus_nat @ N2 @ I2 ) )
% 5.27/5.63 = ( minus_minus_nat @ ( ord_min_nat @ M @ N2 ) @ I2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_diff
% 5.27/5.63 thf(fact_10143_concat__bit__assoc__sym,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,K: int,L: int,R3: int] :
% 5.27/5.63 ( ( bit_concat_bit @ M @ ( bit_concat_bit @ N2 @ K @ L ) @ R3 )
% 5.27/5.63 = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_concat_bit @ ( minus_minus_nat @ M @ N2 ) @ L @ R3 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % concat_bit_assoc_sym
% 5.27/5.63 thf(fact_10144_take__bit__concat__bit__eq,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,K: int,L: int] :
% 5.27/5.63 ( ( bit_se2923211474154528505it_int @ M @ ( bit_concat_bit @ N2 @ K @ L ) )
% 5.27/5.63 = ( bit_concat_bit @ ( ord_min_nat @ M @ N2 ) @ K @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ M @ N2 ) @ L ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_bit_concat_bit_eq
% 5.27/5.63 thf(fact_10145_min__Suc1,axiom,
% 5.27/5.63 ! [N2: nat,M: nat] :
% 5.27/5.63 ( ( ord_min_nat @ ( suc @ N2 ) @ M )
% 5.27/5.63 = ( case_nat_nat @ zero_zero_nat
% 5.27/5.63 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ N2 @ M3 ) )
% 5.27/5.63 @ M ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_Suc1
% 5.27/5.63 thf(fact_10146_min__Suc2,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_min_nat @ M @ ( suc @ N2 ) )
% 5.27/5.63 = ( case_nat_nat @ zero_zero_nat
% 5.27/5.63 @ ^ [M3: nat] : ( suc @ ( ord_min_nat @ M3 @ N2 ) )
% 5.27/5.63 @ M ) ) ).
% 5.27/5.63
% 5.27/5.63 % min_Suc2
% 5.27/5.63 thf(fact_10147_min__enat__simps_I2_J,axiom,
% 5.27/5.63 ! [Q3: extended_enat] :
% 5.27/5.63 ( ( ord_mi8085742599997312461d_enat @ Q3 @ zero_z5237406670263579293d_enat )
% 5.27/5.63 = zero_z5237406670263579293d_enat ) ).
% 5.27/5.63
% 5.27/5.63 % min_enat_simps(2)
% 5.27/5.63 thf(fact_10148_min__enat__simps_I3_J,axiom,
% 5.27/5.63 ! [Q3: extended_enat] :
% 5.27/5.63 ( ( ord_mi8085742599997312461d_enat @ zero_z5237406670263579293d_enat @ Q3 )
% 5.27/5.63 = zero_z5237406670263579293d_enat ) ).
% 5.27/5.63
% 5.27/5.63 % min_enat_simps(3)
% 5.27/5.63 thf(fact_10149_inf__enat__def,axiom,
% 5.27/5.63 inf_in1870772243966228564d_enat = ord_mi8085742599997312461d_enat ).
% 5.27/5.63
% 5.27/5.63 % inf_enat_def
% 5.27/5.63 thf(fact_10150_num__of__integer__code,axiom,
% 5.27/5.63 ( code_num_of_integer
% 5.27/5.63 = ( ^ [K3: code_integer] :
% 5.27/5.63 ( if_num @ ( ord_le3102999989581377725nteger @ K3 @ one_one_Code_integer ) @ one
% 5.27/5.63 @ ( produc7336495610019696514er_num
% 5.27/5.63 @ ^ [L2: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L2 ) @ ( code_num_of_integer @ L2 ) ) @ one ) )
% 5.27/5.63 @ ( code_divmod_integer @ K3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % num_of_integer_code
% 5.27/5.63 thf(fact_10151_card__le__Suc__Max,axiom,
% 5.27/5.63 ! [S2: set_nat] :
% 5.27/5.63 ( ( finite_finite_nat @ S2 )
% 5.27/5.63 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_le_Suc_Max
% 5.27/5.63 thf(fact_10152_divide__nat__def,axiom,
% 5.27/5.63 ( divide_divide_nat
% 5.27/5.63 = ( ^ [M6: nat,N: nat] :
% 5.27/5.63 ( if_nat @ ( N = zero_zero_nat ) @ zero_zero_nat
% 5.27/5.63 @ ( lattic8265883725875713057ax_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [K3: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K3 @ N ) @ M6 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % divide_nat_def
% 5.27/5.63 thf(fact_10153_gcd__is__Max__divisors__nat,axiom,
% 5.27/5.63 ! [N2: nat,M: nat] :
% 5.27/5.63 ( ( ord_less_nat @ zero_zero_nat @ N2 )
% 5.27/5.63 => ( ( gcd_gcd_nat @ M @ N2 )
% 5.27/5.63 = ( lattic8265883725875713057ax_nat
% 5.27/5.63 @ ( collect_nat
% 5.27/5.63 @ ^ [D5: nat] :
% 5.27/5.63 ( ( dvd_dvd_nat @ D5 @ M )
% 5.27/5.63 & ( dvd_dvd_nat @ D5 @ N2 ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % gcd_is_Max_divisors_nat
% 5.27/5.63 thf(fact_10154_upt__rec__numeral,axiom,
% 5.27/5.63 ! [M: num,N2: num] :
% 5.27/5.63 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.63 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.63 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N2 ) ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.63 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N2 ) )
% 5.27/5.63 = nil_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_rec_numeral
% 5.27/5.63 thf(fact_10155_remdups__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( remdups_nat @ ( upt @ M @ N2 ) )
% 5.27/5.63 = ( upt @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % remdups_upt
% 5.27/5.63 thf(fact_10156_tl__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( tl_nat @ ( upt @ M @ N2 ) )
% 5.27/5.63 = ( upt @ ( suc @ M ) @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % tl_upt
% 5.27/5.63 thf(fact_10157_hd__upt,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.27/5.63 => ( ( hd_nat @ ( upt @ I2 @ J ) )
% 5.27/5.63 = I2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % hd_upt
% 5.27/5.63 thf(fact_10158_drop__upt,axiom,
% 5.27/5.63 ! [M: nat,I2: nat,J: nat] :
% 5.27/5.63 ( ( drop_nat @ M @ ( upt @ I2 @ J ) )
% 5.27/5.63 = ( upt @ ( plus_plus_nat @ I2 @ M ) @ J ) ) ).
% 5.27/5.63
% 5.27/5.63 % drop_upt
% 5.27/5.63 thf(fact_10159_length__upt,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( size_size_list_nat @ ( upt @ I2 @ J ) )
% 5.27/5.63 = ( minus_minus_nat @ J @ I2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % length_upt
% 5.27/5.63 thf(fact_10160_take__upt,axiom,
% 5.27/5.63 ! [I2: nat,M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I2 @ M ) @ N2 )
% 5.27/5.63 => ( ( take_nat @ M @ ( upt @ I2 @ N2 ) )
% 5.27/5.63 = ( upt @ I2 @ ( plus_plus_nat @ I2 @ M ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % take_upt
% 5.27/5.63 thf(fact_10161_upt__conv__Nil,axiom,
% 5.27/5.63 ! [J: nat,I2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ J @ I2 )
% 5.27/5.63 => ( ( upt @ I2 @ J )
% 5.27/5.63 = nil_nat ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_conv_Nil
% 5.27/5.63 thf(fact_10162_sorted__list__of__set__range,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N2 ) )
% 5.27/5.63 = ( upt @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_list_of_set_range
% 5.27/5.63 thf(fact_10163_upt__eq__Nil__conv,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ( upt @ I2 @ J )
% 5.27/5.63 = nil_nat )
% 5.27/5.63 = ( ( J = zero_zero_nat )
% 5.27/5.63 | ( ord_less_eq_nat @ J @ I2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_eq_Nil_conv
% 5.27/5.63 thf(fact_10164_nth__upt,axiom,
% 5.27/5.63 ! [I2: nat,K: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_nat @ ( plus_plus_nat @ I2 @ K ) @ J )
% 5.27/5.63 => ( ( nth_nat @ ( upt @ I2 @ J ) @ K )
% 5.27/5.63 = ( plus_plus_nat @ I2 @ K ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % nth_upt
% 5.27/5.63 thf(fact_10165_greaterThanLessThan__upt,axiom,
% 5.27/5.63 ( set_or5834768355832116004an_nat
% 5.27/5.63 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ M6 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThanLessThan_upt
% 5.27/5.63 thf(fact_10166_atLeastLessThan__upt,axiom,
% 5.27/5.63 ( set_or4665077453230672383an_nat
% 5.27/5.63 = ( ^ [I3: nat,J3: nat] : ( set_nat2 @ ( upt @ I3 @ J3 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastLessThan_upt
% 5.27/5.63 thf(fact_10167_atLeastAtMost__upt,axiom,
% 5.27/5.63 ( set_or1269000886237332187st_nat
% 5.27/5.63 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ N @ ( suc @ M6 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeastAtMost_upt
% 5.27/5.63 thf(fact_10168_greaterThanAtMost__upt,axiom,
% 5.27/5.63 ( set_or6659071591806873216st_nat
% 5.27/5.63 = ( ^ [N: nat,M6: nat] : ( set_nat2 @ ( upt @ ( suc @ N ) @ ( suc @ M6 ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % greaterThanAtMost_upt
% 5.27/5.63 thf(fact_10169_atLeast__upt,axiom,
% 5.27/5.63 ( set_ord_lessThan_nat
% 5.27/5.63 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atLeast_upt
% 5.27/5.63 thf(fact_10170_upt__conv__Cons__Cons,axiom,
% 5.27/5.63 ! [M: nat,N2: nat,Ns: list_nat,Q3: nat] :
% 5.27/5.63 ( ( ( cons_nat @ M @ ( cons_nat @ N2 @ Ns ) )
% 5.27/5.63 = ( upt @ M @ Q3 ) )
% 5.27/5.63 = ( ( cons_nat @ N2 @ Ns )
% 5.27/5.63 = ( upt @ ( suc @ M ) @ Q3 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_conv_Cons_Cons
% 5.27/5.63 thf(fact_10171_distinct__upt,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] : ( distinct_nat @ ( upt @ I2 @ J ) ) ).
% 5.27/5.63
% 5.27/5.63 % distinct_upt
% 5.27/5.63 thf(fact_10172_upt__0,axiom,
% 5.27/5.63 ! [I2: nat] :
% 5.27/5.63 ( ( upt @ I2 @ zero_zero_nat )
% 5.27/5.63 = nil_nat ) ).
% 5.27/5.63
% 5.27/5.63 % upt_0
% 5.27/5.63 thf(fact_10173_atMost__upto,axiom,
% 5.27/5.63 ( set_ord_atMost_nat
% 5.27/5.63 = ( ^ [N: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % atMost_upto
% 5.27/5.63 thf(fact_10174_upt__conv__Cons,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_nat @ I2 @ J )
% 5.27/5.63 => ( ( upt @ I2 @ J )
% 5.27/5.63 = ( cons_nat @ I2 @ ( upt @ ( suc @ I2 ) @ J ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_conv_Cons
% 5.27/5.63 thf(fact_10175_upt__add__eq__append,axiom,
% 5.27/5.63 ! [I2: nat,J: nat,K: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.63 => ( ( upt @ I2 @ ( plus_plus_nat @ J @ K ) )
% 5.27/5.63 = ( append_nat @ ( upt @ I2 @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_add_eq_append
% 5.27/5.63 thf(fact_10176_upt__eq__Cons__conv,axiom,
% 5.27/5.63 ! [I2: nat,J: nat,X4: nat,Xs: list_nat] :
% 5.27/5.63 ( ( ( upt @ I2 @ J )
% 5.27/5.63 = ( cons_nat @ X4 @ Xs ) )
% 5.27/5.63 = ( ( ord_less_nat @ I2 @ J )
% 5.27/5.63 & ( I2 = X4 )
% 5.27/5.63 & ( ( upt @ ( plus_plus_nat @ I2 @ one_one_nat ) @ J )
% 5.27/5.63 = Xs ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_eq_Cons_conv
% 5.27/5.63 thf(fact_10177_upt__rec,axiom,
% 5.27/5.63 ( upt
% 5.27/5.63 = ( ^ [I3: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I3 @ J3 ) @ ( cons_nat @ I3 @ ( upt @ ( suc @ I3 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_rec
% 5.27/5.63 thf(fact_10178_upt__Suc,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.63 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.27/5.63 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.27/5.63 & ( ~ ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.63 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.27/5.63 = nil_nat ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_Suc
% 5.27/5.63 thf(fact_10179_upt__Suc__append,axiom,
% 5.27/5.63 ! [I2: nat,J: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ I2 @ J )
% 5.27/5.63 => ( ( upt @ I2 @ ( suc @ J ) )
% 5.27/5.63 = ( append_nat @ ( upt @ I2 @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % upt_Suc_append
% 5.27/5.63 thf(fact_10180_sum__list__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ M @ N2 )
% 5.27/5.63 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N2 ) )
% 5.27/5.63 = ( groups3542108847815614940at_nat
% 5.27/5.63 @ ^ [X: nat] : X
% 5.27/5.63 @ ( set_or4665077453230672383an_nat @ M @ N2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sum_list_upt
% 5.27/5.63 thf(fact_10181_map__Suc__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( map_nat_nat @ suc @ ( upt @ M @ N2 ) )
% 5.27/5.63 = ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % map_Suc_upt
% 5.27/5.63 thf(fact_10182_map__add__upt,axiom,
% 5.27/5.63 ! [N2: nat,M: nat] :
% 5.27/5.63 ( ( map_nat_nat
% 5.27/5.63 @ ^ [I3: nat] : ( plus_plus_nat @ I3 @ N2 )
% 5.27/5.63 @ ( upt @ zero_zero_nat @ M ) )
% 5.27/5.63 = ( upt @ N2 @ ( plus_plus_nat @ M @ N2 ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % map_add_upt
% 5.27/5.63 thf(fact_10183_map__decr__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] :
% 5.27/5.63 ( ( map_nat_nat
% 5.27/5.63 @ ^ [N: nat] : ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.27/5.63 @ ( upt @ ( suc @ M ) @ ( suc @ N2 ) ) )
% 5.27/5.63 = ( upt @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % map_decr_upt
% 5.27/5.63 thf(fact_10184_Divides_Oadjust__div__def,axiom,
% 5.27/5.63 ( adjust_div
% 5.27/5.63 = ( produc8211389475949308722nt_int
% 5.27/5.63 @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % Divides.adjust_div_def
% 5.27/5.63 thf(fact_10185_card__length__sum__list__rec,axiom,
% 5.27/5.63 ! [M: nat,N4: nat] :
% 5.27/5.63 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.27/5.63 => ( ( finite_card_list_nat
% 5.27/5.63 @ ( collect_list_nat
% 5.27/5.63 @ ^ [L2: list_nat] :
% 5.27/5.63 ( ( ( size_size_list_nat @ L2 )
% 5.27/5.63 = M )
% 5.27/5.63 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.27/5.63 = N4 ) ) ) )
% 5.27/5.63 = ( plus_plus_nat
% 5.27/5.63 @ ( finite_card_list_nat
% 5.27/5.63 @ ( collect_list_nat
% 5.27/5.63 @ ^ [L2: list_nat] :
% 5.27/5.63 ( ( ( size_size_list_nat @ L2 )
% 5.27/5.63 = ( minus_minus_nat @ M @ one_one_nat ) )
% 5.27/5.63 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.27/5.63 = N4 ) ) ) )
% 5.27/5.63 @ ( finite_card_list_nat
% 5.27/5.63 @ ( collect_list_nat
% 5.27/5.63 @ ^ [L2: list_nat] :
% 5.27/5.63 ( ( ( size_size_list_nat @ L2 )
% 5.27/5.63 = M )
% 5.27/5.63 & ( ( plus_plus_nat @ ( groups4561878855575611511st_nat @ L2 ) @ one_one_nat )
% 5.27/5.63 = N4 ) ) ) ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_length_sum_list_rec
% 5.27/5.63 thf(fact_10186_card__length__sum__list,axiom,
% 5.27/5.63 ! [M: nat,N4: nat] :
% 5.27/5.63 ( ( finite_card_list_nat
% 5.27/5.63 @ ( collect_list_nat
% 5.27/5.63 @ ^ [L2: list_nat] :
% 5.27/5.63 ( ( ( size_size_list_nat @ L2 )
% 5.27/5.63 = M )
% 5.27/5.63 & ( ( groups4561878855575611511st_nat @ L2 )
% 5.27/5.63 = N4 ) ) ) )
% 5.27/5.63 = ( binomial @ ( minus_minus_nat @ ( plus_plus_nat @ N4 @ M ) @ one_one_nat ) @ N4 ) ) ).
% 5.27/5.63
% 5.27/5.63 % card_length_sum_list
% 5.27/5.63 thf(fact_10187_sorted__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_eq_nat @ ( upt @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_upt
% 5.27/5.63 thf(fact_10188_sorted__wrt__upt,axiom,
% 5.27/5.63 ! [M: nat,N2: nat] : ( sorted_wrt_nat @ ord_less_nat @ ( upt @ M @ N2 ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_wrt_upt
% 5.27/5.63 thf(fact_10189_sorted__wrt__less__idx,axiom,
% 5.27/5.63 ! [Ns: list_nat,I2: nat] :
% 5.27/5.63 ( ( sorted_wrt_nat @ ord_less_nat @ Ns )
% 5.27/5.63 => ( ( ord_less_nat @ I2 @ ( size_size_list_nat @ Ns ) )
% 5.27/5.63 => ( ord_less_eq_nat @ I2 @ ( nth_nat @ Ns @ I2 ) ) ) ) ).
% 5.27/5.63
% 5.27/5.63 % sorted_wrt_less_idx
% 5.27/5.64 thf(fact_10190_sorted__wrt__upto,axiom,
% 5.27/5.64 ! [I2: int,J: int] : ( sorted_wrt_int @ ord_less_int @ ( upto @ I2 @ J ) ) ).
% 5.27/5.64
% 5.27/5.64 % sorted_wrt_upto
% 5.27/5.64 thf(fact_10191_sorted__upto,axiom,
% 5.27/5.64 ! [M: int,N2: int] : ( sorted_wrt_int @ ord_less_eq_int @ ( upto @ M @ N2 ) ) ).
% 5.27/5.64
% 5.27/5.64 % sorted_upto
% 5.27/5.64 thf(fact_10192_pairs__le__eq__Sigma,axiom,
% 5.27/5.64 ! [M: nat] :
% 5.27/5.64 ( ( collec3392354462482085612at_nat
% 5.27/5.64 @ ( produc6081775807080527818_nat_o
% 5.27/5.64 @ ^ [I3: nat,J3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ I3 @ J3 ) @ M ) ) )
% 5.27/5.64 = ( produc457027306803732586at_nat @ ( set_ord_atMost_nat @ M )
% 5.27/5.64 @ ^ [R5: nat] : ( set_ord_atMost_nat @ ( minus_minus_nat @ M @ R5 ) ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % pairs_le_eq_Sigma
% 5.27/5.64 thf(fact_10193_prod__encode__prod__decode__aux,axiom,
% 5.27/5.64 ! [K: nat,M: nat] :
% 5.27/5.64 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.27/5.64 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.27/5.64
% 5.27/5.64 % prod_encode_prod_decode_aux
% 5.27/5.64 thf(fact_10194_le__prod__encode__1,axiom,
% 5.27/5.64 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % le_prod_encode_1
% 5.27/5.64 thf(fact_10195_le__prod__encode__2,axiom,
% 5.27/5.64 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % le_prod_encode_2
% 5.27/5.64 thf(fact_10196_prod__encode__def,axiom,
% 5.27/5.64 ( nat_prod_encode
% 5.27/5.64 = ( produc6842872674320459806at_nat
% 5.27/5.64 @ ^ [M6: nat,N: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M6 @ N ) ) @ M6 ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % prod_encode_def
% 5.27/5.64 thf(fact_10197_list__encode_Oelims,axiom,
% 5.27/5.64 ! [X4: list_nat,Y: nat] :
% 5.27/5.64 ( ( ( nat_list_encode @ X4 )
% 5.27/5.64 = Y )
% 5.27/5.64 => ( ( ( X4 = nil_nat )
% 5.27/5.64 => ( Y != zero_zero_nat ) )
% 5.27/5.64 => ~ ! [X5: nat,Xs2: list_nat] :
% 5.27/5.64 ( ( X4
% 5.27/5.64 = ( cons_nat @ X5 @ Xs2 ) )
% 5.27/5.64 => ( Y
% 5.27/5.64 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) ) ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % list_encode.elims
% 5.27/5.64 thf(fact_10198_list__encode_Osimps_I2_J,axiom,
% 5.27/5.64 ! [X4: nat,Xs: list_nat] :
% 5.27/5.64 ( ( nat_list_encode @ ( cons_nat @ X4 @ Xs ) )
% 5.27/5.64 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X4 @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % list_encode.simps(2)
% 5.27/5.64 thf(fact_10199_list__encode_Opelims,axiom,
% 5.27/5.64 ! [X4: list_nat,Y: nat] :
% 5.27/5.64 ( ( ( nat_list_encode @ X4 )
% 5.27/5.64 = Y )
% 5.27/5.64 => ( ( accp_list_nat @ nat_list_encode_rel @ X4 )
% 5.27/5.64 => ( ( ( X4 = nil_nat )
% 5.27/5.64 => ( ( Y = zero_zero_nat )
% 5.27/5.64 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.27/5.64 => ~ ! [X5: nat,Xs2: list_nat] :
% 5.27/5.64 ( ( X4
% 5.27/5.64 = ( cons_nat @ X5 @ Xs2 ) )
% 5.27/5.64 => ( ( Y
% 5.27/5.64 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X5 @ ( nat_list_encode @ Xs2 ) ) ) ) )
% 5.27/5.64 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X5 @ Xs2 ) ) ) ) ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % list_encode.pelims
% 5.27/5.64 thf(fact_10200_Gcd__int__greater__eq__0,axiom,
% 5.27/5.64 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.27/5.64
% 5.27/5.64 % Gcd_int_greater_eq_0
% 5.27/5.64 thf(fact_10201_Gcd__nat__eq__one,axiom,
% 5.27/5.64 ! [N4: set_nat] :
% 5.27/5.64 ( ( member_nat @ one_one_nat @ N4 )
% 5.27/5.64 => ( ( gcd_Gcd_nat @ N4 )
% 5.27/5.64 = one_one_nat ) ) ).
% 5.27/5.64
% 5.27/5.64 % Gcd_nat_eq_one
% 5.27/5.64 thf(fact_10202_sort__upt,axiom,
% 5.27/5.64 ! [M: nat,N2: nat] :
% 5.27/5.64 ( ( linord738340561235409698at_nat
% 5.27/5.64 @ ^ [X: nat] : X
% 5.27/5.64 @ ( upt @ M @ N2 ) )
% 5.27/5.64 = ( upt @ M @ N2 ) ) ).
% 5.27/5.64
% 5.27/5.64 % sort_upt
% 5.27/5.64 thf(fact_10203_sort__upto,axiom,
% 5.27/5.64 ! [I2: int,J: int] :
% 5.27/5.64 ( ( linord1735203802627413978nt_int
% 5.27/5.64 @ ^ [X: int] : X
% 5.27/5.64 @ ( upto @ I2 @ J ) )
% 5.27/5.64 = ( upto @ I2 @ J ) ) ).
% 5.27/5.64
% 5.27/5.64 % sort_upto
% 5.27/5.64 thf(fact_10204_of__nat__eq__id,axiom,
% 5.27/5.64 semiri1316708129612266289at_nat = id_nat ).
% 5.27/5.64
% 5.27/5.64 % of_nat_eq_id
% 5.27/5.64 thf(fact_10205_Rat_Opositive__def,axiom,
% 5.27/5.64 ( positive
% 5.27/5.64 = ( map_fu898904425404107465nt_o_o @ rep_Rat @ id_o
% 5.27/5.64 @ ^ [X: product_prod_int_int] : ( ord_less_int @ zero_zero_int @ ( times_times_int @ ( product_fst_int_int @ X ) @ ( product_snd_int_int @ X ) ) ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % Rat.positive_def
% 5.27/5.64 thf(fact_10206_rcis__inverse,axiom,
% 5.27/5.64 ! [R3: real,A: real] :
% 5.27/5.64 ( ( invers8013647133539491842omplex @ ( rcis @ R3 @ A ) )
% 5.27/5.64 = ( rcis @ ( divide_divide_real @ one_one_real @ R3 ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % rcis_inverse
% 5.27/5.64 thf(fact_10207_cis__rcis__eq,axiom,
% 5.27/5.64 ( cis
% 5.27/5.64 = ( rcis @ one_one_real ) ) ).
% 5.27/5.64
% 5.27/5.64 % cis_rcis_eq
% 5.27/5.64 thf(fact_10208_DeMoivre2,axiom,
% 5.27/5.64 ! [R3: real,A: real,N2: nat] :
% 5.27/5.64 ( ( power_power_complex @ ( rcis @ R3 @ A ) @ N2 )
% 5.27/5.64 = ( rcis @ ( power_power_real @ R3 @ N2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ A ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % DeMoivre2
% 5.27/5.64 thf(fact_10209_of__rat__dense,axiom,
% 5.27/5.64 ! [X4: real,Y: real] :
% 5.27/5.64 ( ( ord_less_real @ X4 @ Y )
% 5.27/5.64 => ? [Q2: rat] :
% 5.27/5.64 ( ( ord_less_real @ X4 @ ( field_7254667332652039916t_real @ Q2 ) )
% 5.27/5.64 & ( ord_less_real @ ( field_7254667332652039916t_real @ Q2 ) @ Y ) ) ) ).
% 5.27/5.64
% 5.27/5.64 % of_rat_dense
% 5.27/5.64
% 5.27/5.64 % Helper facts (38)
% 5.27/5.64 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.27/5.64 ! [X4: int,Y: int] :
% 5.27/5.64 ( ( if_int @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.27/5.64 ! [X4: int,Y: int] :
% 5.27/5.64 ( ( if_int @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.27/5.64 ! [X4: nat,Y: nat] :
% 5.27/5.64 ( ( if_nat @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.27/5.64 ! [X4: nat,Y: nat] :
% 5.27/5.64 ( ( if_nat @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.27/5.64 ! [X4: num,Y: num] :
% 5.27/5.64 ( ( if_num @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.27/5.64 ! [X4: num,Y: num] :
% 5.27/5.64 ( ( if_num @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.27/5.64 ! [X4: rat,Y: rat] :
% 5.27/5.64 ( ( if_rat @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.27/5.64 ! [X4: rat,Y: rat] :
% 5.27/5.64 ( ( if_rat @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.27/5.64 ! [X4: real,Y: real] :
% 5.27/5.64 ( ( if_real @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.27/5.64 ! [X4: real,Y: real] :
% 5.27/5.64 ( ( if_real @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.27/5.64 ! [P: real > $o] :
% 5.27/5.64 ( ( P @ ( fChoice_real @ P ) )
% 5.27/5.64 = ( ? [X3: real] : ( P @ X3 ) ) ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.27/5.64 ! [X4: complex,Y: complex] :
% 5.27/5.64 ( ( if_complex @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.27/5.64 ! [X4: complex,Y: complex] :
% 5.27/5.64 ( ( if_complex @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.27/5.64 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.64 ( ( if_Code_integer @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.27/5.64 ! [X4: code_integer,Y: code_integer] :
% 5.27/5.64 ( ( if_Code_integer @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: set_int,Y: set_int] :
% 5.27/5.64 ( ( if_set_int @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: set_int,Y: set_int] :
% 5.27/5.64 ( ( if_set_int @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: list_int,Y: list_int] :
% 5.27/5.64 ( ( if_list_int @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: list_int,Y: list_int] :
% 5.27/5.64 ( ( if_list_int @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.27/5.64 ! [X4: list_nat,Y: list_nat] :
% 5.27/5.64 ( ( if_list_nat @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.27/5.64 ! [X4: list_nat,Y: list_nat] :
% 5.27/5.64 ( ( if_list_nat @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: int > int,Y: int > int] :
% 5.27/5.64 ( ( if_int_int @ $false @ X4 @ Y )
% 5.27/5.64 = Y ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.27/5.64 ! [X4: int > int,Y: int > int] :
% 5.27/5.64 ( ( if_int_int @ $true @ X4 @ Y )
% 5.27/5.64 = X4 ) ).
% 5.27/5.64
% 5.27/5.64 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.50/6.83 ! [X4: option_num,Y: option_num] :
% 6.50/6.83 ( ( if_option_num @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 6.50/6.83 ! [X4: option_num,Y: option_num] :
% 6.50/6.83 ( ( if_option_num @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.50/6.83 ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 6.50/6.83 ( ( if_Pro3027730157355071871nt_int @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 6.50/6.83 ! [X4: product_prod_int_int,Y: product_prod_int_int] :
% 6.50/6.83 ( ( if_Pro3027730157355071871nt_int @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.50/6.83 ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.50/6.83 ( ( if_Pro6206227464963214023at_nat @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 6.50/6.83 ! [X4: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 6.50/6.83 ( ( if_Pro6206227464963214023at_nat @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.50/6.83 ! [X4: nat > int > int,Y: nat > int > int] :
% 6.50/6.83 ( ( if_nat_int_int @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Int__Oint_Mt__Int__Oint_J_J_T,axiom,
% 6.50/6.83 ! [X4: nat > int > int,Y: nat > int > int] :
% 6.50/6.83 ( ( if_nat_int_int @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.50/6.83 ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 6.50/6.83 ( ( if_nat_nat_nat @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001_062_It__Nat__Onat_M_062_It__Nat__Onat_Mt__Nat__Onat_J_J_T,axiom,
% 6.50/6.83 ! [X4: nat > nat > nat,Y: nat > nat > nat] :
% 6.50/6.83 ( ( if_nat_nat_nat @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.50/6.83 ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.50/6.83 ( ( if_Pro5737122678794959658eger_o @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 6.50/6.83 ! [X4: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 6.50/6.83 ( ( if_Pro5737122678794959658eger_o @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.50/6.83 ! [P: $o] :
% 6.50/6.83 ( ( P = $true )
% 6.50/6.83 | ( P = $false ) ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.50/6.83 ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.50/6.83 ( ( if_Pro6119634080678213985nteger @ $false @ X4 @ Y )
% 6.50/6.83 = Y ) ).
% 6.50/6.83
% 6.50/6.83 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.50/6.83 ! [X4: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.50/6.83 ( ( if_Pro6119634080678213985nteger @ $true @ X4 @ Y )
% 6.50/6.83 = X4 ) ).
% 6.50/6.83
% 6.50/6.83 % Conjectures (1)
% 6.50/6.83 thf(conj_0,conjecture,
% 6.50/6.83 vEBT_V8194947554948674370ptions @ ( vEBT_Node @ info @ deg @ treeList @ summary ) @ x ).
% 6.50/6.83
% 6.50/6.83 %------------------------------------------------------------------------------
% 6.50/6.83 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.evDYd1IwiG/cvc5---1.0.5_15025.p...
% 6.50/6.83 (declare-sort $$unsorted 0)
% 6.50/6.83 (declare-sort tptp.produc3368934014287244435at_num 0)
% 6.50/6.83 (declare-sort tptp.produc4471711990508489141at_nat 0)
% 6.50/6.83 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.50/6.83 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.50/6.83 (declare-sort tptp.produc2963631642982155120at_num 0)
% 6.50/6.83 (declare-sort tptp.produc7248412053542808358at_nat 0)
% 6.50/6.83 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.50/6.83 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.50/6.83 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.50/6.83 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.50/6.83 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.50/6.83 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.50/6.83 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.50/6.83 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.50/6.83 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.50/6.83 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.50/6.83 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.50/6.83 (declare-sort tptp.list_P8526636022914148096eger_o 0)
% 6.50/6.83 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.50/6.83 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.50/6.83 (declare-sort tptp.list_P3744719386663036955um_num 0)
% 6.50/6.83 (declare-sort tptp.list_P6011104703257516679at_nat 0)
% 6.50/6.83 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.50/6.83 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.50/6.83 (declare-sort tptp.set_Pr1261947904930325089at_nat 0)
% 6.50/6.83 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.50/6.83 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.50/6.83 (declare-sort tptp.list_list_VEBT_VEBT 0)
% 6.50/6.83 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.50/6.83 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.50/6.83 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.50/6.83 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.50/6.83 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.50/6.83 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.50/6.83 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.50/6.83 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.50/6.83 (declare-sort tptp.product_prod_num_num 0)
% 6.50/6.83 (declare-sort tptp.product_prod_nat_num 0)
% 6.50/6.83 (declare-sort tptp.product_prod_nat_nat 0)
% 6.50/6.83 (declare-sort tptp.product_prod_int_int 0)
% 6.50/6.83 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.50/6.83 (declare-sort tptp.list_list_nat 0)
% 6.50/6.83 (declare-sort tptp.list_list_int 0)
% 6.50/6.83 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.50/6.83 (declare-sort tptp.set_list_nat 0)
% 6.50/6.83 (declare-sort tptp.set_list_int 0)
% 6.50/6.83 (declare-sort tptp.product_prod_o_nat 0)
% 6.50/6.83 (declare-sort tptp.product_prod_o_int 0)
% 6.50/6.83 (declare-sort tptp.list_Code_integer 0)
% 6.50/6.83 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.50/6.83 (declare-sort tptp.set_set_nat 0)
% 6.50/6.83 (declare-sort tptp.set_set_int 0)
% 6.50/6.83 (declare-sort tptp.set_Code_integer 0)
% 6.50/6.83 (declare-sort tptp.set_Product_unit 0)
% 6.50/6.83 (declare-sort tptp.list_list_o 0)
% 6.50/6.83 (declare-sort tptp.list_complex 0)
% 6.50/6.83 (declare-sort tptp.set_list_o 0)
% 6.50/6.83 (declare-sort tptp.product_prod_o_o 0)
% 6.50/6.83 (declare-sort tptp.set_complex 0)
% 6.50/6.83 (declare-sort tptp.filter_real 0)
% 6.50/6.83 (declare-sort tptp.option_num 0)
% 6.50/6.83 (declare-sort tptp.filter_nat 0)
% 6.50/6.83 (declare-sort tptp.set_char 0)
% 6.50/6.83 (declare-sort tptp.list_real 0)
% 6.50/6.83 (declare-sort tptp.set_real 0)
% 6.50/6.83 (declare-sort tptp.list_num 0)
% 6.50/6.83 (declare-sort tptp.list_nat 0)
% 6.50/6.83 (declare-sort tptp.list_int 0)
% 6.50/6.83 (declare-sort tptp.vEBT_VEBT 0)
% 6.50/6.83 (declare-sort tptp.set_rat 0)
% 6.50/6.83 (declare-sort tptp.set_num 0)
% 6.50/6.83 (declare-sort tptp.set_nat 0)
% 6.50/6.83 (declare-sort tptp.set_int 0)
% 6.50/6.83 (declare-sort tptp.code_integer 0)
% 6.50/6.83 (declare-sort tptp.extended_enat 0)
% 6.50/6.83 (declare-sort tptp.list_o 0)
% 6.50/6.83 (declare-sort tptp.complex 0)
% 6.50/6.83 (declare-sort tptp.set_o 0)
% 6.50/6.83 (declare-sort tptp.char 0)
% 6.50/6.83 (declare-sort tptp.real 0)
% 6.50/6.83 (declare-sort tptp.rat 0)
% 6.50/6.83 (declare-sort tptp.num 0)
% 6.50/6.83 (declare-sort tptp.nat 0)
% 6.50/6.83 (declare-sort tptp.int 0)
% 6.50/6.83 (declare-fun tptp.archim2889992004027027881ng_rat (tptp.rat) tptp.int)
% 6.50/6.83 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.50/6.83 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.50/6.83 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.50/6.83 (declare-fun tptp.archimedean_frac_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.archim2898591450579166408c_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.50/6.83 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.50/6.83 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.gbinomial_complex (tptp.complex tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.gbinomial_int (tptp.int tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.gbinomial_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.gbinomial_rat (tptp.rat tptp.nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.gbinomial_real (tptp.real tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_and_not_num_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.bit_ri7632146776885996613nteger (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se7788150548672797655nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se3222712562003087583nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bit_se9216721137139052372nteger (tptp.code_integer tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_un1837492267222099188nd_num (tptp.num tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_un5425074673868309765um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.bit_un6178654185764691216or_num (tptp.num tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_un3595099601533988841um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.bit_un7362597486090784418nd_num (tptp.num tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_un4731106466462545111um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.bit_un2480387367778600638or_num (tptp.num tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.bit_un2901131394128224187um_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.50/6.83 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.50/6.83 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.50/6.83 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.50/6.83 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.50/6.83 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.50/6.83 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.50/6.83 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.50/6.83 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.50/6.83 (declare-fun tptp.rcis (tptp.real tptp.real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.50/6.83 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.comm_s8582702949713902594nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.comm_s2602460028002588243omplex (tptp.complex tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.comm_s4660882817536571857er_int (tptp.int tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.comm_s4663373288045622133er_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.comm_s4028243227959126397er_rat (tptp.rat tptp.nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.comm_s7457072308508201937r_real (tptp.real tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.semiri3624122377584611663nteger (tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.semiri4449623510593786356d_enat (tptp.nat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.semiri1406184849735516958ct_int (tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.semiri773545260158071498ct_rat (tptp.nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.50/6.83 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.50/6.83 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.50/6.83 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.50/6.83 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.50/6.83 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.50/6.83 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.50/6.83 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.50/6.83 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite_card_list_nat (tptp.set_list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.50/6.83 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.50/6.83 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.comp_nat_nat_nat ((-> tptp.nat tptp.nat) (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.comp_nat_real_nat ((-> tptp.nat tptp.real) (-> tptp.nat tptp.nat) tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.id_o (Bool) Bool)
% 6.50/6.83 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.inj_on_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.inj_on_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.inj_on_real_real ((-> tptp.real tptp.real) tptp.set_real) Bool)
% 6.50/6.83 (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)
% 6.50/6.83 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.50/6.83 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.minus_1356011639430497352at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.50/6.83 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.one_one_int () tptp.int)
% 6.50/6.83 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.50/6.83 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.50/6.83 (declare-fun tptp.one_one_real () tptp.real)
% 6.50/6.83 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.50/6.83 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.50/6.83 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.50/6.83 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.50/6.83 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.50/6.83 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups7108830773950497114d_enat ((-> tptp.nat tptp.extended_enat) tptp.set_nat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups6381953495645901045omplex ((-> tptp.product_prod_nat_nat tptp.complex) tptp.set_Pr1261947904930325089at_nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups977919841031483927at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.set_Pr1261947904930325089at_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups4567486121110086003t_real ((-> tptp.product_prod_nat_nat tptp.real) tptp.set_Pr1261947904930325089at_nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups3708469109370488835omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups766887009212190081x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups7440179247065528705omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups2316167850115554303t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups6464643781859351333omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups73079841787564623at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups129246275422532515t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups713298508707869441omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.groups4061424788464935467al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.50/6.83 (declare-fun tptp.groups1681761925125756287l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.50/6.83 (declare-fun tptp.groups3417619833198082522nteger ((-> Bool tptp.code_integer) tptp.code_integer tptp.list_o) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.50/6.83 (declare-fun tptp.groups9119017779487936845_o_nat ((-> Bool tptp.nat) tptp.nat tptp.list_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.50/6.83 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.50/6.83 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.50/6.83 (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)
% 6.50/6.83 (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)
% 6.50/6.83 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.50/6.83 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.50/6.83 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.50/6.83 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.ring_11222124179247155820nteger () tptp.set_Code_integer)
% 6.50/6.83 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 6.50/6.83 (declare-fun tptp.ring_1_Ints_int () tptp.set_int)
% 6.50/6.83 (declare-fun tptp.ring_1_Ints_rat () tptp.set_rat)
% 6.50/6.83 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.50/6.83 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.50/6.83 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.50/6.83 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.50/6.83 (declare-fun tptp.inf_in1870772243966228564d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.inf_inf_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.50/6.83 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.50/6.83 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.concat_o (tptp.list_list_o) tptp.list_o)
% 6.50/6.83 (declare-fun tptp.concat_int (tptp.list_list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.concat_nat (tptp.list_list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.concat_VEBT_VEBT (tptp.list_list_VEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.50/6.83 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.drop_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.linord1735203802627413978nt_int ((-> tptp.int tptp.int) tptp.list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.linord738340561235409698at_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.nil_int () tptp.list_int)
% 6.50/6.83 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.hd_nat (tptp.list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.50/6.83 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.50/6.83 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_list_o2 (tptp.list_list_o) tptp.set_list_o)
% 6.50/6.83 (declare-fun tptp.set_list_int2 (tptp.list_list_int) tptp.set_list_int)
% 6.50/6.83 (declare-fun tptp.set_list_nat2 (tptp.list_list_nat) tptp.set_list_nat)
% 6.50/6.83 (declare-fun tptp.set_list_VEBT_VEBT2 (tptp.list_list_VEBT_VEBT) tptp.set_list_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_Pr5648618587558075414at_nat (tptp.list_P6011104703257516679at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.tl_nat (tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.nth_Code_integer (tptp.list_Code_integer tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.nth_list_nat (tptp.list_list_nat tptp.nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.nth_num (tptp.list_num tptp.nat) tptp.num)
% 6.50/6.83 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.50/6.83 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.50/6.83 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.50/6.83 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.50/6.83 (declare-fun tptp.nth_Pr8522763379788166057eger_o (tptp.list_P8526636022914148096eger_o tptp.nat) tptp.produc6271795597528267376eger_o)
% 6.50/6.83 (declare-fun tptp.nth_Pr7617993195940197384at_nat (tptp.list_P6011104703257516679at_nat tptp.nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.nth_Pr6456567536196504476um_num (tptp.list_P3744719386663036955um_num tptp.nat) tptp.product_prod_num_num)
% 6.50/6.83 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.50/6.83 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.50/6.83 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.50/6.83 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.50/6.83 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.50/6.83 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.50/6.83 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.50/6.83 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.50/6.83 (declare-fun tptp.produc3607205314601156340eger_o (tptp.list_Code_integer tptp.list_o) tptp.list_P8526636022914148096eger_o)
% 6.50/6.83 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.50/6.83 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.50/6.83 (declare-fun tptp.product_num_num (tptp.list_num tptp.list_num) tptp.list_P3744719386663036955um_num)
% 6.50/6.83 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.50/6.83 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.50/6.83 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.50/6.83 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.50/6.83 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.50/6.83 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.50/6.83 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.replic4235873036481779905at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.list_P6011104703257516679at_nat)
% 6.50/6.83 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.50/6.83 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.sorted_wrt_int ((-> tptp.int tptp.int Bool) tptp.list_int) Bool)
% 6.50/6.83 (declare-fun tptp.sorted_wrt_nat ((-> tptp.nat tptp.nat Bool) tptp.list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.subseqs_o (tptp.list_o) tptp.list_list_o)
% 6.50/6.83 (declare-fun tptp.subseqs_int (tptp.list_int) tptp.list_list_int)
% 6.50/6.83 (declare-fun tptp.subseqs_nat (tptp.list_nat) tptp.list_list_nat)
% 6.50/6.83 (declare-fun tptp.subseqs_VEBT_VEBT (tptp.list_VEBT_VEBT) tptp.list_list_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.take_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.50/6.83 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.50/6.83 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.semiri2816024913162550771omplex ((-> tptp.complex tptp.complex) tptp.nat tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.semiri8420488043553186161ux_int ((-> tptp.int tptp.int) tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.semiri8422978514062236437ux_nat ((-> tptp.nat tptp.nat) tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.semiri7787848453975740701ux_rat ((-> tptp.rat tptp.rat) tptp.nat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.semiri7260567687927622513x_real ((-> tptp.real tptp.real) tptp.nat tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s3445333598471063425nteger (tptp.list_Code_integer) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s2710708370519433104list_o (tptp.list_list_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s533118279054570080st_int (tptp.list_list_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s3023201423986296836st_nat (tptp.list_list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s8217280938318005548T_VEBT (tptp.list_list_VEBT_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_list_num (tptp.list_num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s5460976970255530739at_nat (tptp.list_P6011104703257516679at_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.50/6.83 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.one () tptp.num)
% 6.50/6.83 (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)
% 6.50/6.83 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.50/6.83 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.50/6.83 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.50/6.83 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.50/6.83 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.50/6.83 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.50/6.83 (declare-fun tptp.none_num () tptp.option_num)
% 6.50/6.83 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.50/6.83 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.50/6.83 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.50/6.83 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.50/6.83 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.50/6.83 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.map_option_num_num ((-> tptp.num tptp.num) tptp.option_num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.50/6.83 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.50/6.83 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.50/6.83 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.ord_less_complex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le549003669493604880_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le7866589430770878221at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le704812498762024988_nat_o ((-> tptp.product_prod_nat_nat Bool) (-> tptp.product_prod_nat_nat Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le6045566169113846134st_nat (tptp.set_list_nat tptp.set_list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le3146513528884898305at_nat (tptp.set_Pr1261947904930325089at_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.50/6.83 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.50/6.83 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.50/6.83 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.ord_mi8085742599997312461d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.ord_min_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.50/6.83 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.50/6.83 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.order_5726023648592871131at_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.50/6.83 (declare-fun tptp.order_7092887310737990675l_real ((-> tptp.real tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.50/6.83 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.50/6.83 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.50/6.83 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.50/6.83 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.power_8040749407984259932d_enat (tptp.extended_enat tptp.nat) tptp.extended_enat)
% 6.50/6.83 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.produc3209952032786966637at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc7248412053542808358at_nat) tptp.produc4471711990508489141at_nat)
% 6.50/6.83 (declare-fun tptp.produc851828971589881931at_num ((-> tptp.nat tptp.num tptp.num) tptp.produc2963631642982155120at_num) tptp.produc3368934014287244435at_num)
% 6.50/6.83 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.50/6.83 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.50/6.83 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.50/6.83 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.50/6.83 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.50/6.83 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.50/6.83 (declare-fun tptp.produc487386426758144856at_nat (tptp.nat tptp.product_prod_nat_nat) tptp.produc7248412053542808358at_nat)
% 6.50/6.83 (declare-fun tptp.produc1195630363706982562at_num (tptp.nat tptp.product_prod_nat_num) tptp.produc2963631642982155120at_num)
% 6.50/6.83 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.50/6.83 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.50/6.83 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.50/6.83 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.50/6.83 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.50/6.83 (declare-fun tptp.produc457027306803732586at_nat (tptp.set_nat (-> tptp.nat tptp.set_nat)) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.50/6.83 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.50/6.83 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.50/6.83 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.50/6.83 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.50/6.83 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.50/6.83 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.50/6.83 (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)
% 6.50/6.83 (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)
% 6.50/6.83 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.50/6.83 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.50/6.83 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.50/6.83 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.50/6.83 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.50/6.83 (declare-fun tptp.rep_Rat (tptp.rat) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.field_5140801741446780682s_real () tptp.set_real)
% 6.50/6.83 (declare-fun tptp.field_7254667332652039916t_real (tptp.rat) tptp.real)
% 6.50/6.83 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.50/6.83 (declare-fun tptp.positive (tptp.rat) Bool)
% 6.50/6.83 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.50/6.83 (declare-fun tptp.real_V470468836141973256s_real () tptp.set_real)
% 6.50/6.83 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.50/6.83 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.50/6.83 (declare-fun tptp.real_V1803761363581548252l_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.50/6.83 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.50/6.83 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.50/6.83 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.50/6.83 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.50/6.83 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.50/6.83 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.50/6.83 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.50/6.83 (declare-fun tptp.suminf_int ((-> tptp.nat tptp.int)) tptp.int)
% 6.50/6.83 (declare-fun tptp.suminf_nat ((-> tptp.nat tptp.nat)) tptp.nat)
% 6.50/6.83 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.50/6.83 (declare-fun tptp.summable_complex ((-> tptp.nat tptp.complex)) Bool)
% 6.50/6.83 (declare-fun tptp.summable_int ((-> tptp.nat tptp.int)) Bool)
% 6.50/6.83 (declare-fun tptp.summable_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.50/6.83 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.sums_complex ((-> tptp.nat tptp.complex) tptp.complex) Bool)
% 6.50/6.83 (declare-fun tptp.sums_int ((-> tptp.nat tptp.int) tptp.int) Bool)
% 6.50/6.83 (declare-fun tptp.sums_nat ((-> tptp.nat tptp.nat) tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.50/6.83 (declare-fun tptp.collect_o ((-> Bool Bool)) tptp.set_o)
% 6.50/6.83 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.50/6.83 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.50/6.83 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.50/6.83 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.50/6.83 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.50/6.83 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.50/6.83 (declare-fun tptp.collec3392354462482085612at_nat ((-> tptp.product_prod_nat_nat Bool)) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.50/6.83 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.50/6.83 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.50/6.83 (declare-fun tptp.collect_VEBT_VEBT ((-> tptp.vEBT_VEBT Bool)) tptp.set_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.50/6.83 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.50/6.83 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.50/6.83 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.50/6.83 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_fo1517530859248394432omplex ((-> tptp.nat tptp.complex tptp.complex) tptp.nat tptp.nat tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.set_fo2581907887559384638at_int ((-> tptp.nat tptp.int tptp.int) tptp.nat tptp.nat tptp.int) tptp.int)
% 6.50/6.83 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.set_fo1949268297981939178at_rat ((-> tptp.nat tptp.rat tptp.rat) tptp.nat tptp.nat tptp.rat) tptp.rat)
% 6.50/6.83 (declare-fun tptp.set_fo3111899725591712190t_real ((-> tptp.nat tptp.real tptp.real) tptp.nat tptp.nat tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.50/6.83 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.50/6.83 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.50/6.83 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_ord_atMost_num (tptp.num) tptp.set_num)
% 6.50/6.83 (declare-fun tptp.set_ord_atMost_rat (tptp.rat) tptp.set_rat)
% 6.50/6.83 (declare-fun tptp.set_ord_atMost_real (tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_or58775011639299419et_int (tptp.set_int) tptp.set_set_int)
% 6.50/6.83 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.50/6.83 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.50/6.83 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.50/6.83 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.50/6.83 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.50/6.83 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.50/6.83 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.50/6.83 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.50/6.83 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.50/6.83 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo4899668324122417113eq_int ((-> tptp.nat tptp.int)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo4902158794631467389eq_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo1459490580787246023eq_num ((-> tptp.nat tptp.num)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo4267028734544971653eq_rat ((-> tptp.nat tptp.rat)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo3100542954746470799et_int ((-> tptp.nat tptp.set_int)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.50/6.83 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.50/6.83 (declare-fun tptp.topolo6517432010174082258omplex ((-> tptp.nat tptp.complex)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.50/6.83 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.50/6.83 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.50/6.83 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.cos_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.cosh_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.cot_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.diffs_complex ((-> tptp.nat tptp.complex) tptp.nat) tptp.complex)
% 6.50/6.83 (declare-fun tptp.diffs_int ((-> tptp.nat tptp.int) tptp.nat) tptp.int)
% 6.50/6.83 (declare-fun tptp.diffs_real ((-> tptp.nat tptp.real) tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.pi () tptp.real)
% 6.50/6.83 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.sin_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.50/6.83 (declare-fun tptp.sinh_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.tan_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.50/6.83 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.50/6.83 (declare-fun tptp.transi2905341329935302413cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.transi6264000038957366511cl_nat (tptp.set_Pr1261947904930325089at_nat) tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.50/6.83 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.50/6.83 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.50/6.83 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.50/6.83 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.50/6.83 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.50/6.83 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.50/6.83 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.50/6.83 (declare-fun tptp.pred_nat () tptp.set_Pr1261947904930325089at_nat)
% 6.50/6.83 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.50/6.83 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.50/6.83 (declare-fun tptp.member_Code_integer (tptp.code_integer tptp.set_Code_integer) Bool)
% 6.50/6.83 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.50/6.83 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.50/6.83 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.50/6.83 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.50/6.83 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.50/6.83 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.50/6.83 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.50/6.83 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.50/6.83 (declare-fun tptp.member8440522571783428010at_nat (tptp.product_prod_nat_nat tptp.set_Pr1261947904930325089at_nat) Bool)
% 6.50/6.83 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.50/6.83 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.50/6.83 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.50/6.83 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.50/6.83 (declare-fun tptp.deg () tptp.nat)
% 6.50/6.83 (declare-fun tptp.info () tptp.option4927543243414619207at_nat)
% 6.50/6.83 (declare-fun tptp.m () tptp.nat)
% 6.50/6.83 (declare-fun tptp.ma () tptp.nat)
% 6.50/6.83 (declare-fun tptp.mi () tptp.nat)
% 6.50/6.83 (declare-fun tptp.n () tptp.nat)
% 6.50/6.83 (declare-fun tptp.na () tptp.nat)
% 6.50/6.83 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.50/6.83 (declare-fun tptp.x () tptp.nat)
% 6.50/6.83 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T) X) (@ (@ tptp.vEBT_VEBT_membermima T) X)))))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.deg))
% 6.50/6.83 (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)))))
% 6.50/6.83 (assert (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary))) (=> (= tptp.summary _let_1) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) tptp.x))))
% 6.50/6.83 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.50/6.83 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) tptp.n))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_nat tptp.x) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.50/6.83 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.x) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.x) _let_1)) (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) tptp.x))))
% 6.50/6.83 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.x) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.x) _let_1)) (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) tptp.x))))
% 6.50/6.83 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high tptp.x) (@ (@ tptp.divide_divide_nat tptp.deg) _let_1))) (@ (@ tptp.power_power_nat _let_1) tptp.m))))
% 6.50/6.83 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_low tptp.x) _let_1))) (let ((_let_3 (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.x) _let_1)))) (or (@ (@ tptp.vEBT_VEBT_membermima _let_3) _let_2) (@ (@ tptp.vEBT_V5719532721284313246member _let_3) _let_2))))))
% 6.50/6.83 (assert (let ((_let_1 (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.x) _let_1))) (@ (@ tptp.vEBT_VEBT_low tptp.x) _let_1))))
% 6.50/6.83 (assert (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X2) tptp.na) (=> (= X2 _let_1) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) tptp.x)))))))
% 6.50/6.83 (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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))))
% 6.50/6.83 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.50/6.83 (assert (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.50/6.83 (assert (forall ((Ma tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))))
% 6.50/6.83 (assert (=> (= tptp.mi tptp.ma) (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))))
% 6.50/6.83 (assert (= tptp.m (@ tptp.suc tptp.na)))
% 6.50/6.83 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.50/6.83 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) N))) (@ (@ tptp.vEBT_VEBT_low X) N)))))
% 6.50/6.83 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.50/6.83 (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 ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X2) (@ (@ tptp.ord_less_eq_nat X2) tptp.ma)))))))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (forall ((B tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.nat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))))
% 6.50/6.83 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.50/6.83 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.50/6.83 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.50/6.83 (assert (forall ((X4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.50/6.83 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N2))))))
% 6.50/6.83 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N2))))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M) (@ tptp.numera1916890842035813515d_enat N2)) (= M N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.83 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.50/6.83 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.50/6.83 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)))
% 6.50/6.83 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.50/6.83 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.50/6.83 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.50/6.83 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.50/6.83 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))))
% 6.50/6.83 (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))))
% 6.50/6.83 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.50/6.83 (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))))
% 6.50/6.83 (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))))
% 6.50/6.83 (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))))
% 6.50/6.83 (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))))
% 6.50/6.83 (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))))
% 6.50/6.83 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.50/6.83 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.50/6.83 (assert (forall ((A tptp.list_nat) (P (-> tptp.list_nat Bool))) (= (@ (@ tptp.member_list_nat A) (@ tptp.collect_list_nat P)) (@ P A))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.50/6.83 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.50/6.83 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat)) (= (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A2))) A2)))
% 6.50/6.83 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A2))) A2)))
% 6.50/6.83 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)))
% 6.50/6.83 (assert (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A2))) A2)))
% 6.50/6.83 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A2))) A2)))
% 6.50/6.83 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A2))) A2)))
% 6.50/6.83 (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)))))
% 6.50/6.83 (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)))))
% 6.50/6.83 (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)))))
% 6.50/6.83 (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)))))
% 6.50/6.83 (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)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.50/6.83 (assert (forall ((B tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.nat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((B tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))))
% 6.50/6.83 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (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))))))
% 6.50/6.83 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.50/6.83 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.50/6.83 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))
% 6.50/6.83 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.50/6.83 (assert (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))))
% 6.50/6.83 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N2)))))))
% 6.50/6.83 (assert (forall ((A tptp.rat) (N2 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 N2)))))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N2)))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N2)))))))
% 6.50/6.83 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.83 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.50/6.83 (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)))))
% 6.50/6.83 (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))))))
% 6.50/6.83 (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))))))
% 6.50/6.83 (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))))))
% 6.50/6.83 (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)))))))))))
% 6.50/6.83 (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))))))))))
% 6.50/6.83 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.50/6.83 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.50/6.83 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.50/6.83 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.50/6.83 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.50/6.83 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X4))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X4))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X4))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X4))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X4))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.50/6.83 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X4))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.50/6.83 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.50/6.83 (assert (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))
% 6.50/6.83 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.50/6.83 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.50/6.83 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.50/6.83 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.50/6.83 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.50/6.83 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.50/6.83 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))))
% 6.50/6.83 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N4)))))))
% 6.50/6.83 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.83 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.83 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.50/6.83 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.50/6.83 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.50/6.83 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.50/6.83 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.50/6.83 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.50/6.83 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.50/6.83 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))))
% 6.50/6.84 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.50/6.84 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))))
% 6.50/6.84 (assert (forall ((X22 tptp.nat) (Y2 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y2)) (= X22 Y2))))
% 6.50/6.84 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.50/6.84 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)))
% 6.50/6.84 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.extended_enat Bool)) (N2 tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N2))))
% 6.50/6.84 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X4) tptp.one) (= X4 tptp.one))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y)) (= X4 Y))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))))
% 6.50/6.84 (assert (forall ((S tptp.nat) (T2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T2) (not (= S T2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N2))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N2))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) M))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X4) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X4) (@ tptp.size_size_list_o Y))) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X4) (@ tptp.size_size_list_nat Y))) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X4) (@ tptp.size_size_list_int Y))) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X4) (@ tptp.size_size_num Y))) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P N2) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P N2) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N2) M3))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (=> (= J (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (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) N2)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (not (= M6 N))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N) (= M6 N)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))))
% 6.50/6.84 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M6) K3))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F N2))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N2))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))))
% 6.50/6.84 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q2 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q2)))))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))
% 6.50/6.84 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.50/6.84 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X4))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N2)) (@ tptp.set_real2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N2)) (@ tptp.set_complex2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N2)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N2)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N2)) (@ tptp.set_o2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N2)) (@ tptp.set_nat2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N2)) (@ tptp.set_int2 Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((X4 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I3) X4))))))
% 6.50/6.84 (assert (forall ((X4 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((X4 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((X4 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X4) (@ 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) X4))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X4 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 X4) (@ tptp.set_real2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X4 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I4)))) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X4 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 X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X4 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 X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X4 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 X4) (@ tptp.set_o2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X4 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 X4) (@ tptp.set_nat2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X4 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 X4) (@ tptp.set_int2 Xs)) (@ P X4)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X4) N3))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (forall ((S2 tptp.set_real)) (=> (exists ((X2 tptp.real)) (@ (@ tptp.member_real X2) S2)) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real X5) Z3)))) (exists ((Y3 tptp.real)) (and (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_eq_real X2) Y3))) (forall ((Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y3) Z3)))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))))
% 6.50/6.84 (assert (forall ((X2 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_12))))
% 6.50/6.84 (assert (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))))
% 6.50/6.84 (assert (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))))
% 6.50/6.84 (assert (forall ((X4 tptp.complex)) (= (= tptp.one_one_complex X4) (= X4 tptp.one_one_complex))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (= (= tptp.one_one_real X4) (= X4 tptp.one_one_real))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (= (= tptp.one_one_rat X4) (= X4 tptp.one_one_rat))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (= (= tptp.one_one_nat X4) (= X4 tptp.one_one_nat))))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (= (= tptp.one_one_int X4) (= X4 tptp.one_one_int))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.50/6.84 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.50/6.84 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.50/6.84 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B3) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B3) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (= (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.set_Pr5648618587558075414at_nat Xs)) B3) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B3) (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B3) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B3) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B3)))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N2))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C2 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C2))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.50/6.84 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.50/6.84 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.50/6.84 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))))
% 6.50/6.84 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (= (@ (@ tptp.nth_VEBT_VEBT Xs3) I3) (@ (@ tptp.nth_VEBT_VEBT Ys3) I3))))))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.list_o) (Z4 tptp.list_o)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I3) (@ (@ tptp.nth_o Ys3) I3))))))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.list_nat) (Z4 tptp.list_nat)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I3) (@ (@ tptp.nth_nat Ys3) I3))))))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.list_int) (Z4 tptp.list_int)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I3) (@ (@ tptp.nth_int Ys3) I3))))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.vEBT_VEBT)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs3) I3)))))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 Bool)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs3) I3)))))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.nat)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs3) I3)))))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.int)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs3) I3)))))))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs Ys)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs Ys)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X4))))
% 6.50/6.84 (assert (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X4))))
% 6.50/6.84 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.50/6.84 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.50/6.84 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.50/6.84 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.pow K) L)))))
% 6.50/6.84 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))))
% 6.50/6.84 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))))
% 6.50/6.84 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))))
% 6.50/6.84 (assert (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))))
% 6.50/6.84 (assert (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T2) D) (@ (@ tptp.vEBT_invar_vebt T2) D))))
% 6.50/6.84 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.50/6.84 (assert (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) D) (@ (@ tptp.vEBT_VEBT_valid T2) D))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.50/6.84 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N2)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) B))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 6.50/6.84 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.50/6.84 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.50/6.84 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) 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)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)))
% 6.50/6.84 (assert (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))
% 6.50/6.84 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))
% 6.50/6.84 (assert (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))
% 6.50/6.84 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.pow X4) tptp.one) X4)))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (X4 tptp.nat) (M7 tptp.nat)) (=> (@ P X4) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X2 tptp.nat)) (=> (@ P X2) (@ (@ tptp.ord_less_eq_nat X2) M5)))))))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) X4)))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) X4)))
% 6.50/6.84 (assert (forall ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) X4)))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) X4)))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) X4)))
% 6.50/6.84 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.50/6.84 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s8217280938318005548T_VEBT (@ tptp.subseqs_VEBT_VEBT Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_o)) (= (@ tptp.size_s2710708370519433104list_o (@ tptp.subseqs_o Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_o Xs)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_nat)) (= (@ tptp.size_s3023201423986296836st_nat (@ tptp.subseqs_nat Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_nat Xs)))))
% 6.50/6.84 (assert (forall ((Xs tptp.list_int)) (= (@ tptp.size_s533118279054570080st_int (@ tptp.subseqs_int Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_int Xs)))))
% 6.50/6.84 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_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) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.50/6.84 (assert (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.50/6.84 (assert (= (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma)) tptp.info))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y)) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.50/6.84 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.50/6.84 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N2)) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X4) M) _let_1) (or (= M tptp.zero_zero_nat) (= X4 _let_1))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X4) N2)) (or (@ _let_1 X4) (= N2 tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.50/6.84 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.50/6.84 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.50/6.84 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.50/6.84 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.50/6.84 (assert (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.50/6.84 (assert (forall ((B tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X4) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X4 Y))))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.50/6.84 (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)))
% 6.50/6.84 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (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_le7866589430770878221at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((X4 tptp.complex)) (= (= tptp.zero_zero_complex X4) (= X4 tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (= (= tptp.zero_zero_real X4) (= X4 tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (= (= tptp.zero_zero_rat X4) (= X4 tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (= (= tptp.zero_zero_nat X4) (= X4 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (= (= tptp.zero_zero_int X4) (= X4 tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.50/6.84 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X4 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X4) (or (= X4 Mi) (= X4 Ma)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X4)))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 6.50/6.84 (assert (forall ((D1 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ _let_1 D1) (@ _let_1 D2)))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))))
% 6.50/6.84 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.50/6.84 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.50/6.84 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.50/6.84 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.50/6.84 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))))
% 6.50/6.84 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (=> (not (= X4 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X4 (@ tptp.suc (@ tptp.suc Va2))))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (@ (@ P X5) tptp.zero_zero_nat)) (=> (forall ((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) N2))))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N2)))))
% 6.50/6.84 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.50/6.84 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.50/6.84 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 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 N2)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))))
% 6.50/6.84 (assert (forall ((N2 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) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (= A B))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X4) Y) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X4) Y) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X4) Y) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X4) Y) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X4) Y) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X4) Y) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X4) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) Y))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) 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 X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Y))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))))
% 6.50/6.84 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B3) N2))))))))
% 6.50/6.84 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.50/6.84 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.50/6.84 (assert (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (= (@ (@ tptp.ord_less_eq_set_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (= (@ (@ tptp.ord_less_eq_rat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (= (@ (@ tptp.ord_less_eq_num X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (= (@ (@ tptp.ord_less_eq_nat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (= (@ (@ tptp.ord_less_eq_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_eq_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_int Y) X4))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_set_int X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_num X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_nat X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_int X4) Y))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (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)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (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)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (= X4 Y)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y5) (@ (@ tptp.ord_less_eq_set_int Y5) X)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((X tptp.rat) (Y5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y5) (@ (@ tptp.ord_less_eq_rat Y5) X)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((X tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y5) (@ (@ tptp.ord_less_eq_num Y5) X)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (@ (@ tptp.ord_less_eq_nat Y5) X)))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (@ (@ tptp.ord_less_eq_int Y5) X)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X4))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (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)))))))))))))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X4))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (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)))))))))))))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (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)))))))))))))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X4))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X4))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X4))) (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)))))))))))))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.50/6.84 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (= Y X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (= Y X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (= Y X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (= Y X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (= Y X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X4) Y) (= X4 Y) (@ (@ tptp.ord_less_real Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X4) Y) (= X4 Y) (@ (@ tptp.ord_less_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X4) Y) (= X4 Y) (@ (@ tptp.ord_less_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X4) Y) (= X4 Y) (@ (@ tptp.ord_less_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X4) Y) (= X4 Y) (@ (@ tptp.ord_less_int Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (@ (@ tptp.ord_less_real Y) X4) P))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X4) Y) (=> (@ (@ tptp.ord_less_rat Y) X4) P))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X4) Y) (=> (@ (@ tptp.ord_less_num Y) X4) P))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X4) Y) (=> (@ (@ tptp.ord_less_nat Y) X4) P))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X4) Y) (=> (@ (@ tptp.ord_less_int Y) X4) P))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_real X4) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (not (@ (@ tptp.ord_less_rat X4) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num)) (not (@ (@ tptp.ord_less_num X4) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (not (@ (@ tptp.ord_less_nat X4) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (not (@ (@ tptp.ord_less_int X4) X4))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (not (= X4 Y)) (or (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (= X4 Y)) (or (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (not (= X4 Y)) (or (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (= X4 Y)) (or (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (not (= X4 Y)) (or (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X4) Y)) (or (@ (@ tptp.ord_less_real Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (or (@ (@ tptp.ord_less_rat Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X4) Y)) (or (@ (@ tptp.ord_less_num Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (or (@ (@ tptp.ord_less_nat Y) X4) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X4) Y)) (or (@ (@ tptp.ord_less_int Y) X4) (= X4 Y)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P4 N) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (not (@ P4 M6)))))))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.50/6.84 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.50/6.84 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.50/6.84 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_real Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_rat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_num Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_nat Y) X4)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_int Y) X4)))))
% 6.50/6.84 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X4)) (= (not (@ (@ tptp.ord_less_real X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X4)) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X4)) (= (not (@ (@ tptp.ord_less_num X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X4)) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X4)) (= (not (@ (@ tptp.ord_less_int X4) Y)) (= X4 Y)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X4) Z2) (@ (@ tptp.ord_less_real Z2) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X4) Z2) (@ (@ tptp.ord_less_rat Z2) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X4) X_12))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_12))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X4) X_12))))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X4) X_12))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X4))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.50/6.84 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat Y) E)))) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat X4) 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 X4) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.50/6.84 (assert (forall ((Y tptp.real) (X4 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.50/6.84 (assert (forall ((Y tptp.rat) (X4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.one_one_real)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 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) N2)) tptp.one_one_rat)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X4 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X4))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((T tptp.real)) (let ((_let_1 (@ tptp.member_real T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T tptp.nat)) (let ((_let_1 (@ tptp.member_nat T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((T tptp.complex)) (let ((_let_1 (@ tptp.member_complex T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((T tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T tptp.int)) (let ((_let_1 (@ tptp.member_int T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))))
% 6.50/6.84 (assert (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X tptp.complex)) (=> (@ P X) (@ Q X))))))
% 6.50/6.84 (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 ((X tptp.real)) (=> (@ P X) (@ Q X))))))
% 6.50/6.84 (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 ((X tptp.list_nat)) (=> (@ P X) (@ Q X))))))
% 6.50/6.84 (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 ((X tptp.nat)) (=> (@ P X) (@ Q X))))))
% 6.50/6.84 (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 ((X tptp.int)) (=> (@ P X) (@ Q X))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C4) (@ (@ tptp.ord_less_set_int A2) C4)))))
% 6.50/6.84 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))
% 6.50/6.84 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger))))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))))
% 6.50/6.84 (assert (forall ((X4 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.50/6.84 (assert (forall ((X4 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))))
% 6.50/6.84 (assert (forall ((X4 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))))
% 6.50/6.84 (assert (forall ((X4 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ 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 N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))))
% 6.50/6.84 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))))
% 6.50/6.84 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) A)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 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 N2))) A)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) A)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) A)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) tptp.one_one_real)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 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 N2))) tptp.one_one_rat)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) tptp.one_one_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) tptp.one_one_int)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N2))))))))
% 6.50/6.84 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.50/6.84 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.50/6.84 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.50/6.84 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.50/6.84 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))))
% 6.50/6.84 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N2))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X4) Y))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (or (@ (@ tptp.ord_less_real X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (or (@ (@ tptp.ord_less_set_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (or (@ (@ tptp.ord_less_rat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (or (@ (@ tptp.ord_less_num X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (or (@ (@ tptp.ord_less_nat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (or (@ (@ tptp.ord_less_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_real Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_int Y) X4))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X4) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X4) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X4) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X4) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X4) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X4) Z)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X4) Y) (@ (@ tptp.ord_less_eq_set_int X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_eq_num X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_eq_nat X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_eq_int X4) Y))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_eq_real Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X4) Y)) (@ (@ tptp.ord_less_real Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X4) Y)) (@ (@ tptp.ord_less_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X4) Y)) (@ (@ tptp.ord_less_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X4) Y)) (@ (@ tptp.ord_less_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X4) Y)) (@ (@ tptp.ord_less_int Y) X4))))
% 6.50/6.84 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (not (= X Y5))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y5 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y5) (= X Y5)))))
% 6.50/6.84 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.50/6.84 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.50/6.84 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.50/6.84 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.50/6.84 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X4) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.50/6.84 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X4) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 6.50/6.84 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))))
% 6.50/6.84 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X4)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.50/6.84 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X4)) (@ (@ tptp.ord_less_rat X4) Y))))
% 6.50/6.84 (assert (forall ((Y tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X4)) (@ (@ tptp.ord_less_num X4) Y))))
% 6.50/6.84 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X4)) (@ (@ tptp.ord_less_nat X4) Y))))
% 6.50/6.84 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X4)) (@ (@ tptp.ord_less_int X4) Y))))
% 6.50/6.84 (assert (= tptp.ord_less_real (lambda ((X tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y5) (not (@ (@ tptp.ord_less_eq_real Y5) X))))))
% 6.50/6.84 (assert (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y5) (not (@ (@ tptp.ord_less_eq_set_int Y5) X))))))
% 6.50/6.84 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y5) (not (@ (@ tptp.ord_less_eq_rat Y5) X))))))
% 6.50/6.84 (assert (= tptp.ord_less_num (lambda ((X tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y5) (not (@ (@ tptp.ord_less_eq_num Y5) X))))))
% 6.50/6.84 (assert (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X))))))
% 6.50/6.84 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (= (not (@ (@ tptp.ord_less_real X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (= (not (@ (@ tptp.ord_less_set_int X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (= (not (@ (@ tptp.ord_less_num X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (= (not (@ (@ tptp.ord_less_int X4) Y)) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (= (@ (@ tptp.ord_less_eq_real X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X4) Y)) (= (@ (@ tptp.ord_less_eq_set_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (= (@ (@ tptp.ord_less_eq_rat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (= (@ (@ tptp.ord_less_eq_num X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (= (@ (@ tptp.ord_less_eq_nat X4) Y) (= X4 Y)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (= (@ (@ tptp.ord_less_eq_int X4) Y) (= X4 Y)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_eq_real Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))))
% 6.50/6.84 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (not (@ (@ tptp.ord_less_real X4) Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (not (@ (@ tptp.ord_less_set_int X4) Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (not (@ (@ tptp.ord_less_rat X4) Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (not (@ (@ tptp.ord_less_num X4) Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (not (@ (@ tptp.ord_less_nat X4) Y)))))
% 6.50/6.84 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (not (@ (@ tptp.ord_less_int X4) Y)))))
% 6.50/6.84 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 6.50/6.84 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 6.50/6.84 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 6.50/6.84 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 6.50/6.84 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.50/6.84 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.50/6.84 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_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) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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 ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (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))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _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))) N)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X) N))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (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))))) (let ((_let_3 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N) _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 N))) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _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 N))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X) N))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))))))
% 6.50/6.84 (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) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 Summary3) X_1))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 Summary3) X_1))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _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 Ma3) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _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 Ma3) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))))))))))))))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat Bool)) (N2 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 N2))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option4927543243414619207at_nat)) (= (forall ((Y5 tptp.product_prod_nat_nat)) (not (= X4 (@ tptp.some_P7363390416028606310at_nat Y5)))) (= X4 tptp.none_P5556105721700978146at_nat))))
% 6.50/6.84 (assert (forall ((X4 tptp.option_num)) (= (forall ((Y5 tptp.num)) (not (= X4 (@ tptp.some_num Y5)))) (= X4 tptp.none_num))))
% 6.50/6.84 (assert (forall ((X4 tptp.option4927543243414619207at_nat)) (= (not (= X4 tptp.none_P5556105721700978146at_nat)) (exists ((Y5 tptp.product_prod_nat_nat)) (= X4 (@ tptp.some_P7363390416028606310at_nat Y5))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option_num)) (= (not (= X4 tptp.none_num)) (exists ((Y5 tptp.num)) (= X4 (@ tptp.some_num Y5))))))
% 6.50/6.84 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))))
% 6.50/6.84 (assert (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 6.50/6.84 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.50/6.84 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.50/6.84 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A2) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ tptp.divide_divide_int B3) N2))))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N2))))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X4) K)) X4)))))
% 6.50/6.84 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))))
% 6.50/6.84 (assert (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))))
% 6.50/6.84 (assert (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)))
% 6.50/6.84 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) (@ tptp.suc N2)) A))))))
% 6.50/6.84 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.50/6.84 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N2) A)) (= Y4 X5)))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) N2) A)))))))
% 6.50/6.84 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))))
% 6.50/6.84 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.50/6.84 (assert (forall ((A Bool) (B Bool) (X4 tptp.nat)) (let ((_let_1 (= X4 tptp.one_one_nat))) (let ((_let_2 (= X4 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X4) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.50/6.84 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) N3)) Y))))))
% 6.50/6.84 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.50/6.84 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.50/6.84 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.50/6.84 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.50/6.84 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.50/6.84 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.50/6.84 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.50/6.84 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.50/6.84 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))))
% 6.50/6.84 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= X4 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X4) Y)))) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.num)) (=> (= X4 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X4) Y)))) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.product_prod_nat_nat)) (=> (= X4 (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X4) Y)))) _let_1))))))
% 6.50/6.84 (assert (forall ((X4 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= X4 (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X4) Y)))) _let_1))))))
% 6.50/6.84 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.50/6.84 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((Q3 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R3)) (= R3 tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((Q3 tptp.int) (R3 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R3)) (= R3 tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (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) N2)))))
% 6.50/6.84 (assert (forall ((X4 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X4) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X4 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((X4 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X4) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X4 X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.50/6.84 (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))))))))))
% 6.50/6.84 (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))))))))))
% 6.50/6.84 (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))))))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.50/6.84 (assert (forall ((U tptp.real) (X4 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 X4) Y)) (=> (@ _let_2 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.50/6.84 (assert (forall ((U tptp.rat) (X4 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 X4) Y)) (=> (@ _let_2 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))))
% 6.50/6.84 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))
% 6.50/6.84 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.50/6.84 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.50/6.84 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.50/6.84 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.50/6.84 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.50/6.84 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.50/6.84 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X4) X4))) (= X4 tptp.zero_zero_real))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.50/6.84 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.50/6.84 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.50/6.84 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.50/6.84 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.50/6.84 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.50/6.84 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N2)))))))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.50/6.84 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.50/6.84 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.50/6.84 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.50/6.84 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.50/6.84 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.50/6.84 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.50/6.84 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) A) B))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((V tptp.num) (B tptp.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.50/6.84 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.50/6.84 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.50/6.84 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (assert (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.50/6.84 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))))
% 6.50/6.84 (assert (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))))
% 6.50/6.84 (assert (forall ((K tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) _let_1) tptp.one_one_nat)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))))
% 6.50/6.84 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P2))) P2)))
% 6.50/6.84 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P2))) P2)))
% 6.50/6.84 (assert (forall ((P2 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P2))) P2)))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))
% 6.50/6.84 (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)))
% 6.50/6.84 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.50/6.84 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.50/6.84 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (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)))))))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((Z tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z) N2)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (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)))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P N2)) (=> (@ (@ 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) (= N2 (@ (@ 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P J3))))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((B4 tptp.int) (Q4 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) Q4)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q4)))))))
% 6.50/6.84 (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)))))))
% 6.50/6.84 (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))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.50/6.84 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))))
% 6.50/6.84 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 tptp.one_one_int))))))
% 6.50/6.84 (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))))
% 6.50/6.84 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))))
% 6.50/6.84 (assert (forall ((B tptp.int) (Q3 tptp.int) (R3 tptp.int) (B4 tptp.int) (Q4 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) Q4)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q3) Q4)))))))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((B tptp.int) (Q3 tptp.int) (R3 tptp.int) (B4 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q4)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R3) 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 Q4) Q3))))))))))
% 6.50/6.85 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.50/6.85 (assert (forall ((B tptp.int) (Q4 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R3) B) (@ (@ tptp.ord_less_eq_int Q4) Q3))))))))
% 6.50/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))))
% 6.50/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.50/6.85 (assert (forall ((B tptp.int) (Q4 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R3 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 Q4)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ _let_1 R3) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q3) Q4)))))))))
% 6.50/6.85 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M) (= M N2))))))))
% 6.50/6.85 (assert (forall ((A tptp.int) (X4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X4) (= A X4) (@ (@ tptp.ord_less_eq_int X4) A))))
% 6.50/6.85 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.50/6.85 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q2 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q2))))))
% 6.50/6.85 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q5))))))
% 6.50/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))))
% 6.50/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))))
% 6.50/6.85 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.50/6.85 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N2) (not (@ (@ tptp.dvd_dvd_int N2) M))))))
% 6.50/6.85 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.50/6.85 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.50/6.85 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))))
% 6.50/6.85 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))))
% 6.50/6.85 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X4 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 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X4) (@ (@ 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)))))))))))))))))
% 6.50/6.85 (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))))))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K2 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K2))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))))
% 6.50/6.85 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_complex (lambda ((B2 tptp.complex) (A3 tptp.complex)) (exists ((K3 tptp.complex)) (= A3 (@ (@ tptp.times_times_complex B2) K3))))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))))
% 6.50/6.85 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.50/6.85 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.50/6.85 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P2 Q3))))
% 6.50/6.85 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P2 Q3))))
% 6.50/6.85 (assert (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q3)) (= P2 Q3))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))))
% 6.50/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (= tptp.times_times_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex B2) A3))))
% 6.50/6.85 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.50/6.85 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.50/6.85 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))))
% 6.50/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.50/6.85 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.50/6.85 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.50/6.85 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.50/6.85 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.50/6.85 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.50/6.85 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.50/6.85 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.50/6.85 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.50/6.85 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.50/6.85 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.50/6.85 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.50/6.85 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.50/6.85 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (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)))))))
% 6.50/6.85 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))))
% 6.50/6.85 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) N2)))))
% 6.50/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.50/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)))))
% 6.50/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.50/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.50/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.50/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.50/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.50/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.50/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.50/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.50/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.50/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.50/6.85 (assert (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (E2 tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E2)) C))))
% 6.50/6.85 (assert (forall ((A tptp.real) (E2 tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E2)) C))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))))
% 6.50/6.85 (assert (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) C))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))))
% 6.50/6.85 (assert (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))))
% 6.50/6.85 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.50/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.50/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.50/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.50/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.50/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.50/6.85 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X4) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.50/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X4) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.50/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.50/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))))
% 6.50/6.85 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))))
% 6.50/6.85 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))))
% 6.50/6.85 (assert (forall ((X4 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X4 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))))
% 6.50/6.85 (assert (forall ((X4 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X4 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))))
% 6.50/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))))
% 6.50/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))))
% 6.50/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))))
% 6.50/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L))))))
% 6.50/6.85 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.50/6.85 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))))
% 6.50/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.50/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.50/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)))
% 6.50/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)))
% 6.50/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q3)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q3)))))
% 6.50/6.85 (assert (forall ((A2 tptp.int) (N2 tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N2)) N2)) (@ (@ tptp.modulo_modulo_int A2) N2)))))
% 6.50/6.85 (assert (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) 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) (= N2 (@ (@ 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3))))))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 6.50/6.85 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.divide_divide_int A) B) Q3))))))
% 6.50/6.85 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.50/6.85 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))))
% 6.50/6.85 (assert (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))))))))))))
% 6.50/6.85 (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)))))))))))))))
% 6.50/6.85 (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)))))))))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))))
% 6.50/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.50/6.85 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.50/6.85 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))))
% 6.50/6.85 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.50/6.85 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.50/6.85 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))
% 6.50/6.85 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.50/6.85 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.50/6.85 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.50/6.85 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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)))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (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))))))
% 6.50/6.85 (assert (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))))
% 6.57/6.85 (assert (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.57/6.85 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.57/6.85 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.57/6.85 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.57/6.85 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) M))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) M))))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M) N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X4) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X4) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X4) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X4) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.57/6.85 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X4) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X4) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.57/6.85 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.57/6.85 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L)))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L)))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger L)) (@ _let_1 (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num K) L)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X4) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X4) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X4) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X4) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X4) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)))
% 6.57/6.85 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q2))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X4) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X4) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) Deg3))))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X4)) X4)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X4)) X4)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X4)) X4)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Y)) X4)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Y)) X4)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Y)) X4)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.57/6.85 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X4) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X4) Y))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X4) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X4) Y))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) Z)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X4) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.complex) (X4 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.57/6.85 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N2)))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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) N2)))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N2)))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N2)))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q3)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q3))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S3 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S3))))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X4) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (exists ((Q2 tptp.nat)) (= X4 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q2))))))))
% 6.57/6.85 (assert (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q3)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q3))) (@ _let_1 N2)))))))
% 6.57/6.85 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.57/6.85 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.57/6.85 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.57/6.85 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.57/6.85 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.57/6.85 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (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))))))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (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))))))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.code_integer) (Z4 tptp.code_integer)) (= Y6 Z4)) (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))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X4))) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X4))) (=> (not (= X4 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X4) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (=> (not (= X4 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X4) (@ (@ tptp.power_8256067586552552935nteger X4) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X4) (@ (@ tptp.power_power_rat X4) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X4) (@ (@ tptp.power_power_nat X4) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X4) (@ (@ tptp.power_power_real X4) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X4) (@ (@ tptp.power_power_int X4) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X4) (@ (@ tptp.power_power_complex X4) N2)))))
% 6.57/6.85 (assert (forall ((X4 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) X4)) Y)))) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.85 (assert (forall ((X4 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) X4)) Y)))) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X4) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X4) Y))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X4) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X4) Y))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) Z)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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)))))))))))
% 6.57/6.85 (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)))))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ 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))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.57/6.85 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X4) X4)) X4)) X4))))
% 6.57/6.85 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X4) X4)) X4)) X4))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat)) (= (@ (@ tptp.power_power_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X4) X4)) X4)) X4))))
% 6.57/6.85 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X4) X4)) X4)) X4))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M) N2) Q3))))))
% 6.57/6.85 (assert (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q3)) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P I3))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P J3))))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3)) X5)))))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (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)))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (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))))))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.57/6.85 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) _let_2))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q5)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))))
% 6.57/6.85 (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))))))))))
% 6.57/6.85 (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))))))))))
% 6.57/6.85 (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))))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))))
% 6.57/6.85 (assert (forall ((N2 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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (@ _let_1 A))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X4) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X4) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X4) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X4)) Y))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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))) N2)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (N2 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 N2))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((X4 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)) X4)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.57/6.85 (assert (forall ((X4 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)) X4)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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))) N2)))) (@ _let_1 A)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 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))) N2)))) tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.57/6.85 (assert (forall ((M tptp.code_integer) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.57/6.85 (assert (forall ((M tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.57/6.85 (assert (forall ((X4 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X4) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((X4 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X4) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X4) (@ _let_2 Y)) (= X4 Y)))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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 ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int K) D))))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)))
% 6.57/6.85 (assert (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (@ (@ tptp.ord_less_real T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (@ (@ tptp.ord_less_rat T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (@ (@ tptp.ord_less_num T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (@ (@ tptp.ord_less_nat T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (@ (@ tptp.ord_less_int T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Z2) (@ _let_1 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X2))) (=> (@ _let_1 Z2) (@ _let_1 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X2))) (=> (@ _let_1 Z2) (@ _let_1 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X2))) (=> (@ _let_1 Z2) (@ _let_1 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X2))) (=> (@ _let_1 Z2) (@ _let_1 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (@ (@ tptp.ord_less_real T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (@ (@ tptp.ord_less_rat T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (@ (@ tptp.ord_less_num T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_nat T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (@ (@ tptp.ord_less_int T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (not (@ (@ tptp.ord_less_real X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (not (@ (@ tptp.ord_less_rat X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (not (@ (@ tptp.ord_less_num X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (not (@ (@ tptp.ord_less_nat X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (not (@ (@ tptp.ord_less_int X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (not (= X2 T2)))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (= (or (@ P X2) (@ Q X2)) (or (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.rat)) (forall ((X5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (@ (@ tptp.ord_less_eq_real T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (@ (@ tptp.ord_less_eq_rat T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (@ (@ tptp.ord_less_eq_num T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (@ (@ tptp.ord_less_eq_nat T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (@ (@ tptp.ord_less_eq_int T2) X2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (@ (@ tptp.ord_less_eq_real X2) T2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (@ (@ tptp.ord_less_eq_rat X2) T2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (@ (@ tptp.ord_less_eq_num X2) T2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (@ (@ tptp.ord_less_eq_nat X2) T2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (@ (@ tptp.ord_less_eq_int X2) T2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (@ (@ tptp.ord_less_eq_real T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (@ (@ tptp.ord_less_eq_rat T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (@ (@ tptp.ord_less_eq_num T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (@ (@ tptp.ord_less_eq_int T2) X2))))))
% 6.57/6.85 (assert (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (not (@ (@ tptp.ord_less_eq_real X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (not (@ (@ tptp.ord_less_eq_rat X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (not (@ (@ tptp.ord_less_eq_num X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (not (@ (@ tptp.ord_less_eq_nat X2) T2)))))))
% 6.57/6.85 (assert (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (not (@ (@ tptp.ord_less_eq_int X2) T2)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X4 (@ tptp.suc N3))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X4 X7) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X4) P) (=> _let_2 P6))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X4 X7) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X4) P) (and _let_2 P6))))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S))))) (=> (@ (@ tptp.ord_less_real X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S))))) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S))))) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S))))) (=> (@ (@ tptp.ord_less_int X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S)))) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int X2) Z2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S))))) (=> (@ (@ tptp.ord_less_real Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S))))) (=> (@ (@ tptp.ord_less_int Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int Z2) X2) (= _let_1 _let_1)))))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_list_VEBT_VEBT) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) (@ tptp.set_list_VEBT_VEBT2 Xs)) (= (@ tptp.size_s6755466524823107622T_VEBT X5) N2))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs)) N2)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_list_o) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) (@ tptp.set_list_o2 Xs)) (= (@ tptp.size_size_list_o X5) N2))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs)) N2)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_list_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) (@ tptp.set_list_nat2 Xs)) (= (@ tptp.size_size_list_nat X5) N2))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N2)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_list_int) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) (@ tptp.set_list_int2 Xs)) (= (@ tptp.size_size_list_int X5) N2))) (= (@ tptp.size_size_list_int (@ tptp.concat_int Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s533118279054570080st_int Xs)) N2)))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))))))
% 6.57/6.85 (assert (forall ((Z tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X4) Y))))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X4) Y)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X4) Y)))))
% 6.57/6.85 (assert (forall ((Z tptp.int) (X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X4) Y)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) N2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) N2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))))
% 6.57/6.85 (assert (= tptp.nat_triangle (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.85 (assert (forall ((B tptp.int) (A tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R3)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R3)))))))))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.57/6.85 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R4)) (= R3 R4))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R4)) (= Q3 Q4))))))
% 6.57/6.85 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (= (@ (@ tptp.divide_divide_int K) L) Q3))))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (= (@ (@ tptp.modulo_modulo_int K) L) R3))))
% 6.57/6.85 (assert (forall ((L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q3) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int))))))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q3)) R3)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (@ (@ tptp.ord_less_int R3) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int))) (=> (not _let_2) (= Q3 tptp.zero_zero_int)))))))))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X4) Y)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X4) Y)))))
% 6.57/6.85 (assert (forall ((Z tptp.int) (X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X4) Y)))))
% 6.57/6.85 (assert (forall ((Q3 tptp.int) (R3 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q3) R3)) (@ (@ tptp.plus_plus_int Q3) (@ tptp.zero_n2684676970156552555ol_int (not (= R3 tptp.zero_zero_int)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))))
% 6.57/6.85 (assert (forall ((B tptp.int) (A tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q3))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R3)) (@ (@ (@ 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 R3)) tptp.one_one_int)))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X4)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X4)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4)))))
% 6.57/6.85 (assert (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R3))) (=> (not (= R3 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)))))))))
% 6.57/6.85 (assert (forall ((R3 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R3))) (=> (not (= R3 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)))))))))
% 6.57/6.85 (assert (forall ((R3 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (=> (not (= R3 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)))))))))
% 6.57/6.85 (assert (forall ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R3))) (=> (not (= R3 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)))))))))
% 6.57/6.85 (assert (forall ((R3 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R3))) (=> (not (= R3 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)))))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.57/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.57/6.85 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.85 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K) L)) (@ _let_1 L)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.complex) (Z4 tptp.complex)) (= Y6 Z4)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.real) (Z4 tptp.real)) (= Y6 Z4)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.57/6.85 (assert (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N2) L)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R3)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L)) R3)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))))
% 6.57/6.85 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))))
% 6.57/6.85 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N2) K)))))
% 6.57/6.85 (assert (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N2) K)))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))))
% 6.57/6.85 (assert (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_rat X4) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) X4)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_complex X4) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real X4) Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) Y)) (@ (@ tptp.minus_minus_int X4) Y)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E2)) C) D))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C) D))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (= (@ (@ 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 X4) A)) B))))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X4))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) A)) B))))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (= (@ (@ 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 X4) A)) B))))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (= (@ (@ 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 X4) A)) B))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.57/6.85 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.57/6.85 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.57/6.85 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N)) N)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))))
% 6.57/6.85 (assert (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X4) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) Y)) Z)))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.57/6.85 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) X4)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X4) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X4) tptp.one_one_int)))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X2) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2)))))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat K4) D4))) T2)))))))))
% 6.57/6.85 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D4))) T2)))))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D4))) T2)))))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D4))) T2)))))))))
% 6.57/6.85 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X2) T2)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X2) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2))))))))
% 6.57/6.85 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat K4) D4))) T2))))))))
% 6.57/6.85 (assert (forall ((D tptp.complex) (D4 tptp.complex) (T2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D4))) T2))))))))
% 6.57/6.85 (assert (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D4))) T2))))))))
% 6.57/6.85 (assert (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D4))) T2))))))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))))
% 6.57/6.85 (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 ((D5 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D5)) (@ P D5)))))))
% 6.57/6.85 (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 ((D5 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D5)) (not (@ P D5)))))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))))
% 6.57/6.85 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.57/6.85 (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 ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M) N2))))))
% 6.57/6.85 (assert (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N)) N)))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.57/6.85 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.57/6.85 (assert (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X4) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X4)) _let_1)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X4)) _let_1)))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X4) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X4)) _let_1)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X4) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X4)) _let_1)))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.57/6.85 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))))
% 6.57/6.85 (assert (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.57/6.85 (assert (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))))
% 6.57/6.85 (assert (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))))
% 6.57/6.85 (assert (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))))
% 6.57/6.85 (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 ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K) D))))))))))
% 6.57/6.85 (assert (forall ((Q3 tptp.nat) (N2 tptp.nat) (R3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R3) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q3))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q3)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q3)))))))))))
% 6.57/6.85 (assert (forall ((R3 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R3) N2) (=> (@ (@ tptp.ord_less_eq_nat R3) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R3)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R3))))))
% 6.57/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))))
% 6.57/6.85 (assert (forall ((U tptp.real) (V tptp.real) (R3 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_eq_real R3) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.57/6.85 (assert (forall ((U tptp.rat) (V tptp.rat) (R3 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (=> (@ (@ tptp.ord_less_eq_rat R3) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R3) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))))
% 6.57/6.85 (assert (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.85 (assert (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.57/6.85 (assert (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.57/6.85 (assert (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.57/6.85 (assert (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.57/6.85 (assert (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))))
% 6.57/6.85 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.57/6.85 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))))
% 6.57/6.85 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.57/6.85 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((W tptp.rat) (Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))))
% 6.57/6.85 (assert (forall ((W tptp.complex) (Y tptp.complex) (X4 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X4))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))))
% 6.57/6.85 (assert (forall ((W tptp.real) (Y tptp.real) (X4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))))
% 6.57/6.85 (assert (forall ((W tptp.nat) (Y tptp.nat) (X4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X4))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))))
% 6.57/6.85 (assert (forall ((W tptp.int) (Y tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (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)))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((L tptp.num) (R3 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R3))))))))))
% 6.57/6.85 (assert (forall ((L tptp.num) (R3 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R3))))))))))
% 6.57/6.85 (assert (forall ((L tptp.num) (R3 tptp.code_integer) (Q3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q3) R3)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R3))))))))))
% 6.57/6.85 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))))
% 6.57/6.85 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))))
% 6.57/6.85 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.57/6.85 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.57/6.85 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N2))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ _let_1 Y)) Y))))
% 6.57/6.85 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)))
% 6.57/6.85 (assert (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.85 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.57/6.85 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.57/6.85 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.57/6.85 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= M N2))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X4))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X4)) Y) (@ (@ tptp.dvd_dvd_real X4) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X4)) Y) (@ (@ tptp.dvd_dvd_int X4) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X4)) Y) (@ (@ tptp.dvd_dvd_complex X4) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X4)) Y) (@ (@ tptp.dvd_dvd_Code_integer X4) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X4)) Y) (@ (@ tptp.dvd_dvd_rat X4) Y))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X4) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X4 A))))
% 6.57/6.85 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) X4) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.57/6.85 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.57/6.85 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.57/6.85 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (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)))))))
% 6.57/6.85 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.57/6.85 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.57/6.85 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.57/6.85 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.57/6.85 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.57/6.85 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.57/6.85 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.57/6.85 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.57/6.85 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.57/6.85 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.57/6.85 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.57/6.85 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.57/6.85 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.57/6.85 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.57/6.85 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.divide_divide_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X4))))
% 6.57/6.85 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X4))))
% 6.57/6.85 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X4))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.57/6.85 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.57/6.85 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.57/6.85 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.57/6.85 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.57/6.85 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera1916890842035813515d_enat N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))))
% 6.57/6.85 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.57/6.85 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.57/6.85 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.57/6.85 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.57/6.85 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.57/6.85 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.85 (assert (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X4) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X4) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X4) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X4) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X4)) (= (@ (@ tptp.power_power_nat B) W) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X4)) (= (@ (@ tptp.power_power_nat B) W) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X4)) (= (@ (@ tptp.power_power_nat B) W) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X4)) (= (@ (@ tptp.power_power_nat B) W) X4))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))))
% 6.57/6.85 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))))
% 6.57/6.85 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.57/6.85 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.57/6.85 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.57/6.85 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= N2 tptp.one))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.57/6.85 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.57/6.85 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.57/6.85 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) tptp.one)))))
% 6.57/6.85 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.57/6.85 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_num N2) M))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))))
% 6.57/6.85 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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))))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y))))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y))))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.57/6.85 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X4)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X4)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))))
% 6.57/6.85 (assert (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat Y) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))))
% 6.57/6.85 (assert (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))))
% 6.57/6.85 (assert (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))))
% 6.57/6.85 (assert (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))))
% 6.57/6.85 (assert (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X4)) N2) (@ tptp.semiri4216267220026989637d_enat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))))
% 6.57/6.85 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))))
% 6.57/6.85 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))))
% 6.57/6.85 (assert (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.85 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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))))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.57/6.85 (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)))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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))))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.57/6.85 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.57/6.85 (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))))
% 6.57/6.85 (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)))
% 6.57/6.85 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.57/6.85 (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))
% 6.57/6.85 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.57/6.85 (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))
% 6.57/6.85 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X4)) N2)) (or (@ _let_1 X4) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (forall ((N2 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))) N2)) tptp.one_one_rat)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_rat _let_1) N2) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_nat X4) _let_1)))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_eq_nat X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y)))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.57/6.86 (assert (= tptp.minus_minus_real (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y5)))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat B) C))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int B) C))))))
% 6.57/6.86 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat B2) A3))))
% 6.57/6.86 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int B2) A3))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se6528837805403552850or_nat M) N2)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se6528837805403552850or_nat M) N2)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.57/6.86 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat B))) (let ((_let_2 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.57/6.86 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int B))) (let ((_let_2 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X4) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X4) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X4) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X4) _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q3)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X4))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X4))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X4))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.57/6.86 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.57/6.86 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.57/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ 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 C4) D4))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ 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 C4) D4))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)))
% 6.57/6.86 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) A2)))
% 6.57/6.86 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B3) (exists ((B5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat B3) A2))))))
% 6.57/6.86 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int) (R3 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R3) S)) (and (= (@ _let_1 K) (@ _let_1 R3)) (= L S)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4)))) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.57/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))))
% 6.57/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.57/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))))
% 6.57/6.86 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N2))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.57/6.86 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.57/6.86 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.57/6.86 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.57/6.86 (assert (forall ((X4 tptp.product_prod_num_num)) (=> (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))))
% 6.57/6.86 (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)))))))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.57/6.86 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((W tptp.num) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real X4) (@ tptp.uminus_uminus_real _let_1))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X4)) (@ (@ tptp.times_times_int X4) (@ tptp.uminus_uminus_int _let_1))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (X4 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex X4) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X4)) (@ (@ tptp.times_3573771949741848930nteger X4) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat X4) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat N2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.times_times_real X4) X4) tptp.one_one_real) (or (= X4 tptp.one_one_real) (= X4 (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (= (@ (@ tptp.times_times_int X4) X4) tptp.one_one_int) (or (= X4 tptp.one_one_int) (= X4 (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X4) X4) tptp.one_one_complex) (or (= X4 tptp.one_one_complex) (= X4 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X4) X4) tptp.one_one_Code_integer) (or (= X4 tptp.one_one_Code_integer) (= X4 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X4) X4) tptp.one_one_rat) (or (= X4 tptp.one_one_rat) (= X4 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.57/6.86 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.57/6.86 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.57/6.86 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.86 (assert (forall ((U tptp.real) (X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X4) X4))))
% 6.57/6.86 (assert (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X4))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.57/6.86 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.57/6.86 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.57/6.86 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.57/6.86 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.57/6.86 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.57/6.86 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.57/6.86 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ (@ tptp.power_power_real X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ (@ tptp.power_power_int X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ (@ tptp.power_power_complex X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ (@ tptp.power_power_rat X4) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X4)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X4)) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X4) D))) _let_1))))))
% 6.57/6.86 (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)))))))))
% 6.57/6.86 (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))))))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))))
% 6.57/6.86 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.57/6.86 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.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)))))))))))))
% 6.57/6.86 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.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)))))))))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.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)))))))))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.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)))))))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.57/6.86 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.57/6.86 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.57/6.86 (assert (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.57/6.86 (assert (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.57/6.86 (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_se3222712562003087583nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.57/6.86 (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_se6528837805403552850or_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.57/6.86 (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_se6526347334894502574or_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_real Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_int Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X4) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_rat Y)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri681578069525770553at_rat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))))
% 6.57/6.86 (assert (= tptp.ord_less_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))))
% 6.57/6.86 (assert (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N2)) (@ (@ tptp.divide_divide_int A2) N2))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.86 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.86 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N2))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.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)))))))))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.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)))))))))))))
% 6.57/6.86 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.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))))))))))))
% 6.57/6.86 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.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))))))))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.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))))))
% 6.57/6.86 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.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))))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.86 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 C) (=> (forall ((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)) X4)) C))) (= X4 tptp.zero_zero_real)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))))
% 6.57/6.86 (assert (forall ((U tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X4) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N2) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))))))
% 6.57/6.86 (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)))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R3 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q3))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (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) R3))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (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)))))))))))))
% 6.57/6.86 (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))))))))))))
% 6.57/6.86 (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))))))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (=> (@ (@ tptp.ord_le3102999989581377725nteger X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (= (@ (@ 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))) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) _let_1))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))))
% 6.57/6.86 (assert (forall ((N2 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))) N2))) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.57/6.86 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.57/6.86 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N2)) tptp.one_one_Code_integer))))))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N2)) tptp.one_one_int))))))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N2)) tptp.one_one_nat))))))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.57/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) N2)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E2)))))))
% 6.57/6.86 (assert (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E2)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X4)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X4))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (= (@ _let_1 K) (@ _let_1 L))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.57/6.86 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.57/6.86 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.57/6.86 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.57/6.86 (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))))))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)))))))
% 6.57/6.86 (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))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)))
% 6.57/6.86 (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)))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.57/6.86 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.57/6.86 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.int Bool)) (X4 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X4) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X4)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ P tptp.zero_zero_int))))))
% 6.57/6.86 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.57/6.86 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.57/6.86 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.57/6.86 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X4) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X4)) Y))))
% 6.57/6.86 (assert (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X4)) (@ (@ tptp.ord_less_eq_set_int X4) (@ tptp.uminus1532241313380277803et_int Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)) _let_1)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X4) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.57/6.86 (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (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)) D6)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X4))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((H tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N2)) (@ _let_4 N2))) H)) (@ _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 H)))))))))))))
% 6.57/6.86 (assert (forall ((H tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N2)) (@ _let_3 N2))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H))))))))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.57/6.86 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))))
% 6.57/6.86 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))))
% 6.57/6.86 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.57/6.86 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))))
% 6.57/6.86 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))))
% 6.57/6.86 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) M)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.57/6.86 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.num Bool)) (X4 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X4))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.57/6.86 (assert (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))))
% 6.57/6.86 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X4)) (@ tptp.bit1 X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X4)) (@ tptp.bit0 (@ tptp.inc X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.plus_plus_num X4) tptp.one) (@ tptp.inc X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X4))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X4)))))
% 6.57/6.86 (assert (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X4)) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X4)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X4)) tptp.one_on7984719198319812577d_enat))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X4)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X4)) tptp.one_one_complex))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X4)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X4)) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X4)) tptp.one_one_nat))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X4)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X4)) tptp.one_one_int))))
% 6.57/6.86 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))
% 6.57/6.86 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))
% 6.57/6.86 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))
% 6.57/6.86 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))
% 6.57/6.86 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.57/6.86 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.57/6.86 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.57/6.86 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.57/6.86 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N)))))))
% 6.57/6.86 (assert (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N)))))))
% 6.57/6.86 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N)))))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X4)) (not (= X4 tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4)) (not (= X4 tptp.zero_zero_complex)))))
% 6.57/6.86 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.57/6.86 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.57/6.86 (assert (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (R3 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.times_times_real R3) S))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (R3 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y))) (@ (@ tptp.times_times_real R3) S))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) E2))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) E2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (R3 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real R3) S))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (R3 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.plus_plus_real R3) S))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) E2))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) E2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (R3 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R3) (=> (@ (@ 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 R3) S))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (R3 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R3) (=> (@ (@ 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 R3) S))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y))) E2))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y))) E2))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X4) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X4) tptp.one_one_real))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.57/6.86 (assert (forall ((Z tptp.rat) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))))
% 6.57/6.86 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))))
% 6.57/6.86 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) N2)))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X4) (@ tptp.ln_ln_real Y)) (= X4 Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X4) Y)))))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (= (@ _let_1 (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (= (@ tptp.ln_ln_real X4) tptp.zero_zero_real) (= X4 tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.57/6.86 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X4) N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X4) N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X4) N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X4) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_rat)))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_rat))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X4)) (=> (@ _let_1 X4) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X4) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X4) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X4) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X4) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X4) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (= (@ tptp.ln_ln_real X4) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (= X4 tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))))
% 6.57/6.86 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2)))))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2)))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) M))))))
% 6.57/6.86 (assert (forall ((Z tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) M))))))
% 6.57/6.86 (assert (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))))
% 6.57/6.86 (assert (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))))
% 6.57/6.86 (assert (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2))) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N2))) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.86 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) Y)) Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X4))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N2) _let_1))) (let ((_let_3 (@ tptp.binomial N2))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4))) (@ tptp.uminus_uminus_real X4))))))
% 6.57/6.86 (assert (forall ((R3 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R3))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R3) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R3) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))))
% 6.57/6.86 (assert (forall ((R3 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R3))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R3) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R3) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))))
% 6.57/6.86 (assert (forall ((R3 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R3))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R3) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R3) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))))
% 6.57/6.86 (assert (forall ((R3 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))))
% 6.57/6.86 (assert (forall ((R3 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R3) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R3) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) K))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))))
% 6.57/6.86 (assert (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) K)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (R3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R3))) (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)))))))))
% 6.57/6.86 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R3)) (@ (@ tptp.power_power_nat N2) R3)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K))) _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.57/6.86 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))))))))
% 6.57/6.86 (assert (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri773545260158071498ct_rat N2))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N2))) (@ tptp.semiri5044797733671781792omplex N2))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N2))) (@ tptp.semiri2265585572941072030t_real N2))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.57/6.86 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.57/6.86 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)))))
% 6.57/6.86 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.zero_zero_nat) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.zero_zero_nat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.zero_zero_nat) tptp.one_one_int))
% 6.57/6.86 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.57/6.86 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.semiri5044797733671781792omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.semiri773545260158071498ct_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.semiri1406184849735516958ct_int tptp.one_one_nat) tptp.one_one_int))
% 6.57/6.86 (assert (= (@ tptp.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.57/6.86 (assert (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.57/6.86 (assert (= (@ tptp.semiri5044797733671781792omplex (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.semiri773545260158071498ct_rat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.57/6.86 (assert (= (@ tptp.semiri1408675320244567234ct_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.57/6.86 (assert (= (@ tptp.semiri2265585572941072030t_real (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X4))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2)) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera1916890842035813515d_enat _let_1))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numera6690914467698888265omplex _let_1))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_int _let_1))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.semiri2265585572941072030t_real (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.numeral_numeral_real _let_1))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))))
% 6.57/6.86 (assert (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= _let_1 _let_1))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (N2 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)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 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)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X4) (@ tptp.abs_abs_real Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_real Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X4) (@ tptp.abs_abs_int Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_int Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X4) (@ tptp.abs_abs_Code_integer Y)) (or (= X4 Y) (= X4 (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X4) (@ tptp.abs_abs_rat Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_rat Y))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.57/6.86 (assert (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))))
% 6.57/6.86 (assert (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L) K))))
% 6.57/6.86 (assert (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) N2) (not (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int A) B)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (= M N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (= M N2))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.57/6.86 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N2) (and B (= N2 tptp.zero_zero_nat)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) A) (@ (@ tptp.bit_se2923211474154528505it_int N2) A)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))))
% 6.57/6.86 (assert (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))
% 6.57/6.86 (assert (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))
% 6.57/6.86 (assert (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))
% 6.57/6.86 (assert (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))
% 6.57/6.86 (assert (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) E))) (= X4 tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) E))) (= X4 tptp.zero_zero_rat))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X4) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X4) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X4) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X4) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X4))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))))
% 6.57/6.86 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X4)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X4) Y))))))
% 6.57/6.86 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X4)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X4) Y))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R3) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X4) (@ (@ tptp.ord_le3102999989581377725nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R3) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R3)) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R3) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R3)) X4) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R3) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R3)) X4) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.plus_plus_int A) R3))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R3) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X4) (@ (@ tptp.ord_le6747313008572928689nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R3) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R3)) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R3) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R3)) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat A) R3))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R3) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R3)) X4) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.plus_plus_int A) R3))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Y4))) D3) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X4 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 X4) U)) Y))) V)))))
% 6.57/6.86 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N) A3))))
% 6.57/6.86 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A3) N)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N) A3))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X4)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))))
% 6.57/6.86 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R3)))) (@ (@ tptp.power_power_nat N2) R3)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Y4))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y4) (@ (@ tptp.ord_less_eq_real Y4) B))))))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.semiri4449623510593786356d_enat (@ tptp.pred_numeral K))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc N2)) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N2))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((X4 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 X4)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 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 X4)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 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 X4)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 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 X4)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X4) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X4) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X4) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X4) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))))
% 6.57/6.86 (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)))))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.57/6.86 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))))
% 6.57/6.86 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int _let_1) N))))))))
% 6.57/6.86 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat _let_1) N))))))))
% 6.57/6.86 (assert (forall ((Y tptp.code_integer) (X4 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 X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) Y))))))
% 6.57/6.86 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) Y))))))
% 6.57/6.86 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) Y))))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_rat B) N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))))
% 6.57/6.86 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N))))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri5044797733671781792omplex N2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ tptp.semiri5044797733671781792omplex N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ tptp.semiri773545260158071498ct_rat N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K))))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N2) (= N2 tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))))
% 6.57/6.86 (assert (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.57/6.86 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.57/6.86 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))))
% 6.57/6.86 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.57/6.86 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))))
% 6.57/6.86 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X4 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 X4)) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X4 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 X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X4 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 X4)) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X4 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 X4)) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.86 (assert (= tptp.sin_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N)))))))
% 6.57/6.86 (assert (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K3))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))))
% 6.57/6.86 (assert (= tptp.cos_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ tptp.semiri2265585572941072030t_real N))) tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.57/6.86 (assert (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.57/6.86 (assert (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.57/6.86 (assert (= tptp.semiri2265585572941072030t_real (lambda ((N tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))))
% 6.57/6.86 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X4) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X4)) (@ tptp.abs_abs_int Y))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))))
% 6.57/6.86 (assert (= tptp.abs_abs_int (lambda ((I3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I3)) I3))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))))
% 6.57/6.86 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X4))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X4 Xa) Xc))))))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))))
% 6.57/6.86 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N))))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))))
% 6.57/6.86 (assert (forall ((D tptp.int) (Z tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Z))) tptp.one_one_int)) D))))))
% 6.57/6.86 (assert (forall ((D tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X4))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X4) Y)))))))))
% 6.57/6.86 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 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 L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N2)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N2)))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))) _let_1)))))))))))))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))))))))))))))))
% 6.57/6.86 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.57/6.86 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4)))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.bit_ri7919022796975470100ot_int X4) (@ tptp.bit_ri7919022796975470100ot_int Y)) (= X4 Y))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X4) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.sgn_sgn_Code_integer A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.sgn_sgn_rat A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.sgn_sgn_real A)) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.sgn_sgn_int A)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) Y) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int Y)) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 Y))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))))
% 6.57/6.86 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.57/6.86 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4)))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) X4)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.57/6.86 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.57/6.86 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real X4) tptp.one_one_real) (= X4 tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))))
% 6.57/6.86 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.57/6.86 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (@ tptp.bit_ri7632146776885996613nteger X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (@ tptp.bit_ri7919022796975470100ot_int X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X4)) X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.bit_ri7632146776885996613nteger X4)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.57/6.86 (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))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ tptp.inc N2)))))
% 6.57/6.86 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7632146776885996613nteger A)) (not (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (not (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.57/6.86 (assert (= (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.57/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B) N3) (@ (@ tptp.bit_se1146084159140164899it_int A) N3))) (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X4))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X4))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X4)))))
% 6.57/6.86 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.57/6.86 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N)))))
% 6.57/6.86 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.57/6.86 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))))
% 6.57/6.86 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))))
% 6.57/6.86 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))))
% 6.57/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))))
% 6.57/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))))
% 6.57/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))))
% 6.57/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ (@ tptp.minus_minus_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ _let_1 A))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X4))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (Z tptp.int) (X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) X4) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X4)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X4)))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int B))) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 A))) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int)))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2))) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.zero_zero_int)))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (= (@ tptp.exp_real X5) Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.57/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.57/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.57/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.sgn_sgn_real _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.sgn_sgn_int _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1)))
% 6.57/6.86 (assert (forall ((Y tptp.int) (Z tptp.int) (X4 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 X4) Y)) Z)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X4) Y))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 6.57/6.86 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))))
% 6.57/6.86 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))))
% 6.57/6.86 (assert (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))))
% 6.57/6.86 (assert (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))))
% 6.57/6.86 (assert (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)))
% 6.57/6.86 (assert (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X4)) (@ tptp.abs_abs_Code_integer X4)) X4)))
% 6.57/6.86 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X4)) (@ tptp.abs_abs_rat X4)) X4)))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) (@ tptp.abs_abs_real X4)) X4)))
% 6.57/6.86 (assert (forall ((X4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X4)) (@ tptp.abs_abs_int X4)) X4)))
% 6.57/6.86 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ 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))))))
% 6.57/6.86 (assert (forall ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.57/6.86 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.57/6.86 (assert (forall ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ (@ tptp.times_times_complex Y) X4)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ (@ tptp.times_times_real Y) X4)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y)))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (Z tptp.int) (X4 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 X4) Y)) Z)))))
% 6.57/6.86 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A3)) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A3)) tptp.one_one_int))))
% 6.57/6.86 (assert (= tptp.bit_ri7632146776885996613nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A3)) tptp.one_one_Code_integer))))
% 6.57/6.86 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((A3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A3)) tptp.one_one_int))))
% 6.57/6.86 (assert (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A3) tptp.one_one_Code_integer)))))
% 6.57/6.86 (assert (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A3) tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.57/6.86 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))) tptp.one_one_real)))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X4))) tptp.one_one_complex)))
% 6.57/6.86 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X4) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N2))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X4) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X4)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4)) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N2))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L)) (@ tptp.sgn_sgn_int L))))))
% 6.57/6.86 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.86 (assert (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.57/6.86 (assert (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.57/6.86 (assert (= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= X tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.57/6.86 (assert (= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.57/6.86 (assert (= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= X tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4)))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X4)))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) X4))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X4)))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X4)))) (let ((_let_2 (= X4 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N2) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bitM N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))))))
% 6.57/6.86 (assert (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bitM N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X4)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X4) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X4)))))
% 6.57/6.86 (assert (forall ((R3 tptp.int) (L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) L)) R3)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)))))))
% 6.57/6.86 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.57/6.86 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))))
% 6.57/6.86 (assert (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))))
% 6.57/6.86 (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)))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.86 (assert (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int A)) N2) (and (not (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2))))))
% 6.57/6.86 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.57/6.86 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.57/6.86 (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 ((L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q5) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L2)) R5))))))))
% 6.57/6.86 (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 ((Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q2) A23)))))) (not (forall ((R2 tptp.int) (Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) A23)) R2)))))))))))))
% 6.57/6.86 (assert (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K)))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N2)) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2)) (= N2 tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))
% 6.57/6.86 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))
% 6.57/6.86 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.57/6.86 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.57/6.86 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))
% 6.57/6.86 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X4))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) _let_1))) N2)) (@ tptp.exp_real X4)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))))))))
% 6.57/6.86 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.57/6.86 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.log _let_1) X4) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X4)))))))
% 6.57/6.86 (assert (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) 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 L2) K3))))) _let_2)))))))))))
% 6.57/6.86 (assert (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K3))))))))))))
% 6.57/6.86 (assert (= tptp.arctan (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 X4) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X4)))))))
% 6.57/6.86 (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))))))))))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X4)) (@ _let_1 X4)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.86 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sqrt X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.57/6.86 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.57/6.86 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.57/6.86 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.57/6.86 (assert (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))))
% 6.57/6.86 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X4) Y)))))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) A))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_real A) X4)))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X4) (= (@ _let_2 (@ (@ tptp.log A) X4)) (@ _let_1 X4))))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real A) X4))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) A))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.57/6.86 (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)))
% 6.57/6.86 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X4))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))
% 6.57/6.86 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.86 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.86 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.86 (assert (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))))
% 6.57/6.86 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) K))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sqrt X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))))
% 6.57/6.86 (assert (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y)))))
% 6.57/6.86 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))))
% 6.57/6.86 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.57/6.86 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.57/6.86 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real X4) _let_1) _let_1)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y))))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) N2) (@ (@ tptp.ord_less_eq_int X4) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.86 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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))))
% 6.57/6.86 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.57/6.86 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X4) (@ (@ tptp.divide_divide_real (@ _let_1 X4)) (@ _let_1 B))))))))
% 6.57/6.86 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.57/6.86 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((P (-> tptp.nat Bool)) (I2 tptp.int)) (= (@ P (@ tptp.nat2 I2)) (and (forall ((N tptp.nat)) (=> (= I2 (@ tptp.semiri1314217659103216013at_int N)) (@ P N))) (=> (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))))
% 6.57/6.86 (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))))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))))
% 6.57/6.86 (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)))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))
% 6.57/6.86 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))
% 6.57/6.86 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X4) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.57/6.86 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.57/6.86 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.57/6.86 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real)) (=> (not (= X4 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X4))))))
% 6.57/6.86 (assert (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X4) (@ tptp.sqrt Y)))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt Y)))))
% 6.57/6.86 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X4) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X4)) (@ _let_1 Y)))))))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat) (X4 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X4) (=> (= X4 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X4)) (@ _let_1 Y)))))))))))
% 6.57/6.86 (assert (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))))
% 6.57/6.86 (assert (forall ((A tptp.real) (N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X4)) (@ tptp.semiri5074537144036343181t_real N2))))))
% 6.57/6.86 (assert (forall ((X4 tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X4)))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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))))))
% 6.57/6.86 (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)))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.57/6.87 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.57/6.87 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y)))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X4) Y)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X4) (= Y tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X4 tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.log A) X4) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X4)))))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) Y)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X4) Y))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real Y))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.sqrt X4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) N2) (@ (@ tptp.power_power_real X4) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.57/6.87 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 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 X4)) _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 X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (= (@ tptp.arcosh_real X4) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X4) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.87 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))))
% 6.57/6.87 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.57/6.87 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.57/6.87 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.57/6.87 (assert (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.57/6.87 (assert (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.57/6.87 (assert (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int))
% 6.57/6.87 (assert (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int))
% 6.57/6.87 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X4))) (let ((_let_2 (@ tptp.cos_complex X4))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (let ((_let_2 (@ tptp.cos_real X4))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.numeral_numeral_rat V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))) A) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (=> (= (@ tptp.cos_complex X4) tptp.one_one_complex) (= (@ tptp.sin_complex X4) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.cos_real X4) tptp.one_one_real) (= (@ tptp.sin_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.sin_complex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.sin_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X4)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (=> (= (@ tptp.sin_complex X4) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X4)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X4)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X4))) (@ tptp.cos_complex X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X4))) (@ tptp.cos_real X4))))))
% 6.57/6.87 (assert (forall ((X4 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 X4)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X4))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X4)))))
% 6.57/6.87 (assert (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) (@ tptp.abs_abs_real X4))))
% 6.57/6.87 (assert (forall ((X4 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 X4)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real R3) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R3))))))
% 6.57/6.87 (assert (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R3) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R3))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) (@ tptp.sin_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X4) (@ tptp.cos_real Y)) (= X4 Y)))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)) (@ _let_1 X4))))))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X4))) tptp.one_one_real)))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_2)))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X4)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.pi) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X4)))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _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) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X4)))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _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)))) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real 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)) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real 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)) (=> (= X4 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X4))) tptp.one_one_real))))))
% 6.57/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X4) (@ tptp.sin_real Y)) (= X4 Y))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X4))))))))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X4))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.cos_real X4))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X4) Y))))))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X4))))))))
% 6.57/6.87 (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)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sin_real X4) 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) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.cos_real X4) 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)) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X4) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X4)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.57/6.87 (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)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X4)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X4) (@ (@ tptp.ord_less_eq_real X4) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X4) tptp.zero_zero_real))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) A)) (not (= X4 tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X4) tptp.one_one_real) (= X4 tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.57/6.87 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X4)) X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X4))))
% 6.57/6.87 (assert (forall ((T2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T2)) (@ tptp.sin_real T2))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X4)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X4) A)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) Y))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real A) B))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.57/6.87 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X4) A)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 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 X4) (@ _let_1 Y)) (= X4 Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X4) Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X4) A)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 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) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) tptp.one_one_real)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X4) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X4) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.57/6.87 (assert (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))
% 6.57/6.87 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X4) N2)))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X4))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X4)) Y) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B) Y)))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X4)) Y))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X4) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real X4) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X4))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X4)) Y) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B) Y)))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X4)) Y))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X4) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X4)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X4))))))
% 6.57/6.87 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.plus_plus_real (@ _let_1 X4)) Y) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X4))))))))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X4))))))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X4))))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 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 X4) (=> (@ (@ tptp.ord_less_real X4) _let_2) (= (@ _let_1 X4) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X4))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.minus_minus_real (@ _let_1 X4)) Y) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X4) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X4)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N2)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))))))))
% 6.57/6.87 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X4))) tptp.one_one_real))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (= (@ tptp.tan_real X4) Y) (= (@ tptp.arctan Y) X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X4)) X4))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X4)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.minus_minus_real X4) Y))) (=> (not (= (@ tptp.cos_real X4) 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))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X4) Y))) (=> (not (= (@ tptp.cos_complex X4) 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))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.plus_plus_real X4) Y))) (=> (not (= (@ tptp.cos_real X4) 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))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X4) Y))) (=> (not (= (@ tptp.cos_complex X4) 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))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X4)))))))
% 6.57/6.87 (assert (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))))
% 6.57/6.87 (assert (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))))
% 6.57/6.87 (assert (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.57/6.87 (assert (= tptp.arsinh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_real))))
% 6.57/6.87 (assert (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.87 (assert (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex))
% 6.57/6.87 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X4)) N2))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X4)) N2))))
% 6.57/6.87 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.57/6.87 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.57/6.87 (assert (= (@ tptp.cos_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real B))))))
% 6.57/6.87 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.zero_zero_complex))
% 6.57/6.87 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.57/6.87 (assert (= (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) tptp.one_one_complex))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y))))))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X4)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X4) (@ tptp.arccos Y)) (= X4 Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X4) (@ tptp.arcsin Y)) (= X4 Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X4)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X4))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X4)) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X4) Y))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.57/6.87 (assert (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X4)) tptp.zero_zero_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (= (@ tptp.arccos (@ tptp.cos_real X4)) (@ tptp.uminus_uminus_real X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X4)) tptp.zero_zero_real))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4))))))
% 6.57/6.87 (assert (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.57/6.87 (assert (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.57/6.87 (assert (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))
% 6.57/6.87 (assert (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X4)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X4)) X4))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.57/6.87 (assert (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X4))))))))))
% 6.57/6.87 (assert (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N2)) (= Z (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.57/6.87 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.57/6.87 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.57/6.87 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))))
% 6.57/6.87 (assert (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int))
% 6.57/6.87 (assert (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N2))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N2))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N2))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N2))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X4)) (= (@ (@ tptp.power_power_int B) W) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X4)) (= (@ (@ tptp.power_power_int B) W) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X4)) (= (@ (@ tptp.power_power_int B) W) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X4)) (= (@ (@ tptp.power_power_int B) W) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X4) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X4) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X4) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X4) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) Z))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) Z))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_rat _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))))
% 6.57/6.87 (assert (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_real Z)))))
% 6.57/6.87 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)))
% 6.57/6.87 (assert (forall ((N2 tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z2)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X4)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))))))
% 6.57/6.87 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.57/6.87 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4))) X4)))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4))) X4)))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X4))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (=> (= X4 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (=> (= X4 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_real R3) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3))) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N2))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real R3) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3))) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3)))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3)))))
% 6.57/6.87 (assert (forall ((P (-> tptp.int Bool)) (T2 tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T2) (@ (@ tptp.ord_less_real T2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I3)))))))
% 6.57/6.87 (assert (forall ((P (-> tptp.int Bool)) (T2 tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T2) (@ (@ tptp.ord_less_rat T2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I3)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X4) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X4) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) Z))))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X4) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X4) Z))))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N2))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim7802044766580827645g_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim2889992004027027881ng_rat X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))))
% 6.57/6.87 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)) P2))))
% 6.57/6.87 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)) P2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.57/6.87 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.57/6.87 (assert (forall ((K tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.bit_ri7919022796975470100ot_int K)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.ring_1_of_int_int K)))))
% 6.57/6.87 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P2) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)))))
% 6.57/6.87 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat P2) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) A))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X4))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X4))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4)))))
% 6.57/6.87 (assert (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R3)))) R3))))
% 6.57/6.87 (assert (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R3)))) R3))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X4)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X4) (@ (@ tptp.ord_less_real X4) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X4)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) A) (@ (@ tptp.ord_less_eq_nat X4) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X4) (@ (@ tptp.ord_less_real X4) (@ 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)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X4) (@ (@ tptp.ord_less_rat X4) (@ 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)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R3))) (@ (@ tptp.plus_plus_real R3) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R3))) (@ (@ tptp.plus_plus_rat R3) tptp.one_one_rat))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 6.57/6.87 (assert (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R3))) tptp.one_one_real)) R3)))
% 6.57/6.87 (assert (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R3))) tptp.one_one_rat)) R3)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim6058952711729229775r_real X4))) tptp.one_one_int)))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim3151403230148437115or_rat X4))) tptp.one_one_int)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X4))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X4))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X4)) (@ _let_1 X4)))))
% 6.57/6.87 (assert (= tptp.ord_less_eq_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))))
% 6.57/6.87 (assert (= tptp.ord_less_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))))
% 6.57/6.87 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X4) D))) _let_1))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N2)))))
% 6.57/6.87 (assert (forall ((P (-> tptp.int Bool)) (T2 tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T2) (@ (@ tptp.ord_less_eq_real T2) _let_1)) (@ P I3)))))))
% 6.57/6.87 (assert (forall ((P (-> tptp.int Bool)) (T2 tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T2) (@ (@ tptp.ord_less_eq_rat T2) _let_1)) (@ P I3)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X4) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X4) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1))))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.archim7802044766580827645g_real X4) Z))))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X4) Z))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1)))))
% 6.57/6.87 (assert (= tptp.cot_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))))
% 6.57/6.87 (assert (= tptp.cot_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X)) (@ tptp.sin_complex X)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4)))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)))))
% 6.57/6.87 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)))))
% 6.57/6.87 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.57/6.87 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.57/6.87 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))
% 6.57/6.87 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))
% 6.57/6.87 (assert (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)) P2))))
% 6.57/6.87 (assert (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)) P2))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X4) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N2))) (=> (@ (@ tptp.ord_less_rat _let_1) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X4) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (exists ((X tptp.int)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.57/6.87 (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))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X4)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.cot_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) 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)) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) 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) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ 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) X4) (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)))))))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X4) _let_1)) (= (@ tptp.archim8280529875227126926d_real X4) Y)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X4) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X4) Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.ring_1_of_int_rat N2)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X4) N2))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) (@ tptp.ring_1_of_int_real N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X4) N2))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) X4))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) X4))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))))
% 6.57/6.87 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.57/6.87 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X4)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim8280529875227126926d_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim7778729529865785530nd_rat X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X4)) (@ tptp.archim7802044766580827645g_real X4))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X))) (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X)))))
% 6.57/6.87 (assert (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X))) (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))))
% 6.57/6.87 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A)))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A)))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X4) tptp.one_one_rat) (= X4 tptp.one_one_rat))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.inverse_inverse_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_complex))))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real))
% 6.57/6.87 (assert (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.inverse_inverse_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real B) A))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex B) A))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat A)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real A)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A)))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_rat A)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.abs_abs_real A)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.abs_abs_complex A)))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.inverse_inverse_real _let_1) _let_1))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.sgn_sgn_rat A)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.sgn_sgn_real A)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.sgn_sgn_complex A)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_complex tptp.zero_zero_complex) (@ tptp.suc K)) tptp.zero_zero_complex)))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_real tptp.zero_zero_real) (@ tptp.suc K)) tptp.zero_zero_real)))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_rat tptp.zero_zero_rat) (@ tptp.suc K)) tptp.zero_zero_rat)))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_nat tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.gbinomial_int tptp.zero_zero_int) (@ tptp.suc K)) tptp.zero_zero_int)))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.gbinomial_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ (@ tptp.gbinomial_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.gbinomial_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.57/6.87 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gbinomial_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.57/6.87 (assert (forall ((A tptp.int)) (= (@ (@ tptp.gbinomial_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.57/6.87 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.invers8013647133539491842omplex A)) tptp.one_one_complex))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.invers8013647133539491842omplex _let_1) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_1)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))
% 6.57/6.87 (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))
% 6.57/6.87 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.57/6.87 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.57/6.87 (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)))
% 6.57/6.87 (assert (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X4))) (=> (= (@ (@ tptp.times_times_real Y) X4) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X4) (@ _let_2 _let_1)))))))
% 6.57/6.87 (assert (forall ((Y tptp.complex) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X4))) (=> (= (@ (@ tptp.times_times_complex Y) X4) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ _let_2 _let_1)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N2) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N2) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N2)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) (@ tptp.inverse_inverse_real B)) (= A B))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) (@ tptp.invers8013647133539491842omplex B)) (= A B))))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.57/6.87 (assert (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.57/6.87 (assert (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.inverse_inverse_rat A)) A))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.inverse_inverse_real (@ tptp.inverse_inverse_real A)) A))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.invers8013647133539491842omplex A)) A))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ tptp.inverse_inverse_real A) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ tptp.invers8013647133539491842omplex A) tptp.zero_zero_complex)))))
% 6.57/6.87 (assert (forall ((R3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R3) (@ tptp.real_V7735802525324610683m_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X4))) (@ tptp.inverse_inverse_real R3))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R3) (@ tptp.real_V1022390504157884413omplex X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X4))) (@ tptp.inverse_inverse_real R3))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.invers8013647133539491842omplex A))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.one_one_real) (= (@ tptp.inverse_inverse_real A) B))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.one_one_complex) (= (@ tptp.invers8013647133539491842omplex A) B))))
% 6.57/6.87 (assert (let ((_let_1 (@ tptp.numeral_numeral_real tptp.one))) (= (@ tptp.inverse_inverse_real _let_1) _let_1)))
% 6.57/6.87 (assert (let ((_let_1 (@ tptp.numera6690914467698888265omplex tptp.one))) (= (@ tptp.invers8013647133539491842omplex _let_1) _let_1)))
% 6.57/6.87 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))))
% 6.57/6.87 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))))
% 6.57/6.87 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.57/6.87 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.57/6.87 (assert (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real A3) (@ tptp.inverse_inverse_real B2)))))
% 6.57/6.87 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex A3) (@ tptp.invers8013647133539491842omplex B2)))))
% 6.57/6.87 (assert (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))
% 6.57/6.87 (assert (= tptp.inverse_inverse_real (@ tptp.divide_divide_real tptp.one_one_real)))
% 6.57/6.87 (assert (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X4))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X4)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X4)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))))
% 6.57/6.87 (assert (forall ((Xa tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X4) (@ (@ tptp.times_times_real X4) _let_1)))))
% 6.57/6.87 (assert (forall ((Xa tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ (@ tptp.times_times_complex X4) _let_1)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (= tptp.divide_divide_real (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y5)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X4)) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X4)) tptp.one_one_rat)))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X4))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex A)) A) tptp.one_one_complex))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ tptp.invers8013647133539491842omplex A) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X4) Y) tptp.imaginary_unit) (and (= X4 tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.57/6.87 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) X4)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))))
% 6.57/6.87 (assert (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (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) E2) (@ P E2))))))
% 6.57/6.87 (assert (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N)))) (and (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real _let_1) X4) (@ tptp.inverse_inverse_real _let_1))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N3))) X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))) X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (not (= X4 tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X4)) M))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (not (= X4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X4)) M))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (not (= X4 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X4)) M))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (assert (forall ((K tptp.nat) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ _let_1 (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ _let_1 X4))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) X4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) X4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))))
% 6.57/6.87 (assert (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))))
% 6.57/6.87 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.57/6.87 (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)))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X4)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_complex))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (or (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (or (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4)) (not (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4)) (not (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat)))))
% 6.57/6.87 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.57/6.87 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N2)) tptp.ring_1_Ints_real))))
% 6.57/6.87 (assert (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.power_power_int A) N2)) tptp.ring_1_Ints_int))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N2)) tptp.ring_1_Ints_complex))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.ring_1_Ints_complex)))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N2)) tptp.ring_1_Ints_real)))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N2)) tptp.ring_1_Ints_int)))
% 6.57/6.87 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.ring_1_Ints_complex))
% 6.57/6.87 (assert (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat))
% 6.57/6.87 (assert (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int))
% 6.57/6.87 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.ring_1_Ints_real))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.ring_1_Ints_complex)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.ring_1_Ints_real)))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.ring_1_Ints_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B)) tptp.ring_1_Ints_int)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (= (= (@ (@ tptp.plus_plus_complex A) A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.57/6.87 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))))
% 6.57/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) tptp.ring_1_Ints_rat))))
% 6.57/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_int (@ (@ tptp.divide_divide_int (@ tptp.ring_1_of_int_int A)) (@ tptp.ring_1_of_int_int B))) tptp.ring_1_Ints_int))))
% 6.57/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) tptp.ring_1_Ints_real))))
% 6.57/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.ring_17405671764205052669omplex A)) (@ tptp.ring_17405671764205052669omplex B))) tptp.ring_1_Ints_complex))))
% 6.57/6.87 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_Code_integer (@ (@ tptp.divide6298287555418463151nteger (@ tptp.ring_18347121197199848620nteger A)) (@ tptp.ring_18347121197199848620nteger B))) tptp.ring_11222124179247155820nteger))))
% 6.57/6.87 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.57/6.87 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (not (= X4 tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (not (= X4 tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (not (= X4 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer) (= X4 tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= X4 tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat) (= X4 tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int) (= X4 tptp.zero_zero_int)))))
% 6.57/6.87 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger) (= (= X4 Y) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) Y))) tptp.one_one_Code_integer))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real) (= (= X4 Y) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y))) tptp.one_one_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X4 Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) Y))) tptp.one_one_rat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X4 Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Y))) tptp.one_one_int))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X4)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X4)))) (let ((_let_2 (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X4)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X4)))) (let ((_let_2 (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X4)))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X4) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X4) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_real))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((Z tptp.complex) (X4 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X4)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arg Z) X4))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_2)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (= (@ tptp.cosh_real X4) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N2) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N2) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) A)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.plus_plus_nat M) N2)) A))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat M) (@ (@ tptp.bit_se547839408752420682it_nat N2) A)) (@ (@ tptp.bit_se547839408752420682it_nat (@ (@ tptp.plus_plus_nat M) N2)) A))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N2) L))))
% 6.57/6.87 (assert (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.57/6.87 (assert (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger N2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.57/6.87 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))))
% 6.57/6.87 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N2)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) A) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N2)) A) (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7788150548672797655nteger N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se547839408752420682it_nat N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.pred_numeral L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))))
% 6.57/6.87 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.semiri1314217659103216013at_int N2)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N2)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat N2) M)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se7788150548672797655nteger N2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ _let_1 X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N2)) A))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat M) N2)) A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X4) Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X4))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q3)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N2) M))))))
% 6.57/6.87 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.arcosh_real (@ tptp.cosh_real X4)) X4))))
% 6.57/6.87 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.57/6.87 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X4)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X4)) (@ tptp.sinh_complex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex X4)) (@ tptp.exp_complex X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real X4)) (@ tptp.exp_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex X4)) (@ tptp.exp_complex X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4)) (@ tptp.exp_real X4))))
% 6.57/6.87 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.57/6.87 (assert (= tptp.tanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)))))
% 6.57/6.87 (assert (= tptp.tanh_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_2 (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int (@ _let_2 A)) _let_1))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_2 (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 A)) _let_1))))))
% 6.57/6.87 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.57/6.87 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat N2) M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int M))))))
% 6.57/6.87 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))))
% 6.57/6.87 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))))
% 6.57/6.87 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.87 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.87 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.times_times_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.87 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.times_times_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.bit_se7788150548672797655nteger N2) B5))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.bit_se545348938243370406it_int N2) B5))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.bit_se547839408752420682it_nat N2) B5))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X4))) (@ tptp.cosh_complex X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X4))) (@ tptp.cosh_real X4))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y))) (let ((_let_2 (@ tptp.tanh_real X4))) (=> (not (= (@ tptp.cosh_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y))) (let ((_let_2 (@ tptp.tanh_complex X4))) (=> (not (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))))
% 6.57/6.87 (assert (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) tptp.one_one_complex)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ (@ tptp.groups3417619833198082522nteger tptp.zero_n356916108424825756nteger) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 6.57/6.87 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ (@ tptp.groups9119017779487936845_o_nat tptp.zero_n2687167440665602831ol_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 6.57/6.87 (assert (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))))
% 6.57/6.87 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X3 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X3 M6)) (@ X3 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa Mi3) (= Xa Ma3)))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (= Y (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3))))))))))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.57/6.87 (assert (= (lambda ((H2 tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.57/6.87 (assert (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.57/6.87 (assert (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.57/6.87 (assert (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.57/6.87 (assert (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_le7866589430770878221at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le549003669493604880_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))))
% 6.57/6.87 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))))
% 6.57/6.87 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ P X))))) A2)))
% 6.57/6.87 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ P X))))) A2)))
% 6.57/6.87 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) A2)))
% 6.57/6.87 (assert (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) A2) (@ P X))))) A2)))
% 6.57/6.87 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ P X))))) A2)))
% 6.57/6.87 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) A2)))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.57/6.87 (assert (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.57/6.87 (assert (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.57/6.87 (assert (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)))
% 6.57/6.87 (assert (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.57/6.87 (assert (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_int)))
% 6.57/6.87 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X4)) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.57/6.87 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.57/6.87 (assert (= tptp.set_complex2 (lambda ((Xs3 tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu3 tptp.complex)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_complex Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_real2 (lambda ((Xs3 tptp.list_real)) (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_real Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_list_nat2 (lambda ((Xs3 tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu3 tptp.list_nat)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_list_nat Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_VEBT_VEBT2 (lambda ((Xs3 tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu3 tptp.vEBT_VEBT)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_VEBT_VEBT Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_o2 (lambda ((Xs3 tptp.list_o)) (@ tptp.collect_o (lambda ((Uu3 Bool)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_o Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_nat2 (lambda ((Xs3 tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu3 tptp.nat)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_nat Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs3)))))))))
% 6.57/6.87 (assert (= tptp.set_int2 (lambda ((Xs3 tptp.list_int)) (@ tptp.collect_int (lambda ((Uu3 tptp.int)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_int Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs3)))))))))
% 6.57/6.87 (assert (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.57/6.87 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.57/6.87 (assert (= tptp.nat_set_decode (lambda ((X tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat _let_1) N))))))))))
% 6.57/6.87 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A3))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))
% 6.57/6.87 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A3))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))))
% 6.57/6.87 (assert (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N tptp.nat)) (@ (@ (@ tptp.if_rat (= N 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 N) tptp.one_one_nat)) tptp.one_one_rat)))))
% 6.57/6.87 (assert (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_complex)))))
% 6.57/6.87 (assert (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_real)))))
% 6.57/6.87 (assert (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int)))))
% 6.57/6.87 (assert (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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 ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))))
% 6.57/6.87 (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 ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex K3))))))
% 6.57/6.87 (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 ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))))
% 6.57/6.87 (assert (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))))
% 6.57/6.87 (assert (forall ((X8 (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M2)) (@ X8 N6)))) E2))))))))))
% 6.57/6.87 (assert (forall ((X8 (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M2)) (@ X8 N6)))) E2))))))))))
% 6.57/6.87 (assert (forall ((X8 (-> tptp.nat tptp.complex))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M5)) (@ X8 N3)))) E)))))))) (@ tptp.topolo6517432010174082258omplex X8))))
% 6.57/6.87 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M5)) (@ X8 N3)))) E)))))))) (@ tptp.topolo4055970368930404560y_real X8))))
% 6.57/6.87 (assert (= tptp.topolo6517432010174082258omplex (lambda ((X3 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X3 M6)) (@ X3 N)))) E3)))))))))))
% 6.57/6.87 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X3 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X3 M6)) (@ X3 N)))) E3)))))))))))
% 6.57/6.87 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))))
% 6.57/6.87 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc2)) X4) (or (= X4 Mi) (= X4 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa Mi3) (= Xa Ma3))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3)))))))))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))))
% 6.57/6.87 (assert (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))))
% 6.57/6.87 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.57/6.87 (assert (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_rat (= K3 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))))))
% 6.57/6.87 (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)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X4) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ tptp.suc N))))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ F tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ F tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_real (@ tptp.re X4)) N2)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X4) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.im X4))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X4)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X4)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X4) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.57/6.87 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.real_V1022390504157884413omplex X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X4) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X4) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X4))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X4))) (@ tptp.im X4))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X4))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X4))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.57/6.87 (assert (forall ((X4 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 X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.57/6.87 (assert (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y5))) (let ((_let_3 (@ tptp.re Y5))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.57/6.87 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat)))))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arctan X4) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))))))))
% 6.57/6.87 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (= (@ tptp.suminf_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.57/6.87 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (= (@ tptp.suminf_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X4) Y) (=> (=> (= X4 tptp.zero_zero_nat) _let_1) (=> (=> (= X4 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X4 _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)))))))))))))))))))))))
% 6.57/6.87 (assert (forall ((R3 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R3))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X4)) I2))))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X4)) I2))))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) I2))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (X4 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X4) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X4 Y))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) N2)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X4)) N2)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X4)) N2)))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X4)) N2)))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_real F))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X4) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.product_prod_nat_nat) (N2 tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X4)) I2) X4))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X4)) I2) X4))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) I2) X4))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))))
% 6.57/6.87 (assert (forall ((C tptp.real)) (= (@ tptp.summable_real (@ tptp.power_power_real C)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((C tptp.complex)) (= (@ tptp.summable_complex (@ tptp.power_power_complex C)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N2)) tptp.real_V470468836141973256s_real))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N2)) tptp.real_V2521375963428798218omplex))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.real_V470468836141973256s_real)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.real_V2521375963428798218omplex)))))
% 6.57/6.87 (assert (@ (@ tptp.member_real tptp.one_one_real) tptp.real_V470468836141973256s_real))
% 6.57/6.87 (assert (@ (@ tptp.member_complex tptp.one_one_complex) tptp.real_V2521375963428798218omplex))
% 6.57/6.87 (assert (forall ((W tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex W)) tptp.real_V2521375963428798218omplex)))
% 6.57/6.87 (assert (forall ((W tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real W)) tptp.real_V470468836141973256s_real)))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))))
% 6.57/6.87 (assert (@ tptp.summable_real (@ tptp.power_power_real tptp.zero_zero_real)))
% 6.57/6.87 (assert (@ tptp.summable_int (@ tptp.power_power_int tptp.zero_zero_int)))
% 6.57/6.87 (assert (@ tptp.summable_complex (@ tptp.power_power_complex tptp.zero_zero_complex)))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.complex)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_complex G) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.member_complex (@ G N3)) tptp.real_V2521375963428798218omplex)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ G N3)))) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ tptp.real_V1022390504157884413omplex (@ G N3))))) (@ tptp.summable_real F)))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.complex)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex G) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.member_complex (@ G N3)) tptp.real_V2521375963428798218omplex)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ G N3)))) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ tptp.real_V1022390504157884413omplex (@ G N3))))) (@ tptp.summable_complex F)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X4 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (= (@ tptp.suminf_real F) tptp.zero_zero_real) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_real)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (= (@ tptp.suminf_nat F) tptp.zero_zero_nat) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_nat)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (= (@ tptp.suminf_int F) tptp.zero_zero_int) (forall ((N tptp.nat)) (= (@ F N) tptp.zero_zero_int)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F N3))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F N3))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F N3))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F N)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_real) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_real N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_complex) (N2 tptp.nat) (X4 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N2) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_complex N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_P6011104703257516679at_nat) (N2 tptp.nat) (X4 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs) N2) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replic4235873036481779905at_nat N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_o) (N2 tptp.nat) (X4 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N2) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_o N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X4 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_nat N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_int) (N2 tptp.nat) (X4 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_int N2) X4))))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X4 tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X4) Xs))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_o) (X4 Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X4) Xs))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_nat) (X4 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X4) Xs))))
% 6.57/6.87 (assert (forall ((Xs tptp.list_int) (X4 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X4) Xs))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (=> (not (= B tptp.zero_zero_real)) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real))))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (=> (not (= B tptp.zero_zero_complex)) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_real F))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_nat F))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (I2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (=> (@ _let_1 (@ F I2)) (@ _let_1 (@ tptp.suminf_int F))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F N3))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.suminf_real F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I3))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F N3))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suminf_nat F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I3))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F N3))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.suminf_int F)) (exists ((I3 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I3))))))))
% 6.57/6.87 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real C)))))
% 6.57/6.87 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex C)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X4)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X4 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N))) (@ (@ tptp.power_power_complex X4) N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N6)))))) R3))))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N6)))))) R3))))))))
% 6.57/6.87 (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))))))))))
% 6.57/6.87 (assert (forall ((R3 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_real R3) 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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R3) N)))))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))))
% 6.57/6.87 (assert (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))))
% 6.57/6.87 (assert (forall ((R3 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R3)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.sin_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (= Y (or (= Xa Mi3) (= Xa Ma3))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))))
% 6.57/6.87 (assert (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.57/6.87 (assert (forall ((A (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X4) (= (@ A tptp.zero_zero_nat) X4))))
% 6.57/6.87 (assert (forall ((A (-> tptp.nat tptp.real)) (X4 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X4) (= (@ A tptp.zero_zero_nat) X4))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T2) (@ (@ tptp.ord_less_eq_real S) T2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T2) (@ (@ tptp.ord_less_eq_nat S) T2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T2 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T2) (@ (@ tptp.ord_less_eq_int S) T2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real A) C)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))))
% 6.57/6.87 (assert (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_complex F) S)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) S)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.power_power_complex Z) M))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.power_power_real Z) M))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N)))) (@ (@ tptp.power_power_int Z) M))))
% 6.57/6.87 (assert (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ A tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ A tptp.zero_zero_nat))))
% 6.57/6.87 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))))
% 6.57/6.87 (assert (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))))
% 6.57/6.87 (assert (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N)))) tptp.one_one_real))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) X4))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ F (@ (@ tptp.divide_divide_nat N) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X4) Y))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi3) (= Xa Ma3))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_1) (=> (= 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) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N))))))))
% 6.57/6.87 (assert (= tptp.diffs_complex (lambda ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C2 _let_1))))))
% 6.57/6.87 (assert (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))
% 6.57/6.87 (assert (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N)))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N)))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N)))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N))))))))
% 6.57/6.87 (assert (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.57/6.87 (assert (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) X)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1)))))))))
% 6.57/6.87 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X3 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X3 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X3 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X3 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X3 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X3 N)) (@ X3 M6))))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X4) Y)) N2) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X4) Y)) N2) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_complex Y) N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ tptp.uminus_uminus_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ tptp.uminus1482373934393186551omplex X4))))
% 6.57/6.87 (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)))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X4)) (@ _let_1 Y))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X4) Y)) Xa) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X4) Xa)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa)))))
% 6.57/6.87 (assert (= tptp.real_V1803761363581548252l_real (lambda ((R5 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real R5) tptp.one_one_real))))
% 6.57/6.87 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.real_V2046097035970521341omplex R5) tptp.one_one_complex))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) X4))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X4)))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))))
% 6.57/6.87 (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)))))))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (X4 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 X4) Y) (=> (@ _let_1 B) (=> (@ _let_1 X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) Y)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) X4)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4) (@ (@ tptp.plus_plus_real X4) X4))))
% 6.57/6.87 (assert (forall ((M tptp.real) (X4 tptp.real) (C tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X4)) C) Y) (= X4 (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C))))))))
% 6.57/6.87 (assert (forall ((M tptp.real) (Y tptp.real) (X4 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X4)) C)) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C)) X4))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.sin_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.sin_complex X4))))
% 6.57/6.87 (assert (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.57/6.87 (assert (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.cos_complex X4))))
% 6.57/6.87 (assert (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X) N)))))))
% 6.57/6.87 (assert (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X4) N)))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))))
% 6.57/6.87 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.exp_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.exp_complex X4))))
% 6.57/6.87 (assert (= tptp.exp_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 6.57/6.87 (assert (= tptp.exp_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) N))))) (@ tptp.sin_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) N))))) (@ tptp.sin_complex X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) N)))) (@ tptp.cos_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) N)))) (@ tptp.cos_complex X4))))
% 6.57/6.87 (assert (= tptp.cosh_real (lambda ((X tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))))
% 6.57/6.87 (assert (= tptp.cosh_complex (lambda ((X tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))))
% 6.57/6.87 (assert (= tptp.sinh_real (lambda ((X tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))))
% 6.57/6.87 (assert (= tptp.sinh_complex (lambda ((X tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))))
% 6.57/6.87 (assert (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))
% 6.57/6.87 (assert (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))) tptp.zero_zero_real))) (@ tptp.cosh_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))) tptp.zero_zero_complex))) (@ tptp.cosh_complex X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))) (@ tptp.sinh_real X4))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_complex) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))))) (@ tptp.sinh_complex X4))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (= tptp.topolo6980174941875973593q_real (lambda ((X3 (-> tptp.nat tptp.real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.topolo3100542954746470799et_int (lambda ((X3 (-> tptp.nat tptp.set_int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.topolo4267028734544971653eq_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.topolo1459490580787246023eq_num (lambda ((X3 (-> tptp.nat tptp.num))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.topolo4902158794631467389eq_nat (lambda ((X3 (-> tptp.nat tptp.nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.topolo4899668324122417113eq_int (lambda ((X3 (-> tptp.nat tptp.int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X3 (@ tptp.suc N))) (@ X3 N)))))))
% 6.57/6.87 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N) tptp.zero_zero_real))))
% 6.57/6.87 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N) tptp.zero_zero_int))))
% 6.57/6.87 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N) tptp.zero_zero_nat))))
% 6.57/6.87 (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))))))))
% 6.57/6.87 (assert (= tptp.vEBT_set_vebt (lambda ((T tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X4) (@ tptp.set_ord_atMost_nat Y)) (= X4 Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X4) (@ tptp.set_ord_atMost_int Y)) (= X4 Y))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X4)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X4)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X4)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X4)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X4)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X4) Y))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S2))) (@ (@ tptp.groups8097168146408367636l_real G) S2)))))
% 6.57/6.87 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S2))) (@ (@ tptp.groups8778361861064173332t_real G) S2)))))
% 6.57/6.87 (assert (forall ((S2 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) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S2))) (@ (@ tptp.groups4567486121110086003t_real G) S2)))))
% 6.57/6.87 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.57/6.87 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ 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) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.57/6.87 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S2))) (@ (@ tptp.groups5808333547571424918x_real G) S2)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ 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 N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) U2))))))
% 6.57/6.87 (assert (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))
% 6.57/6.87 (assert (forall ((R3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R3) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R3) N2))) N2))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) tptp.zero_zero_complex))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) tptp.zero_zero_real))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 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 N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 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 N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (N2 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 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))))
% 6.57/6.87 (assert (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat) (R3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R3) K3))))) (@ tptp.set_ord_atMost_nat R3)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R3))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))
% 6.57/6.87 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 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))) N2)))) (@ (@ 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 N2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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 N2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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 N2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N2)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N2 tptp.nat) (B (-> tptp.nat tptp.rat)) (X4 tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) 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 X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B (-> tptp.nat tptp.int)) (X4 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X4 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))))
% 6.57/6.87 (assert (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s2602460028002588243omplex A) K3))) (@ (@ tptp.comm_s2602460028002588243omplex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))))
% 6.57/6.87 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.57/6.87 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.rat)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.57/6.87 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.int)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.57/6.87 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.nat)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.57/6.87 (assert (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.real)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.complex) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.rat) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.real) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ (@ tptp.times_times_complex Y) X4)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) N2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I3))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I3))) (@ (@ tptp.power_power_complex X4) I3))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ (@ tptp.times_times_real Y) X4)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I3))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I3))) (@ (@ tptp.power_power_real X4) I3))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z) N2) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I3 N2)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z) N2) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I3 N2)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N2) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I3 N2)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_rat Z) N2) 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 N2)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat)))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z) N2) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I3 N2)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.rat) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.complex) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (A tptp.real) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N2) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))))
% 6.57/6.87 (assert (forall ((E2 tptp.real) (C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.real)) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z3))) (=> (@ (@ tptp.ord_less_eq_real M9) _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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.57/6.87 (assert (forall ((E2 tptp.real) (C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.real)) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z3))) (=> (@ (@ tptp.ord_less_eq_real M9) _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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (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)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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 N2) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N2) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (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))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (@ _let_2 N))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (@ _let_2 N))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ 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 P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y)))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ 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 P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.57/6.87 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))))
% 6.57/6.87 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_real) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_nat) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_complex) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_int) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_real) (X4 (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_complex) (X4 (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_int) (X4 (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_real) (X4 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_nat) (X4 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((I5 tptp.set_complex) (X4 (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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.groups5058264527183730370ex_rat (lambda ((I3 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X4 I3)))) I5)) B))) Delta))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X4) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X4) (@ tptp.set_ord_lessThan_nat Y)) (= X4 Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X4) (@ tptp.set_ord_lessThan_int Y)) (= X4 Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X4) (@ tptp.set_or5984915006950818249n_real Y)) (= X4 Y))))
% 6.57/6.87 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)))
% 6.57/6.87 (assert (forall ((I2 tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I2) K))))
% 6.57/6.87 (assert (forall ((I2 tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I2) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I2) K))))
% 6.57/6.87 (assert (forall ((I2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I2) K))))
% 6.57/6.87 (assert (forall ((I2 tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I2) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I2) K))))
% 6.57/6.87 (assert (forall ((I2 tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I2) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I2) K))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X4)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X4)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X4)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X4)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X4) Y))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X4)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)))
% 6.57/6.87 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N2))) (=> (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 ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.57/6.87 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.57/6.87 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))))
% 6.57/6.87 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))
% 6.57/6.87 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))
% 6.57/6.87 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))
% 6.57/6.87 (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 ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.57/6.87 (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 ((X tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.57/6.87 (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 ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.57/6.87 (assert (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (G (-> tptp.product_prod_nat_nat tptp.nat)) (F (-> tptp.product_prod_nat_nat tptp.nat))) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) A2) (@ (@ tptp.ord_less_eq_nat (@ G X5)) (@ F X5)))) (= (@ (@ tptp.groups977919841031483927at_nat (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups977919841031483927at_nat F) A2)) (@ (@ tptp.groups977919841031483927at_nat G) A2))))))
% 6.57/6.87 (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 ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))))
% 6.57/6.87 (assert (forall ((M tptp.rat) (N2 tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N2)) (@ (@ tptp.ord_less_rat M) N2))))
% 6.57/6.87 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))))
% 6.57/6.87 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.87 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))))
% 6.57/6.87 (assert (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X4)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X4)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X4)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ 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 N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (X4 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))) X4)) (@ tptp.summable_int F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (X4 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))) X4)) (@ tptp.summable_nat F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (X4 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))) X4)) (@ tptp.summable_real F)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (not (= X4 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (not (= X4 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (not (= X4 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ 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 N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real F) (@ (@ tptp.plus_plus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))))
% 6.57/6.87 (assert (forall ((Z tptp.rat) (H tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.57/6.87 (assert (forall ((Z tptp.complex) (H tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.57/6.87 (assert (forall ((Z tptp.int) (H tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.57/6.87 (assert (forall ((Z tptp.real) (H tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X4) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X4) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X4) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X4) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X4) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N2 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 N2)) tptp.zero_zero_rat) (not (forall ((B5 (-> tptp.nat tptp.rat))) (not (forall ((Z3 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z3) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N2 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 N2)) tptp.zero_zero_complex) (not (forall ((B5 (-> tptp.nat tptp.complex))) (not (forall ((Z3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N2 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 N2)) tptp.zero_zero_int) (not (forall ((B5 (-> tptp.nat tptp.int))) (not (forall ((Z3 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N2 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 N2)) tptp.zero_zero_real) (not (forall ((B5 (-> tptp.nat tptp.real))) (not (forall ((Z3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.rat)) (N2 tptp.nat) (A tptp.rat)) (exists ((B5 (-> tptp.nat tptp.rat))) (forall ((Z3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z3) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat A) I3)))) _let_1))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B5 (-> tptp.nat tptp.complex))) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex A) I3)))) _let_1))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B5 (-> tptp.nat tptp.int))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int A) I3)))) _let_1))))))))
% 6.57/6.87 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (A tptp.real)) (exists ((B5 (-> tptp.nat tptp.real))) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) _let_1))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) K5))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.times_times_int (@ _let_1 X4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ _let_1 X4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))))
% 6.57/6.87 (assert (forall ((H tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B7 tptp.real)) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B7) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((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))) N2))) (@ (@ 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))))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H) A2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H) A2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H) A2)))))
% 6.57/6.87 (assert (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H) A2)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R3 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) R3))) A2))))
% 6.57/6.87 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) R3))) A2))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1))))))))))
% 6.57/6.87 (assert (forall ((K tptp.nat)) (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X4)) N2)))))
% 6.57/6.87 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (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)))))
% 6.57/6.87 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((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))))))
% 6.57/6.87 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)) (=> (forall ((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))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (not (= X4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (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 X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))))
% 6.57/6.87 (assert (forall ((H tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H 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) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) Q5)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.57/6.87 (assert (forall ((H tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) Q5)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.57/6.87 (assert (forall ((H tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H 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) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) Q5)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.57/6.87 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X4) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X4)))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X4)))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))))))))))))
% 6.57/6.88 (assert (forall ((R3 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 R3) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R3) (@ 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 R3) _let_1))))))
% 6.57/6.88 (assert (forall ((R3 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R3) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R3) (@ 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 R3) _let_1))))))
% 6.57/6.88 (assert (forall ((R3 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 R3) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R3) (@ 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 R3) _let_1))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))))
% 6.57/6.88 (assert (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))))
% 6.57/6.88 (assert (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I2) (@ (@ tptp.ord_less_eq_num I2) U)))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I2) (@ (@ tptp.ord_less_eq_int I2) U)))))
% 6.57/6.88 (assert (forall ((I2 tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I2) (@ (@ tptp.ord_less_eq_real I2) U)))))
% 6.57/6.88 (assert (forall ((L tptp.set_int) (H tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.57/6.88 (assert (forall ((L tptp.rat) (H tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.57/6.88 (assert (forall ((L tptp.num) (H tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (H tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.57/6.88 (assert (forall ((L tptp.int) (H tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.57/6.88 (assert (forall ((L tptp.real) (H tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((L tptp.set_int) (H tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H)) (@ (@ tptp.ord_less_eq_set_int H) H3)))))
% 6.57/6.88 (assert (forall ((L tptp.rat) (H tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H)) (@ (@ tptp.ord_less_eq_rat H) H3)))))
% 6.57/6.88 (assert (forall ((L tptp.num) (H tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H)) (@ (@ tptp.ord_less_eq_num H) H3)))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (H tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H)) (@ (@ tptp.ord_less_eq_nat H) H3)))))
% 6.57/6.88 (assert (forall ((L tptp.int) (H tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H)) (@ (@ tptp.ord_less_eq_int H) H3)))))
% 6.57/6.88 (assert (forall ((L tptp.real) (H tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H)) (@ (@ tptp.ord_less_eq_real H) H3)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((H3 tptp.int) (L tptp.int) (H tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H)))))
% 6.57/6.88 (assert (forall ((H3 tptp.real) (L tptp.real) (H tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H)))))
% 6.57/6.88 (assert (forall ((H tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))))
% 6.57/6.88 (assert (forall ((H tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.57/6.88 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 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 N2))) (=> (@ (@ 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 N2))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 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 N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N2 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 N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.complex)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_complex))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.rat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo1949268297981939178at_rat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_rat))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.int)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.plus_plus_int (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_int))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_nat))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.plus_plus_real (@ F A3)) __flatten_var_0))) A) B) tptp.zero_zero_real))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (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))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (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 N2) 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)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ 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)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N6)))) E2)))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N6)))) E2)))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 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 N2)))) (@ (@ 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) N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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) N2))))))
% 6.57/6.88 (assert (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_complex)))))))
% 6.57/6.88 (assert (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_real)))))))
% 6.57/6.88 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.57/6.88 (assert (forall ((K tptp.nat) (N2 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) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.57/6.88 (assert (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.88 (assert (forall ((A tptp.rat) (D tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (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) N2))) (@ (@ 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))))))))
% 6.57/6.88 (assert (forall ((A tptp.extended_enat) (D tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.57/6.88 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.57/6.88 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((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) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.57/6.88 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.88 (assert (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))))
% 6.57/6.88 (assert (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.57/6.88 (assert (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.57/6.88 (assert (forall ((X4 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) 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 N2))))) (@ _let_1 X4)))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X4)))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X4)))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_rat X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_complex X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_int X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_real X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))))
% 6.57/6.88 (assert (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ 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)) N2)) tptp.one_one_nat))))))))
% 6.57/6.88 (assert (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.57/6.88 (assert (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))))
% 6.57/6.88 (assert (forall ((X4 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 X4) Y) (=> (@ _let_2 X4) (=> (=> (= X4 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X4 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X4 _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)))))))))))))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ 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) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ 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) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.57/6.88 (assert (= tptp.arctan (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y5))))))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups705719431365010083at_int (lambda ((Uu3 tptp.nat)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.57/6.88 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups1705073143266064639nt_int (lambda ((Uu3 tptp.int)) tptp.one_one_int)) A2) tptp.one_one_int)))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_complex (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1681761925125756287l_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups129246275422532515t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups766887009212190081x_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups2316167850115554303t_real G) A2) tptp.one_one_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.one_one_real)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups73079841787564623at_rat G) A2) tptp.one_one_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.one_one_rat)))))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N2))) A2))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N2))) A2))))
% 6.57/6.88 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N2))) A2))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) A2)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X4) (@ tptp.the_real (lambda ((X tptp.real)) false))))))
% 6.57/6.88 (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 ((X3 tptp.int)) (@ P X3)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B3) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (= X2 T2) (= (@ (@ tptp.minus_minus_int X2) D4) T2))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B3) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (not (= X2 T2)) (not (= (@ (@ tptp.minus_minus_int X2) D4) T2)))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X2) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X2) D4)) T2)))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.minus_minus_int X2) D4))))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (= X2 T2) (= (@ (@ tptp.plus_plus_int X2) D4) T2))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (not (= X2 T2)) (not (= (@ (@ tptp.plus_plus_int X2) D4) T2)))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X2) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) D4)) T2))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.plus_plus_int X2) D4)))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X2) D4)) T2)))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.minus_minus_int X2) D4))))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X2) D4)) T2))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.plus_plus_int X2) D4)))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X3 tptp.int)) (@ P X3)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A2) (@ P (@ (@ tptp.minus_minus_int Y5) X))))))))))))))
% 6.57/6.88 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X3 tptp.int)) (@ P X3)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B3) (@ P (@ (@ tptp.plus_plus_int Y5) X))))))))))))))
% 6.57/6.88 (assert (= tptp.arccos (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.cos_real X) Y5)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))))
% 6.57/6.88 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.57/6.88 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.57/6.88 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))))
% 6.57/6.88 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))))
% 6.57/6.88 (assert (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.57/6.88 (assert (= tptp.arcsin (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y5))))))))
% 6.57/6.88 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q5)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N)) (@ (@ tptp.modulo_modulo_nat M6) N)))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.88 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.57/6.88 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.57/6.88 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))))
% 6.57/6.88 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J2))))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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))))))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 6.57/6.88 (assert (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.57/6.88 (assert (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))
% 6.57/6.88 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A12)))))
% 6.57/6.88 (assert (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.57/6.88 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))
% 6.57/6.88 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (and (@ _let_1 K) (@ _let_1 L))))))
% 6.57/6.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.57/6.88 (assert (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.57/6.88 (assert (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))))
% 6.57/6.88 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.57/6.88 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)))))))
% 6.57/6.88 (assert (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L)))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)) (@ (@ tptp.plus_plus_int X4) Y))))
% 6.57/6.88 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.57/6.88 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.57/6.88 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))
% 6.57/6.88 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 6.57/6.88 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L2)))))
% 6.57/6.88 (assert (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))))
% 6.57/6.88 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))))
% 6.57/6.88 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)) _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))))
% 6.57/6.88 (assert (= tptp.code_integer_of_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))))
% 6.57/6.88 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa) X4)))))
% 6.57/6.88 (assert (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))))
% 6.57/6.88 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.57/6.88 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ (@ tptp.ord_less_int Xa) X4))))
% 6.57/6.88 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.57/6.88 (assert (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ (@ tptp.ord_less_eq_int Xa) X4))))
% 6.57/6.88 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.57/6.88 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X4 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X4 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N2) M))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2))))))
% 6.57/6.88 (assert (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))))
% 6.57/6.88 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _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))))))))))))))))))))))))
% 6.57/6.88 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.57/6.88 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)))
% 6.57/6.88 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)))
% 6.57/6.88 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))))
% 6.57/6.88 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q3)) (@ (@ tptp.plus_plus_nat N2) Q3)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N2)))) M)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M3)))) M)))))
% 6.57/6.88 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))
% 6.57/6.88 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))
% 6.57/6.88 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))
% 6.57/6.88 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L2)) (@ (@ tptp.modulo364778990260209775nteger K3) L2)))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R3 (@ (@ tptp.plus_plus_rat S3) T3)))))))))))
% 6.57/6.88 (assert (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y5) (= X Y5)))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.57/6.88 (assert (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.57/6.88 (assert (forall ((Q3 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q3)))))))
% 6.57/6.88 (assert (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X4))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))))
% 6.57/6.88 (assert (forall ((R3 tptp.product_prod_int_int) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R3) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ tptp.suc X4))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))))
% 6.57/6.88 (assert (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (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 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S4)))))) _let_1))))))))))))
% 6.57/6.88 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))))
% 6.57/6.88 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_eq_nat X) M6)))))))
% 6.57/6.88 (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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N4) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N4))))
% 6.57/6.88 (assert (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_nat X) M6)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M)))))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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_int I3) B)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))))))
% 6.57/6.88 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.57/6.88 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K3))))))
% 6.57/6.88 (assert (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K3))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S2) (@ tptp.set_ord_lessThan_nat K2))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M6 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M6 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_int M6) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))))
% 6.57/6.88 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N6) (@ (@ tptp.member_nat N6) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ (@ tptp.member_nat N) S2)))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.member_nat N) S2)))))))
% 6.57/6.88 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N2) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N2)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X4) X4)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X4) (@ _let_1 Y)) (= X4 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X4) Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) tptp.one_one_real) tptp.one_one_real))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X4) tptp.one_one_real) (= X4 tptp.one_one_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N2) X4))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X4) K)) (@ (@ tptp.power_power_real (@ _let_1 X4)) K))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real (@ _let_1 X4)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X4)) (@ tptp.sgn_sgn_real X4)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N2) X4)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X4)) (@ (@ tptp.root N2) X4)))))))
% 6.57/6.88 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.abs_abs_real (@ (@ tptp.root N2) (@ (@ tptp.power_power_real Y) N2))) (@ tptp.abs_abs_real Y)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X4))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) (@ (@ tptp.root N4) X4))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X4)) (@ (@ tptp.root N2) X4)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X4) (= (@ (@ tptp.root N2) X4) Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X4) N2)) X4)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X4) N2)) X4))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X4) (= (@ (@ tptp.root N2) X4) Y)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) (@ (@ tptp.root N4) X4))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2))) Y))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X4)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N2) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (B tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X4)))))))
% 6.57/6.88 (assert (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X4 tptp.real)) (= (@ P (@ (@ tptp.root N2) X4)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y5 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)) X4) (@ P Y5))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N2) X4) (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))))
% 6.57/6.88 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.57/6.88 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N2)))) N2)))
% 6.57/6.88 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N2)))) (@ tptp.suc N2))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat N2) (@ _let_1 N2))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))))
% 6.57/6.88 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.57/6.88 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2)))))) tptp.zero_zero_nat)))))
% 6.57/6.88 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M7) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.57/6.88 (assert (forall ((M7 tptp.set_nat) (I2 tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M7)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K3)) M7) (@ (@ tptp.ord_less_nat K3) I2))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ (@ tptp.member_nat K3) M7) (@ (@ tptp.ord_less_nat K3) (@ tptp.suc I2))))))))))
% 6.57/6.88 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.57/6.88 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N2))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S2))))
% 6.57/6.88 (assert (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))))
% 6.57/6.88 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L)) (@ (@ tptp.modulo364778990260209775nteger K) L))))
% 6.57/6.88 (assert (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L)))))
% 6.57/6.88 (assert (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2)))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2))))))))
% 6.57/6.88 (assert (= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Xa 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 X4)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X4) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) 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 X4) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))))
% 6.57/6.88 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) 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 X4) Xa))))))))))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X4) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X4) 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 X4) Y)))))))))))
% 6.57/6.88 (assert (= tptp.bezw (lambda ((X tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X) Y5)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y5 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y5)))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) 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 X4) Xa)))))))) (not _let_1)))))))))))
% 6.57/6.88 (assert (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X4)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X4) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) 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 X4) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))))
% 6.57/6.88 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.57/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.57/6.88 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.57/6.88 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.57/6.88 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.57/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.57/6.88 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((K2 tptp.int) (L4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K2) L4)) (=> (=> (not (and (@ (@ tptp.member_int K2) _let_2) (@ (@ tptp.member_int L4) _let_2))) (@ (@ P (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L4) _let_1))) (@ (@ P K2) L4)))))) (@ (@ P A0) A12)))))
% 6.57/6.88 (assert (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.57/6.88 (assert (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N2)) (or (not (= M tptp.zero_zero_int)) (not (= N2 tptp.zero_zero_int))))))
% 6.57/6.88 (assert (= tptp.gcd_gcd_int (lambda ((X tptp.int) (Y5 tptp.int)) (@ (@ tptp.gcd_gcd_int Y5) (@ (@ tptp.modulo_modulo_int X) Y5)))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X4) Y))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X4))) (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 X4)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X4) 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 X4))) (=> (=> _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)))))))))))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X4) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X4) Y))))))
% 6.57/6.88 (assert (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L2) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L2))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.57/6.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N2)) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))))
% 6.57/6.88 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y5) (@ (@ tptp.modulo_modulo_nat X) Y5)))))
% 6.57/6.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 6.57/6.88 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N2)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N2) M)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))))
% 6.57/6.88 (assert (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X4) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X4) Y))))))
% 6.57/6.88 (assert (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y5 tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y5) (@ (@ tptp.modulo_modulo_nat X) Y5))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y) (and (=> _let_1 (= Y X4)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))))))))
% 6.57/6.88 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L2 tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X4)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa))))) (not _let_1)))))))))
% 6.57/6.88 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R2 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R2) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R2 N6)) S2))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.57/6.88 (assert (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N2) M)) K)))))
% 6.57/6.88 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))))
% 6.57/6.88 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)) K)))))
% 6.57/6.88 (assert (forall ((K tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X4)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))))
% 6.57/6.88 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.57/6.88 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X))) (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X))))
% 6.57/6.88 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.57/6.88 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.57/6.88 (assert (= tptp.code_nat_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.57/6.88 (assert (= tptp.code_int_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K3)))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X4) Xa)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))))
% 6.57/6.88 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.57/6.88 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.57/6.88 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))
% 6.57/6.88 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))
% 6.57/6.88 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 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 Y5))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa) X4)))))
% 6.57/6.88 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.57/6.88 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa) X4))))
% 6.57/6.88 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa) X4))))
% 6.57/6.88 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa) X4)))))
% 6.57/6.88 (assert (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))) Xa) X4)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.57/6.88 (assert (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M6)))))))
% 6.57/6.88 (assert (forall ((Q3 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q3)) Q3)))
% 6.57/6.88 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))))
% 6.57/6.88 (assert (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 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 Y5) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.57/6.88 (assert (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 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 Y5) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (not (and (= Deg2 Xa) (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 Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (= Y (not (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))))))
% 6.57/6.88 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima2)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (= Y (= Xa tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X4 _let_1) (=> (= Y (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (= Xa tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 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) Summary3))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (= Deg2 Xa) (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 Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (= Xa tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 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) Summary3))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))))))))))))))
% 6.57/6.88 (assert (= tptp.complete_Sup_Sup_int (lambda ((X3 tptp.set_int)) (@ tptp.the_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X3) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) X3) (@ (@ tptp.ord_less_eq_int Y5) X)))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q5 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 Q5)))))) (@ (@ tptp.bit_take_bit_num _let_1) N2))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.57/6.88 (assert (forall ((R3 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N2) M)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))))
% 6.57/6.88 (assert (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M)))))
% 6.57/6.88 (assert (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))))
% 6.57/6.88 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N) M)))) N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N2) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num tptp.one))) N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.57/6.88 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y3 tptp.nat)) (=> (@ P Y3) (@ (@ tptp.ord_less_eq_nat Y3) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))) N2))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q3)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q3)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.57/6.88 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit0 N3))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))))))))))))))))))))))
% 6.57/6.88 (assert (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X))) A3))) (@ (@ tptp.product_Pair_nat_num N) M6)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))))))))))))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X4 (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (=> (exists ((M5 tptp.num)) (= X4 (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)))))))))))))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))))))))))))))))
% 6.57/6.88 (assert (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)))
% 6.57/6.88 (assert (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N2)) tptp.none_num)))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.57/6.88 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) tptp.one) (@ tptp.some_num (@ tptp.bit1 M)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))))))))))))))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))))))))))))))))))))))))
% 6.57/6.88 (assert (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))
% 6.57/6.88 (assert (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))
% 6.57/6.88 (assert (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))
% 6.57/6.88 (assert (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X4)))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))))
% 6.57/6.88 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.57/6.88 (assert (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))))
% 6.57/6.88 (assert (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))))
% 6.57/6.88 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))))
% 6.57/6.88 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.57/6.88 (assert (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.57/6.88 (assert (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (N tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N))) (not (= N tptp.zero_zero_nat))))))))
% 6.57/6.88 (assert (forall ((C tptp.nat) (Y tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X4) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X4) 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 X4) 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))))))))))
% 6.57/6.88 (assert (forall ((M7 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X4)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X5) (@ (@ tptp.ord_less_real X5) Y))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X4)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X4) X5)))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2))))))
% 6.57/6.88 (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))))))))
% 6.57/6.88 (assert (= tptp.comple4887499456419720421f_real (lambda ((X3 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X3))))))
% 6.57/6.88 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))
% 6.57/6.88 (assert (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_lessThan_int K3))))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.57/6.88 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))))
% 6.57/6.88 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.57/6.88 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.57/6.88 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.57/6.88 (assert (= tptp.root (lambda ((N tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N)))) X)))))
% 6.57/6.88 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((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)))))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (X4 tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (= (@ F X4) (@ F Y)))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (= (@ F X4) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.minus_minus_real X4) H4))))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X4) H4))) (@ F X4)))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X4) H4))) (@ F X4)))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.plus_plus_real X4) H4))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((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)))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X4)))) (= L tptp.zero_zero_real))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (= L tptp.zero_zero_real))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X4)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X4) S))))
% 6.57/6.88 (assert (forall ((Z tptp.real) (R3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R3))) (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X4))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) R3))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.57/6.88 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real)) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (let ((_let_3 (@ F X4))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R3) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R3) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F4 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F4 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ F X) 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 ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X4)))) (=> (not (= X4 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))))
% 6.57/6.88 (assert (forall ((X4 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A2))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A2)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) A2)))))
% 6.57/6.88 (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X5) N)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) (@ tptp.suc N))))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X0) N))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))
% 6.57/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))
% 6.57/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X4 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))
% 6.57/6.88 (assert (forall ((H tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real H) 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 H) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2))))))))))))
% 6.57/6.88 (assert (forall ((H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2)))))))))))
% 6.57/6.88 (assert (forall ((H tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2))))))))))))
% 6.57/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X4 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 X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))))))
% 6.57/6.88 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4))) (@ (@ (@ 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 X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N2)))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (=> (not (= X4 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X4))) (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 X4))) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) N2))))))))))))))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (H 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) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real 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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T4) P5)))) (@ 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))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (X4 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X4 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))))))))
% 6.57/6.88 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 6.57/6.88 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.57/6.88 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.57/6.88 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.57/6.88 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))))
% 6.57/6.88 (assert (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) tptp.nil_int))))
% 6.57/6.88 (assert (forall ((I2 tptp.int)) (= (@ (@ tptp.upto I2) I2) (@ (@ tptp.cons_int I2) tptp.nil_int))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (K tptp.nat) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.57/6.88 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.57/6.88 (assert (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J3) tptp.nil_int))))
% 6.57/6.88 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X2))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (not (= (@ F X2) tptp.zero_zero_real))))))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (@ (@ tptp.ord_less_real (@ F X2)) tptp.zero_zero_real)))))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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)))))))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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))))))))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_nat_nat tptp.suc) tptp.at_top_nat) tptp.at_top_nat))
% 6.57/6.88 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.57/6.88 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.57/6.88 (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))))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.57/6.88 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R2 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R2) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.57/6.88 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.57/6.88 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X4)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X4) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) (@ tptp.semiri5074537144036343181t_real N)))) N))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_nat)))
% 6.57/6.88 (assert (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N))))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N)))))))))
% 6.57/6.88 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K2 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.57/6.88 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K2 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K2 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N))))) (@ 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)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((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))) N2)))) (@ 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))))))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N))))) (@ 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))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N6 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))) N6)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N))))) _let_1) tptp.at_top_nat) (forall ((N6 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))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N)) 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)))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N)) 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))))))
% 6.57/6.88 (assert (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((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))) N2)) tptp.one_one_nat)))))))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N) (@ P N)))))))
% 6.57/6.88 (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))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) K)) (@ tptp.exp_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) Y5))) Y5))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_real)))
% 6.57/6.88 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.57/6.88 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X4)) tptp.at_top_nat)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_top_real) F5))))))
% 6.57/6.88 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.57/6.88 (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))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_bot_real) F5))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X4) Y5))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y5)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.57/6.88 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))))
% 6.57/6.88 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.57/6.88 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.57/6.88 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.57/6.88 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.57/6.88 (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)))))))))))
% 6.57/6.88 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.57/6.88 (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) (M9 tptp.real)) (and (forall ((X2 tptp.real)) (let ((_let_1 (@ F X2))) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_eq_real X2) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y4)))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N2))))
% 6.57/6.88 (assert (forall ((A tptp.real) (X4 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4)) tptp.top_top_set_real)) G)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X4)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arccos)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.57/6.88 (assert (forall ((B tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X4) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.57/6.88 (assert (forall ((D tptp.real) (X4 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X4)) tptp.top_top_set_real)) G))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((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))))))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((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))))))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((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)))))))))
% 6.57/6.88 (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 ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.57/6.88 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.57/6.88 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.57/6.88 (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 ((X tptp.real)) (@ tptp.artanh_real (@ F X)))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ 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) (= (@ F4 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (exists ((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.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (exists ((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.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.57/6.88 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X4 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) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (= (@ F X4) (@ F A)))))))))
% 6.57/6.88 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))))
% 6.57/6.88 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))))
% 6.57/6.88 (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)))))
% 6.57/6.88 (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))))))))))
% 6.57/6.88 (assert (forall ((K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ tptp.order_mono_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M6)) M6))))))
% 6.57/6.88 (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 ((X tptp.nat)) (@ F (@ G X)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))))
% 6.57/6.88 (assert (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.inj_on_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)))) tptp.top_top_set_real))))
% 6.57/6.88 (assert (forall ((B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.inj_on_real_real (@ tptp.log B)) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.57/6.88 (assert (forall ((F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F4 X5))) (@ tptp.order_7092887310737990675l_real F)))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N4) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N4))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)))
% 6.57/6.88 (assert (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.57/6.88 (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))))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (let ((_let_1 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (= _let_1 _let_1)))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N2))))
% 6.57/6.88 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y5)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.57/6.88 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y5 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y5)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.57/6.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.57/6.88 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.57/6.88 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.57/6.88 (assert (forall ((P (-> tptp.rat Bool)) (Q3 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q3))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.57/6.88 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.57/6.88 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.positive (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B)))))
% 6.57/6.88 (assert (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y5) X)))))
% 6.57/6.88 (assert (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) (@ tptp.pred_numeral K))))))
% 6.57/6.88 (assert (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N2)))))
% 6.57/6.88 (assert (= tptp.inf_inf_nat tptp.ord_min_nat))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N2)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q3))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N2) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N2)) I2))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L tptp.int) (R3 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N2) K) L)) R3) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N2)) L) R3)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N2) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N2)) L)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M3)))) M))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N2)))) M))))
% 6.57/6.88 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q3) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)))
% 6.57/6.88 (assert (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q3) tptp.zero_z5237406670263579293d_enat)))
% 6.57/6.88 (assert (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))
% 6.57/6.88 (assert (= tptp.code_num_of_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K3) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.57/6.88 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))))
% 6.57/6.88 (assert (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N)) M6))))))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.gcd_gcd_nat M) N2) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M) (@ _let_1 N2))))))))))
% 6.57/6.88 (assert (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) N2))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M) (@ _let_2 N2)) (@ _let_2 _let_1)))))))
% 6.57/6.88 (assert (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.upt M) N2))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))))
% 6.57/6.88 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) M6)))))
% 6.57/6.88 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))))
% 6.57/6.88 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N) (@ tptp.suc M6))))))
% 6.57/6.88 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) (@ tptp.suc M6))))))
% 6.57/6.88 (assert (= tptp.set_ord_lessThan_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q3))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.57/6.88 (assert (= tptp.set_ord_atMost_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat) (X4 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X4) Xs)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X4) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) Xs)))))
% 6.57/6.88 (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))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))))
% 6.57/6.88 (assert (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2)))))
% 6.57/6.88 (assert (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.upt M) N2))))
% 6.57/6.88 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N4)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N4))))))))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N4 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))))
% 6.57/6.88 (assert (forall ((Ns tptp.list_nat) (I2 tptp.nat)) (=> (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) Ns) (=> (@ (@ tptp.ord_less_nat I2) (@ tptp.size_size_list_nat Ns)) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.nth_nat Ns) I2))))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))))
% 6.57/6.88 (assert (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))))
% 6.57/6.88 (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)))))))
% 6.57/6.88 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.57/6.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.57/6.88 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.57/6.88 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N))) M6)))))
% 6.57/6.88 (assert (forall ((X4 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X4) Y) (=> (=> (= X4 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X4 (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X4) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X4) Y) (=> (@ _let_1 X4) (=> (=> (= X4 tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X4 _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.57/6.88 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.57/6.88 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.57/6.88 (assert (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X tptp.nat)) X)) _let_1) _let_1))))
% 6.57/6.88 (assert (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X tptp.int)) X)) _let_1) _let_1))))
% 6.57/6.88 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.57/6.88 (assert (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))))
% 6.57/6.88 (assert (forall ((R3 tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R3) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R3)) (@ tptp.uminus_uminus_real A)))))
% 6.57/6.88 (assert (= tptp.cis (@ tptp.rcis tptp.one_one_real)))
% 6.57/6.88 (assert (forall ((R3 tptp.real) (A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R3) A)) N2) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R3) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)))))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((Q2 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q2))) (and (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real _let_1) Y)))))))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X3 tptp.real)) (@ P X3)))))
% 6.57/6.88 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X4) Y) Y)))
% 6.57/6.88 (assert (forall ((X4 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X4) Y) X4)))
% 6.57/6.88 (assert (forall ((X4 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X4) Y) X4)))
% 106.83/107.21 (assert (forall ((X4 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X4) Y) X4)))
% 106.83/107.21 (assert (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X4) Y) X4)))
% 106.83/107.21 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X4) Y) X4)))
% 106.83/107.21 (assert (forall ((X4 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X4) Y) X4)))
% 106.83/107.21 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 106.83/107.21 (assert (forall ((X4 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X4) Y) Y)))
% 106.83/107.21 (assert (forall ((X4 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X4) Y) X4)))
% 106.83/107.21 (assert (not (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary)) tptp.x)))
% 106.83/107.21 (set-info :filename cvc5---1.0.5_15025)
% 106.83/107.21 (check-sat-assuming ( true ))
% 106.83/107.21 ------- get file name : TPTP file name is ITP221^3
% 106.83/107.21 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_15025.smt2...
% 106.83/107.21 --- Run --ho-elim --full-saturate-quant at 10...
% 106.83/107.21 --- Run --ho-elim --no-e-matching --full-saturate-quant at 10...
% 106.83/107.21 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 10...
% 106.83/107.21 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 5...
% 106.83/107.21 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 5...
% 106.83/107.21 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 10...
% 106.83/107.21 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 10...
% 106.83/107.21 --- Run --ho-elim --full-saturate-quant --enum-inst-interleave at 10...
% 106.83/107.21 --- Run --no-ho-matching --full-saturate-quant --ho-elim-store-ax at 10...
% 106.83/107.21 --- Run --ho-elim --no-ho-elim-store-ax --full-saturate-quant...
% 106.83/107.21 % SZS status Theorem for ITP221^3
% 106.83/107.21 % SZS output start Proof for ITP221^3
% 106.83/107.21 (
% 106.83/107.21 (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary))) (let ((_let_2 (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) tptp.x))) (let ((_let_3 (not _let_2))) (let ((_let_4 (= tptp.cis (@ tptp.rcis tptp.one_one_real)))) (let ((_let_5 (= tptp.semiri1316708129612266289at_nat tptp.id_nat))) (let ((_let_6 (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M6) N))) M6)))))) (let ((_let_7 (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))) (let ((_let_8 (= tptp.set_or6659071591806873216st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) (@ tptp.suc M6))))))) (let ((_let_9 (= tptp.set_or1269000886237332187st_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N) (@ tptp.suc M6))))))) (let ((_let_10 (= tptp.set_or4665077453230672383an_nat (lambda ((I3 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I3) J3)))))) (let ((_let_11 (= tptp.set_or5834768355832116004an_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N)) M6)))))) (let ((_let_12 (= tptp.inf_in1870772243966228564d_enat tptp.ord_mi8085742599997312461d_enat))) (let ((_let_13 (= tptp.inf_inf_nat tptp.ord_min_nat))) (let ((_let_14 (= tptp.positive (lambda ((X tptp.rat)) (let ((_let_1 (@ tptp.rep_Rat X))) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.product_snd_int_int _let_1)))))))) (let ((_let_15 (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (let ((_let_16 (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X tptp.complex) (Y5 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X) Y5)) E3))))))) _let_15))))) (let ((_let_17 (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X) Y5)) E3))))))) _let_15))))) (let ((_let_18 (@ (@ tptp.comp_nat_nat_nat tptp.suc) tptp.suc))) (let ((_let_19 (@ tptp.bit0 tptp.one))) (let ((_let_20 (@ tptp.bit0 _let_19))) (let ((_let_21 (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 _let_20))))))))) (let ((_let_22 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (let ((_let_23 (@ _let_22 _let_21))) (let ((_let_24 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_25 (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real _let_24) tptp.one_one_real)))) (let ((_let_26 (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))) (let ((_let_27 (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat))) (let ((_let_28 (= _let_27 tptp.top_top_set_nat))) (let ((_let_29 (@ tptp.filterlim_real_real tptp.artanh_real))) (let ((_let_30 (@ tptp.topolo2177554685111907308n_real tptp.one_one_real))) (let ((_let_31 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (let ((_let_32 (@ tptp.numeral_numeral_real _let_19))) (let ((_let_33 (@ tptp.divide_divide_real tptp.pi))) (let ((_let_34 (@ _let_33 _let_32))) (let ((_let_35 (@ tptp.uminus_uminus_real _let_34))) (let ((_let_36 (@ tptp.filterlim_real_real tptp.tan_real))) (let ((_let_37 (@ tptp.filterlim_real_real tptp.arctan))) (let ((_let_38 (@ tptp.filterlim_real_real tptp.tanh_real))) (let ((_let_39 (@ tptp.topolo2177554685111907308n_real _let_34))) (let ((_let_40 (@ tptp.topolo2815343760600316023s_real tptp.one_one_real))) (let ((_let_41 (= 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))))))) (let ((_let_42 (= 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)))))) (let ((_let_43 (= 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))))))) (let ((_let_44 (= tptp.set_or1266510415728281911st_int (lambda ((I3 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I3) J3)))))) (let ((_let_45 (= tptp.sup_sup_nat tptp.ord_max_nat))) (let ((_let_46 (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))) (let ((_let_47 (= 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))))) (let ((_let_48 (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) _let_23)))) (let ((_let_49 (= tptp.root (lambda ((N tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N)))) X)))))) (let ((_let_50 (@ tptp.numeral_numeral_nat _let_19))) (let ((_let_51 (@ tptp.insert_nat tptp.zero_zero_nat))) (let ((_let_52 (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))) (let ((_let_53 (= tptp.comple4887499456419720421f_real (lambda ((X3 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X3))))))) (let ((_let_54 (= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.int) (N tptp.nat)) (and (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N))) (not (= N tptp.zero_zero_nat))))))))) (let ((_let_55 (@ tptp.numera6620942414471956472nteger _let_19))) (let ((_let_56 (= tptp.sqr (lambda ((X tptp.num)) (@ (@ tptp.times_times_num X) X))))) (let ((_let_57 (= tptp.bit_un7362597486090784418nd_num tptp.bit_un1837492267222099188nd_num))) (let ((_let_58 (= tptp.bit_un2901131394128224187um_rel tptp.bit_un3595099601533988841um_rel))) (let ((_let_59 (= tptp.bit_un4731106466462545111um_rel tptp.bit_un5425074673868309765um_rel))) (let ((_let_60 (= tptp.bit_un2480387367778600638or_num tptp.bit_un6178654185764691216or_num))) (let ((_let_61 (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))) (let ((_let_62 (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))) (let ((_let_63 (= tptp.complete_Sup_Sup_int (lambda ((X3 tptp.set_int)) (@ tptp.the_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X3) (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) X3) (@ (@ tptp.ord_less_eq_int Y5) X)))))))))) (let ((_let_64 (= tptp.pred_nat (@ tptp.collec3392354462482085612at_nat (@ tptp.produc6081775807080527818_nat_o (lambda ((M6 tptp.nat) (N tptp.nat)) (= N (@ tptp.suc M6)))))))) (let ((_let_65 (= tptp.ord_le3102999989581377725nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))))) (let ((_let_66 (= tptp.ord_le6747313008572928689nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))))) (let ((_let_67 (= tptp.bit_se8570568707652914677it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_68 (= tptp.bit_se8568078237143864401it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_69 (= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))) (let ((_let_70 (= tptp.bot_bot_nat tptp.zero_zero_nat))) (let ((_let_71 (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))) (let ((_let_72 (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat))) (let ((_let_73 (= _let_72 tptp.bot_bot_set_nat))) (let ((_let_74 (= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))))) (let ((_let_75 (= tptp.sqrt (@ tptp.root _let_50)))) (let ((_let_76 (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_eq_nat X) M6)))))))) (let ((_let_77 (= tptp.code_divmod_abs (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L2))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_78 (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))) (let ((_let_79 (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K3) L2)) (@ (@ tptp.modulo364778990260209775nteger K3) L2)))))) (let ((_let_80 (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K3) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K3)))))))) (let ((_let_81 (= tptp.archim3151403230148437115or_rat (lambda ((X tptp.rat)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))) (let ((_let_82 (= tptp.archim6058952711729229775r_real (lambda ((X tptp.real)) (@ tptp.the_int (lambda ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))))) (let ((_let_83 (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))) (let ((_let_84 (= tptp.bit_se7882103937844011126it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))))) (let ((_let_85 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_86 (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int L2))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) L2)))))) (let ((_let_87 (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))) (let ((_let_88 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (let ((_let_89 (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ tptp.bit_ri7919022796975470100ot_int L2))))))) (let ((_let_90 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_91 (= tptp.unique4921790084139445826nteger (lambda ((L2 tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L2))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))) (let ((_let_92 (= tptp.int_ge_less_than (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z7) (@ (@ tptp.ord_less_int Z7) Z5))))))))) (let ((_let_93 (= tptp.int_ge_less_than2 (lambda ((D5 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z7 tptp.int) (Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D5) Z5) (@ (@ tptp.ord_less_int Z7) Z5))))))))) (let ((_let_94 (@ tptp.power_power_nat _let_50))) (let ((_let_95 (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat _let_94)))) (let ((_let_96 (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M6) N)) (@ (@ tptp.modulo_modulo_nat M6) N)))))) (let ((_let_97 (= tptp.arcsin (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.sin_real X) Y5))))))))) (let ((_let_98 (@ tptp.times_times_real _let_32))) (let ((_let_99 (= tptp.unique5024387138958732305ep_int (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))) (let ((_let_100 (= tptp.unique5026877609467782581ep_nat (lambda ((L2 tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))) (let ((_let_101 (= tptp.arctan (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.tan_real X) Y5))))))))) (let ((_let_102 (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_real X) U2))))))) (let ((_let_103 (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_int X) U2))))))) (let ((_let_104 (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_nat X) U2))))))) (let ((_let_105 (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_num X) U2))))))) (let ((_let_106 (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_rat X) U2))))))) (let ((_let_107 (= tptp.set_ord_atMost_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) U2))))))) (let ((_let_108 (= tptp.set_ord_atMost_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) U2))))))) (let ((_let_109 (= tptp.set_ord_atMost_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) U2))))))) (let ((_let_110 (= tptp.set_ord_atMost_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) U2))))))) (let ((_let_111 (= tptp.set_or58775011639299419et_int (lambda ((U2 tptp.set_int)) (@ tptp.collect_set_int (lambda ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) U2))))))) (let ((_let_112 (= tptp.set_ord_atMost_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) U2))))))) (let ((_let_113 (= tptp.vEBT_set_vebt (lambda ((T tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T)))))) (let ((_let_114 (= 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))))))))) (let ((_let_115 (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8422978514062236437ux_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) tptp.one_one_nat))) N) tptp.zero_zero_nat))))) (let ((_let_116 (= tptp.semiri1314217659103216013at_int (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) tptp.one_one_int))) N) tptp.zero_zero_int))))) (let ((_let_117 (= tptp.semiri5074537144036343181t_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7260567687927622513x_real (lambda ((I3 tptp.real)) (@ (@ tptp.plus_plus_real I3) tptp.one_one_real))) N) tptp.zero_zero_real))))) (let ((_let_118 (= tptp.semiri681578069525770553at_rat (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri7787848453975740701ux_rat (lambda ((I3 tptp.rat)) (@ (@ tptp.plus_plus_rat I3) tptp.one_one_rat))) N) tptp.zero_zero_rat))))) (let ((_let_119 (= tptp.semiri8010041392384452111omplex (lambda ((N tptp.nat)) (@ (@ (@ tptp.semiri2816024913162550771omplex (lambda ((I3 tptp.complex)) (@ (@ tptp.plus_plus_complex I3) tptp.one_one_complex))) N) tptp.zero_zero_complex))))) (let ((_let_120 (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X) N)))))))) (let ((_let_121 (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X) N)))))))) (let ((_let_122 (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.real_V2046097035970521341omplex R5) tptp.one_one_complex))))) (let ((_let_123 (= tptp.real_V1803761363581548252l_real (lambda ((R5 tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real R5) tptp.one_one_real))))) (let ((_let_124 (= tptp.topolo4899668324122417113eq_int (lambda ((X3 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_int (@ X3 N)) (@ X3 M6))))))))) (let ((_let_125 (= tptp.topolo4902158794631467389eq_nat (lambda ((X3 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_nat (@ X3 N)) (@ X3 M6))))))))) (let ((_let_126 (= tptp.topolo1459490580787246023eq_num (lambda ((X3 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_num (@ X3 N)) (@ X3 M6))))))))) (let ((_let_127 (= tptp.topolo4267028734544971653eq_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_rat (@ X3 N)) (@ X3 M6))))))))) (let ((_let_128 (= tptp.topolo3100542954746470799et_int (lambda ((X3 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_set_int (@ X3 N)) (@ X3 M6))))))))) (let ((_let_129 (= tptp.topolo6980174941875973593q_real (lambda ((X3 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.ord_less_eq_real (@ X3 N)) (@ X3 M6))))))))) (let ((_let_130 (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) X)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1)))))))))) (let ((_let_131 (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))))) (let ((_let_132 (= tptp.diffs_int (lambda ((C2 (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ C2 _let_1))))))) (let ((_let_133 (= tptp.diffs_real (lambda ((C2 (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ C2 _let_1))))))) (let ((_let_134 (= tptp.diffs_complex (lambda ((C2 (-> tptp.nat tptp.complex)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ C2 _let_1))))))) (let ((_let_135 (@ tptp.power_power_complex tptp.zero_zero_complex))) (let ((_let_136 (@ tptp.power_power_int tptp.zero_zero_int))) (let ((_let_137 (@ tptp.power_power_real tptp.zero_zero_real))) (let ((_let_138 (@ tptp.member_complex tptp.one_one_complex))) (let ((_let_139 (@ tptp.member_real tptp.one_one_real))) (let ((_let_140 (@ tptp.numeral_numeral_real _let_20))) (let ((_let_141 (@ _let_33 _let_140))) (let ((_let_142 (= tptp.invers8013647133539491842omplex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (let ((_let_3 (@ tptp.re X))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))) (let ((_let_143 (= tptp.real_V1022390504157884413omplex (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z5)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z5)) _let_1)))))))) (let ((_let_144 (= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))) (let ((_let_145 (= tptp.topolo6517432010174082258omplex (lambda ((X3 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X3 M6)) (@ X3 N)))) E3)))))))))))) (let ((_let_146 (= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat (lambda ((O tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A3) (@ tptp.semiri1316708129612266289at_nat O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_nat)))))) (let ((_let_147 (= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ (@ (@ tptp.set_fo2581907887559384638at_int (lambda ((O tptp.nat) (__flatten_var_0 tptp.int)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A3) (@ tptp.semiri1314217659103216013at_int O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_int)))))) (let ((_let_148 (= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N tptp.nat)) (@ (@ (@ tptp.if_real (= N tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ (@ (@ tptp.set_fo3111899725591712190t_real (lambda ((O tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A3) (@ tptp.semiri5074537144036343181t_real O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_real)))))) (let ((_let_149 (= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N tptp.nat)) (@ (@ (@ tptp.if_complex (= N tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ (@ (@ tptp.set_fo1517530859248394432omplex (lambda ((O tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A3) (@ tptp.semiri8010041392384452111omplex O))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) tptp.one_one_complex)))))) (let ((_let_150 (= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N tptp.nat)) (@ (@ (@ tptp.if_rat (= N 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 N) tptp.one_one_nat)) tptp.one_one_rat)))))) (let ((_let_151 (= tptp.bit_ri6519982836138164636nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger _let_1) A3))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) _let_2))))))) (let ((_let_152 (= tptp.nat_set_decode (lambda ((X tptp.nat)) (@ tptp.collect_nat (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat _let_1) N))))))))))) (let ((_let_153 (= tptp.set_int2 (lambda ((Xs3 tptp.list_int)) (@ tptp.collect_int (lambda ((Uu3 tptp.int)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_int Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs3)))))))))) (let ((_let_154 (= tptp.set_nat2 (lambda ((Xs3 tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu3 tptp.nat)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_nat Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs3)))))))))) (let ((_let_155 (= tptp.set_o2 (lambda ((Xs3 tptp.list_o)) (@ tptp.collect_o (lambda ((Uu3 Bool)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_o Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs3)))))))))) (let ((_let_156 (= tptp.set_VEBT_VEBT2 (lambda ((Xs3 tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu3 tptp.vEBT_VEBT)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_VEBT_VEBT Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs3)))))))))) (let ((_let_157 (= tptp.set_list_nat2 (lambda ((Xs3 tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu3 tptp.list_nat)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_list_nat Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs3)))))))))) (let ((_let_158 (= tptp.set_real2 (lambda ((Xs3 tptp.list_real)) (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_real Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs3)))))))))) (let ((_let_159 (= tptp.set_complex2 (lambda ((Xs3 tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu3 tptp.complex)) (exists ((I3 tptp.nat)) (and (= Uu3 (@ (@ tptp.nth_complex Xs3) I3)) (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs3)))))))))) (let ((_let_160 (= 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))))))) (let ((_let_161 (= 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))))))) (let ((_let_162 (= tptp.ord_le7866589430770878221at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le549003669493604880_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))))) (let ((_let_163 (= tptp.ord_less_set_complex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_less_complex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6))))))) (let ((_let_164 (= tptp.ord_less_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))))) (let ((_let_165 (= tptp.ord_less_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))))) (let ((_let_166 (= tptp.topolo4055970368930404560y_real (lambda ((X3 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X3 M6)) (@ X3 N)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))) (let ((_let_167 (= tptp.cosh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_168 (= tptp.cosh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_169 (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.times_times_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_170 (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_171 (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))))) (let ((_let_172 (= tptp.sinh_complex (lambda ((Z5 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex Z5)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex Z5)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (let ((_let_173 (= tptp.sinh_real (lambda ((Z5 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.exp_real Z5)) (@ tptp.exp_real (@ tptp.uminus_uminus_real Z5)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_174 (@ tptp.sqrt _let_32))) (let ((_let_175 (@ tptp.plus_plus_complex tptp.one_one_complex))) (let ((_let_176 (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit))) (let ((_let_177 (= 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)))))) (let ((_let_178 (= 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)))))) (let ((_let_179 (= 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)))))) (let ((_let_180 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_181 (= tptp.inverse_inverse_rat (@ tptp.divide_divide_rat tptp.one_one_rat)))) (let ((_let_182 (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex B2)) A3))))) (let ((_let_183 (= tptp.divide_divide_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real B2)) A3))))) (let ((_let_184 (@ tptp.numera6690914467698888265omplex tptp.one))) (let ((_let_185 (@ tptp.numeral_numeral_real tptp.one))) (let ((_let_186 (= (@ tptp.invers8013647133539491842omplex tptp.zero_zero_complex) tptp.zero_zero_complex))) (let ((_let_187 (= (@ tptp.inverse_inverse_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_188 (= (@ tptp.inverse_inverse_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_189 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_190 (@ tptp.cis _let_34))) (let ((_let_191 (= _let_190 tptp.imaginary_unit))) (let ((_let_192 (@ tptp.real_V4546457046886955230omplex tptp.pi))) (let ((_let_193 (@ tptp.numera6690914467698888265omplex _let_19))) (let ((_let_194 (@ _let_98 tptp.pi))) (let ((_let_195 (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))) (let ((_let_196 (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))) (let ((_let_197 (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 K3))))))) (let ((_let_198 (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 K3))))))) (let ((_let_199 (= tptp.ring_1_of_int_rat (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 K3))))))) (let ((_let_200 (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri4939895301339042750nteger (@ tptp.nat2 K3))))))) (let ((_let_201 (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 (@ tptp.uminus_uminus_int K3))))) (@ tptp.semiri8010041392384452111omplex (@ tptp.nat2 K3))))))) (let ((_let_202 (= tptp.cot_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex X)) (@ tptp.sin_complex X)))))) (let ((_let_203 (= tptp.cot_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))))) (let ((_let_204 (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))))) (let ((_let_205 (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))))) (let ((_let_206 (@ (@ tptp.divide1717551699836669952omplex _let_192) _let_193))) (let ((_let_207 (@ tptp.real_V1803761363581548252l_real tptp.pi))) (let ((_let_208 (@ (@ tptp.divide_divide_real _let_207) _let_32))) (let ((_let_209 (@ tptp.arccos _let_24))) (let ((_let_210 (= _let_209 tptp.pi))) (let ((_let_211 (= tptp.arcosh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))))) (let ((_let_212 (@ tptp.bit1 tptp.one))) (let ((_let_213 (@ tptp.numeral_numeral_real _let_212))) (let ((_let_214 (@ tptp.sqrt _let_213))) (let ((_let_215 (@ _let_33 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_212))))) (let ((_let_216 (@ _let_33 _let_213))) (let ((_let_217 (= tptp.tan_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex X)) (@ tptp.cos_complex X)))))) (let ((_let_218 (= tptp.tan_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real X)) (@ tptp.cos_real X)))))) (let ((_let_219 (@ (@ tptp.divide_divide_real _let_214) _let_32))) (let ((_let_220 (@ _let_180 _let_32))) (let ((_let_221 (@ (@ tptp.divide_divide_real _let_174) _let_32))) (let ((_let_222 (@ tptp.cos_real _let_32))) (let ((_let_223 (@ tptp.divide_divide_real _let_213))) (let ((_let_224 (@ (@ tptp.times_times_real (@ _let_223 _let_32)) tptp.pi))) (let ((_let_225 (= tptp.arsinh_real (lambda ((X tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))) (let ((_let_226 (@ tptp.bit1 _let_212))) (let ((_let_227 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_19)))) (let ((_let_228 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_229 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_230 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_231 (@ tptp.suc _let_230))) (let ((_let_232 (@ tptp.numeral_numeral_int _let_19))) (let ((_let_233 (@ tptp.nat2 _let_232))) (let ((_let_234 (@ tptp.ord_less_real tptp.pi))) (let ((_let_235 (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))) (let ((_let_236 (@ tptp.exp_real tptp.one_one_real))) (let ((_let_237 (= tptp.ln_ln_real (@ tptp.log _let_236)))) (let ((_let_238 (= tptp.bit_se4205575877204974255it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M6) (@ tptp.semiri1314217659103216013at_int N))))))) (let ((_let_239 (@ tptp.nat2 tptp.one_one_int))) (let ((_let_240 (= tptp.numeral_numeral_nat (lambda ((I3 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I3)))))) (let ((_let_241 (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M6)) (@ tptp.semiri1314217659103216013at_int N))))))) (let ((_let_242 (= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) 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 L2) K3))))) _let_2)))))))))))) (let ((_let_243 (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))))) (let ((_let_244 (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))) (let ((_let_245 (= 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 ((L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L2 tptp.zero_zero_int)) (= K3 (@ (@ tptp.times_times_int Q5) L2)))) (exists ((R5 tptp.int) (L2 tptp.int) (K3 tptp.int) (Q5 tptp.int)) (and (= A1 K3) (= A22 L2) (= A32 (@ (@ tptp.product_Pair_int_int Q5) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L2)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L2)) (= K3 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L2)) R5))))))))) (let ((_let_246 (= tptp.tanh_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))) (let ((_let_2 (@ tptp.exp_complex X))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))) (let ((_let_247 (= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= X tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))) (let ((_let_248 (= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= X tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))) (let ((_let_249 (= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= X tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))) (let ((_let_250 (= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= X tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (let ((_let_251 (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A3)) tptp.one_one_int))))) (let ((_let_252 (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.bit_ri7632146776885996613nteger A3)) tptp.one_one_Code_integer))))) (let ((_let_253 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_254 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_255 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_256 (@ tptp.uminus_uminus_int _let_232))) (let ((_let_257 (@ tptp.uminus1351360451143612070nteger _let_55))) (let ((_let_258 (= (@ tptp.sgn_sgn_complex tptp.one_one_complex) tptp.one_one_complex))) (let ((_let_259 (= (@ tptp.sgn_sgn_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_260 (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))) (let ((_let_261 (= tptp.cos_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ tptp.semiri2265585572941072030t_real N))) tptp.zero_zero_real)))))) (let ((_let_262 (= tptp.sin_coeff (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N)))))))) (let ((_let_263 (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.minus_minus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))) (let ((_let_264 (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.plus_plus_int K3) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))) (let ((_let_265 (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat A3) (@ (@ tptp.power_power_nat _let_1) N))))))))) (let ((_let_266 (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int A3) (@ (@ tptp.power_power_int _let_1) N))))))))) (let ((_let_267 (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger A3) (@ (@ tptp.power_8256067586552552935nteger _let_1) N))))))))) (let ((_let_268 (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ (@ (@ (@ tptp.if_nat_nat_nat (@ (@ tptp.bit_se1148574629649215175it_nat A3) N)) tptp.bit_se4205575877204974255it_nat) tptp.bit_se7882103937844011126it_nat) N) A3))))) (let ((_let_269 (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ (@ (@ (@ tptp.if_nat_int_int (@ (@ tptp.bit_se1146084159140164899it_int A3) N)) tptp.bit_se4203085406695923979it_int) tptp.bit_se7879613467334960850it_int) N) A3))))) (let ((_let_270 (= 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))))) (let ((_let_271 (= 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))))) (let ((_let_272 (= 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))))) (let ((_let_273 (= 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))))) (let ((_let_274 (= tptp.semiri2265585572941072030t_real (@ tptp.comm_s7457072308508201937r_real tptp.one_one_real)))) (let ((_let_275 (= tptp.semiri1408675320244567234ct_nat (@ tptp.comm_s4663373288045622133er_nat tptp.one_one_nat)))) (let ((_let_276 (= tptp.semiri1406184849735516958ct_int (@ tptp.comm_s4660882817536571857er_int tptp.one_one_int)))) (let ((_let_277 (= tptp.semiri773545260158071498ct_rat (@ tptp.comm_s4028243227959126397er_rat tptp.one_one_rat)))) (let ((_let_278 (= tptp.semiri5044797733671781792omplex (@ tptp.comm_s2602460028002588243omplex tptp.one_one_complex)))) (let ((_let_279 (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))) (let ((_let_280 (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))) (let ((_let_281 (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_282 (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))) (let ((_let_283 (@ tptp.numera1916890842035813515d_enat _let_19))) (let ((_let_284 (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))) (let ((_let_285 (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))) (let ((_let_286 (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))) (let ((_let_287 (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))) (let ((_let_288 (= tptp.artanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (let ((_let_289 (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))) (let ((_let_290 (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))) (let ((_let_291 (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))) (let ((_let_292 (= tptp.neg_nu5851722552734809277nc_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))) (let ((_let_293 (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))) (let ((_let_294 (= tptp.neg_nu8295874005876285629c_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))) (let ((_let_295 (= tptp.neg_nu8557863876264182079omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))) (let ((_let_296 (= tptp.pred_numeral (lambda ((K3 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K3)) tptp.one_one_nat))))) (let ((_let_297 (@ tptp.numeral_numeral_int _let_212))) (let ((_let_298 (@ tptp.numera6690914467698888265omplex _let_212))) (let ((_let_299 (@ tptp.numeral_numeral_rat _let_212))) (let ((_let_300 (= tptp.neg_nu3811975205180677377ec_int (lambda ((X tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X) X)) tptp.one_one_int))))) (let ((_let_301 (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X) X)) tptp.one_one_rat))))) (let ((_let_302 (= tptp.neg_nu6075765906172075777c_real (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) X)) tptp.one_one_real))))) (let ((_let_303 (= tptp.neg_nu6511756317524482435omplex (lambda ((X tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X) X)) tptp.one_one_complex))))) (let ((_let_304 (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N)))))))) (let ((_let_305 (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))) (let ((_let_306 (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int K3) _let_1))) _let_1)))))) (let ((_let_307 (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_308 (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_309 (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_310 (@ tptp.numeral_numeral_rat tptp.one))) (let ((_let_311 (@ tptp.numeral_numeral_int tptp.one))) (let ((_let_312 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_313 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_314 (@ tptp.ord_less_rat _let_253))) (let ((_let_315 (@ tptp.ord_le6747313008572928689nteger _let_254))) (let ((_let_316 (@ tptp.ord_less_int _let_255))) (let ((_let_317 (@ tptp.ord_less_real _let_24))) (let ((_let_318 (@ tptp.ord_less_eq_int _let_255))) (let ((_let_319 (@ tptp.ord_less_eq_rat _let_253))) (let ((_let_320 (@ tptp.ord_le3102999989581377725nteger _let_254))) (let ((_let_321 (@ tptp.ord_less_eq_real _let_24))) (let ((_let_322 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_323 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_324 (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))) (let ((_let_325 (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))) (let ((_let_326 (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))) (let ((_let_327 (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))) (let ((_let_328 (@ tptp.ord_less_rat tptp.one_one_rat))) (let ((_let_329 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_330 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_331 (@ tptp.ord_less_eq_int tptp.one_one_int))) (let ((_let_332 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (let ((_let_333 (@ tptp.ord_less_eq_real tptp.one_one_real))) (let ((_let_334 (= tptp.minus_minus_real (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real Y5)))))) (let ((_let_335 (@ tptp.numeral_numeral_rat _let_19))) (let ((_let_336 (@ tptp.uminus_uminus_rat _let_335))) (let ((_let_337 (@ tptp.uminus1482373934393186551omplex _let_193))) (let ((_let_338 (@ tptp.uminus_uminus_real _let_32))) (let ((_let_339 (= (@ (@ tptp.modulo364778990260209775nteger _let_254) _let_55) tptp.one_one_Code_integer))) (let ((_let_340 (= (@ (@ tptp.modulo_modulo_int _let_255) _let_232) tptp.one_one_int))) (let ((_let_341 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_342 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_343 (@ tptp.minus_minus_int tptp.one_one_int))) (let ((_let_344 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_345 (@ tptp.minus_minus_rat _let_253))) (let ((_let_346 (@ tptp.minus_8373710615458151222nteger _let_254))) (let ((_let_347 (@ tptp.minus_minus_complex _let_189))) (let ((_let_348 (@ tptp.minus_minus_int _let_255))) (let ((_let_349 (@ tptp.minus_minus_real _let_24))) (let ((_let_350 (@ tptp.plus_plus_rat _let_253))) (let ((_let_351 (@ tptp.plus_p5714425477246183910nteger _let_254))) (let ((_let_352 (@ tptp.plus_plus_complex _let_189))) (let ((_let_353 (@ tptp.plus_plus_int _let_255))) (let ((_let_354 (@ tptp.plus_plus_real _let_24))) (let ((_let_355 (@ tptp.plus_plus_rat tptp.one_one_rat))) (let ((_let_356 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_357 (@ tptp.plus_plus_real tptp.one_one_real))) (let ((_let_358 (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.minus_minus_nat M6) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M6) N)) N)))))) (let ((_let_359 (= tptp.nat_triangle (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (let ((_let_360 (@ tptp.dvd_dvd_int _let_232))) (let ((_let_361 (@ tptp.dvd_dvd_nat _let_50))) (let ((_let_362 (@ tptp.dvd_dvd_Code_integer _let_55))) (let ((_let_363 (= tptp.zero_n2684676970156552555ol_int (lambda ((P5 Bool)) (@ (@ (@ tptp.if_int P5) tptp.one_one_int) tptp.zero_zero_int))))) (let ((_let_364 (= tptp.zero_n2687167440665602831ol_nat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_nat P5) tptp.one_one_nat) tptp.zero_zero_nat))))) (let ((_let_365 (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))) (let ((_let_366 (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K3 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K3))))))) (let ((_let_367 (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K3 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K3))))))) (let ((_let_368 (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K3 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K3))))))) (let ((_let_369 (= tptp.dvd_dvd_complex (lambda ((B2 tptp.complex) (A3 tptp.complex)) (exists ((K3 tptp.complex)) (= A3 (@ (@ tptp.times_times_complex B2) K3))))))) (let ((_let_370 (= 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))))))) (let ((_let_371 (not (@ _let_313 tptp.zero_zero_int)))) (let ((_let_372 (@ _let_322 tptp.zero_zero_int))) (let ((_let_373 (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))) (let ((_let_374 (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))) (let ((_let_375 (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))) (let ((_let_376 (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))) (let ((_let_377 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_378 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_379 (= tptp.ord_less_num (lambda ((X tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y5) (not (= X Y5))))))) (let ((_let_380 (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y5) (not (= X Y5))))))) (let ((_let_381 (@ tptp.numeral_numeral_nat tptp.one))) (let ((_let_382 (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))) (let ((_let_383 (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_384 (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_385 (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_386 (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_387 (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))) (let ((_let_388 (@ _let_356 tptp.one_one_int))) (let ((_let_389 (@ tptp.plus_plus_nat tptp.one_one_nat))) (let ((_let_390 (@ _let_389 tptp.one_one_nat))) (let ((_let_391 (@ _let_355 tptp.one_one_rat))) (let ((_let_392 (@ _let_357 tptp.one_one_real))) (let ((_let_393 (@ _let_313 tptp.one_one_int))) (let ((_let_394 (@ _let_378 tptp.one_one_nat))) (let ((_let_395 (@ _let_312 tptp.one_one_rat))) (let ((_let_396 (@ _let_229 tptp.one_one_real))) (let ((_let_397 (@ tptp.ord_less_nat tptp.one_one_nat))) (let ((_let_398 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (let ((_let_399 (@ _let_322 tptp.one_one_int))) (let ((_let_400 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_401 (@ _let_400 tptp.one_one_nat))) (let ((_let_402 (@ _let_323 tptp.one_one_rat))) (let ((_let_403 (@ _let_228 tptp.one_one_real))) (let ((_let_404 (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) _let_55) tptp.zero_z3403309356797280102nteger))) (let ((_let_405 (@ (@ tptp.divide_divide_int tptp.one_one_int) _let_232))) (let ((_let_406 (= _let_405 tptp.zero_zero_int))) (let ((_let_407 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) _let_50))) (let ((_let_408 (= _let_407 tptp.zero_zero_nat))) (let ((_let_409 (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma)))) (let ((_let_410 (= _let_409 tptp.info))) (let ((_let_411 (= tptp.neg_numeral_dbl_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) X))))) (let ((_let_412 (= tptp.neg_numeral_dbl_rat (lambda ((X tptp.rat)) (@ (@ tptp.plus_plus_rat X) X))))) (let ((_let_413 (= tptp.neg_numeral_dbl_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real X) X))))) (let ((_let_414 (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) _let_55) tptp.one_one_Code_integer))) (let ((_let_415 (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) _let_232) tptp.one_one_int))) (let ((_let_416 (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) _let_50) tptp.one_one_nat))) (let ((_let_417 (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))) (let ((_let_418 (= tptp.vEBT_VEBT_low (lambda ((X tptp.nat) (N tptp.nat)) (@ (@ tptp.modulo_modulo_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_419 (= 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))))) (let ((_let_420 (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y5) (= X Y5)))))) (let ((_let_421 (= tptp.suc (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (let ((_let_422 (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M6) K3))))))) (let ((_let_423 (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (not (= M6 N))))))) (let ((_let_424 (= _let_390 _let_50))) (let ((_let_425 (= _let_381 tptp.one_one_nat))) (let ((_let_426 (= _let_311 tptp.one_one_int))) (let ((_let_427 (= _let_185 tptp.one_one_real))) (let ((_let_428 (= _let_184 tptp.one_one_complex))) (let ((_let_429 (= (@ tptp.numera1916890842035813515d_enat tptp.one) tptp.one_on7984719198319812577d_enat))) (let ((_let_430 (= _let_310 tptp.one_one_rat))) (let ((_let_431 (= tptp.mi tptp.ma))) (let ((_let_432 (= tptp.vEBT_V5917875025757280293ildren (lambda ((N tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X) N))) (@ (@ tptp.vEBT_VEBT_low X) N)))))) (let ((_let_433 (@ _let_94 tptp.m))) (let ((_let_434 (= tptp.m (@ tptp.suc tptp.na)))) (let ((_let_435 (= tptp.vEBT_VEBT_high (lambda ((X tptp.nat) (N tptp.nat)) (@ (@ tptp.divide_divide_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))) (let ((_let_436 (@ _let_94 tptp.deg))) (let ((_let_437 (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))) (let ((_let_438 (@ (@ tptp.divide_divide_nat tptp.deg) _let_50))) (let ((_let_439 (@ (@ tptp.vEBT_VEBT_low tptp.x) _let_438))) (let ((_let_440 (@ (@ tptp.vEBT_VEBT_high tptp.x) _let_438))) (let ((_let_441 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_442 (@ _let_441 _let_440))) (let ((_let_443 (@ (@ tptp.vEBT_V5719532721284313246member _let_442) _let_439))) (let ((_let_444 (@ (@ tptp.vEBT_VEBT_membermima _let_442) _let_439))) (let ((_let_445 (or _let_444 _let_443))) (let ((_let_446 (=> _let_444 (@ (@ tptp.vEBT_VEBT_membermima _let_1) tptp.x)))) (let ((_let_447 (=> _let_443 (@ (@ tptp.vEBT_V5719532721284313246member _let_1) tptp.x)))) (let ((_let_448 (= tptp.vEBT_V8194947554948674370ptions (lambda ((T tptp.vEBT_VEBT) (X tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T) X) (@ (@ tptp.vEBT_VEBT_membermima T) X)))))) (let ((_let_449 (ho_3935 k_3934 (ho_3932 k_3931 tptp.one)))) (let ((_let_450 (ho_3935 k_3934 tptp.one))) (let ((_let_451 (ho_3943 (ho_3942 k_3941 _let_450) _let_449))) (let ((_let_452 (ho_3946 k_3945 k_3944))) (let ((_let_453 (ho_3942 k_3972 (ho_3943 (ho_3947 _let_452 tptp.na) _let_451)))) (let ((_let_454 (ho_3937 k_3936 (ho_3943 _let_453 (ho_3943 (ho_3947 _let_452 (ho_3937 k_3936 (ho_3943 _let_453 (ho_3943 (ho_3947 _let_452 (ho_3937 k_3936 _let_450)) _let_451)))) _let_451))))) (let ((_let_455 (ho_8441 (ho_8440 (ho_8439 (ho_8438 k_8437 (ho_8427 k_8426 (ho_4125 (ho_4124 k_4123 tptp.mi) tptp.ma))) _let_454) tptp.treeList) tptp.summary))) (let ((_let_456 (ho_4002 (ho_4978 k_4977 _let_455) tptp.x))) (let ((_let_457 (ho_3937 k_3936 _let_449))) (let ((_let_458 (ho_3940 (ho_3939 k_3938 _let_457) (ho_3937 k_3936 (ho_3943 (ho_3942 k_3941 (ho_3943 (ho_3947 _let_452 _let_454) _let_451)) (ho_3943 (ho_3947 _let_452 _let_457) _let_451)))))) (let ((_let_459 (ho_3937 k_3936 (ho_3943 (ho_3942 k_3941 (ho_3943 (ho_3947 _let_452 tptp.x) _let_451)) (ho_3943 (ho_3947 _let_452 _let_458) _let_451))))) (let ((_let_460 (ho_3940 (ho_3939 k_3949 tptp.x) (ho_3940 (ho_3939 k_3948 _let_459) _let_458)))) (let ((_let_461 (ho_4106 (ho_4105 k_4104 tptp.treeList) _let_459))) (let ((_let_462 (ho_4002 (ho_4978 k_4977 _let_461) _let_460))) (let ((_let_463 (ho_4002 (ho_4978 k_4979 _let_461) _let_460))) (let ((_let_464 (ho_4002 (ho_4978 k_4979 _let_455) tptp.x))) (let ((_let_465 (not _let_463))) (let ((_let_466 (@ (@ tptp.divide_divide_int _let_311) _let_232))) (let ((_let_467 (@ tptp.nat2 _let_311))) (let ((_let_468 (@ tptp.semiri8420488043553186161ux_int ll_2))) (let ((_let_469 (@ tptp.plus_plus_int (@ (@ _let_468 tptp.na) _let_466)))) (let ((_let_470 (@ tptp.nat2 (@ _let_469 (@ (@ _let_468 (@ tptp.nat2 (@ _let_469 (@ (@ _let_468 _let_467) _let_466)))) _let_466))))) (let ((_let_471 (@ tptp.vEBT_Node _let_409))) (let ((_let_472 (@ (@ (@ _let_471 _let_470) tptp.treeList) tptp.summary))) (let ((_let_473 (@ (@ tptp.vEBT_VEBT_membermima _let_472) tptp.x))) (let ((_let_474 (@ (@ tptp.vEBT_V5719532721284313246member _let_472) tptp.x))) (let ((_let_475 (not (or _let_474 _let_473)))) (let ((_let_476 (@ tptp.semiri8420488043553186161ux_int (lambda ((I3 tptp.int)) (@ (@ tptp.plus_plus_int I3) (@ tptp.numeral_numeral_int tptp.one)))))) (let ((_let_477 (@ tptp.plus_plus_int (@ (@ _let_476 tptp.na) _let_466)))) (let ((_let_478 (@ tptp.nat2 (@ _let_477 (@ (@ _let_476 (@ tptp.nat2 (@ _let_477 (@ (@ _let_476 _let_467) _let_466)))) _let_466))))) (let ((_let_479 (@ (@ (@ _let_471 _let_478) tptp.treeList) tptp.summary))) (let ((_let_480 (@ (@ tptp.vEBT_VEBT_membermima _let_479) tptp.x))) (let ((_let_481 (@ (@ tptp.vEBT_V5719532721284313246member _let_479) tptp.x))) (let ((_let_482 (ASSUME :args (_let_448)))) (let ((_let_483 (ASSUME :args (_let_437)))) (let ((_let_484 (ASSUME :args (_let_435)))) (let ((_let_485 (ASSUME :args (_let_434)))) (let ((_let_486 (EQ_RESOLVE (ASSUME :args (_let_432)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_485 _let_484 _let_483 _let_482) :args (_let_432 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_487 (SYMM (ASSUME :args (_let_430))))) (let ((_let_488 (SYMM (ASSUME :args (_let_429))))) (let ((_let_489 (SYMM (ASSUME :args (_let_428))))) (let ((_let_490 (SYMM (ASSUME :args (_let_427))))) (let ((_let_491 (SYMM (ASSUME :args (_let_425))))) (let ((_let_492 (SYMM (ASSUME :args (_let_426))))) (let ((_let_493 (ASSUME :args (_let_423)))) (let ((_let_494 (EQ_RESOLVE (ASSUME :args (_let_422)) (MACRO_SR_EQ_INTRO :args (_let_422 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_495 (EQ_RESOLVE (ASSUME :args (_let_421)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_421 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_496 (ASSUME :args (_let_420)))) (let ((_let_497 (EQ_RESOLVE (ASSUME :args (_let_419)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_419 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_498 (ASSUME :args (_let_418)))) (let ((_let_499 (ASSUME :args (_let_417)))) (let ((_let_500 (ASSUME :args (_let_413)))) (let ((_let_501 (ASSUME :args (_let_412)))) (let ((_let_502 (ASSUME :args (_let_411)))) (let ((_let_503 (SYMM (ASSUME :args (_let_410))))) (let ((_let_504 (EQ_RESOLVE (SYMM (ASSUME :args (_let_408))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.zero_zero_nat _let_407) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_505 (EQ_RESOLVE (SYMM (ASSUME :args (_let_406))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.zero_zero_int _let_405) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_506 (SYMM (ASSUME :args (_let_404))))) (let ((_let_507 (EQ_RESOLVE (ASSUME :args (_let_387)) (MACRO_SR_EQ_INTRO :args (_let_387 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_508 (EQ_RESOLVE (ASSUME :args (_let_386)) (MACRO_SR_EQ_INTRO :args (_let_386 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_509 (EQ_RESOLVE (ASSUME :args (_let_385)) (MACRO_SR_EQ_INTRO :args (_let_385 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_510 (EQ_RESOLVE (ASSUME :args (_let_384)) (MACRO_SR_EQ_INTRO :args (_let_384 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_511 (EQ_RESOLVE (ASSUME :args (_let_383)) (MACRO_SR_EQ_INTRO :args (_let_383 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_512 (EQ_RESOLVE (ASSUME :args (_let_382)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_382 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_513 (ASSUME :args (_let_380)))) (let ((_let_514 (ASSUME :args (_let_379)))) (let ((_let_515 (SYMM (ASSUME :args (_let_376))))) (let ((_let_516 (SYMM (ASSUME :args (_let_375))))) (let ((_let_517 (SYMM (ASSUME :args (_let_374))))) (let ((_let_518 (SYMM (ASSUME :args (_let_373))))) (let ((_let_519 (EQ_RESOLVE (ASSUME :args (_let_370)) (MACRO_SR_EQ_INTRO :args (_let_370 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_520 (EQ_RESOLVE (ASSUME :args (_let_369)) (MACRO_SR_EQ_INTRO :args (_let_369 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_521 (EQ_RESOLVE (ASSUME :args (_let_368)) (MACRO_SR_EQ_INTRO :args (_let_368 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_522 (EQ_RESOLVE (ASSUME :args (_let_367)) (MACRO_SR_EQ_INTRO :args (_let_367 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_523 (EQ_RESOLVE (ASSUME :args (_let_366)) (MACRO_SR_EQ_INTRO :args (_let_366 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_524 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_365)) (MACRO_SR_EQ_INTRO :args (_let_365 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= tptp.zero_zero_rat A3) (= tptp.zero_zero_rat B2)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_525 (EQ_RESOLVE (ASSUME :args (_let_364)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_364 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_526 (EQ_RESOLVE (ASSUME :args (_let_363)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_363 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_527 (EQ_RESOLVE (ASSUME :args (_let_359)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_359 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_528 (ASSUME :args (_let_358)))) (let ((_let_529 (ASSUME :args (_let_334)))) (let ((_let_530 (ASSUME :args (_let_327)))) (let ((_let_531 (ASSUME :args (_let_326)))) (let ((_let_532 (ASSUME :args (_let_325)))) (let ((_let_533 (ASSUME :args (_let_324)))) (let ((_let_534 (ASSUME :args (_let_309)))) (let ((_let_535 (ASSUME :args (_let_308)))) (let ((_let_536 (EQ_RESOLVE (ASSUME :args (_let_307)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_307 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_537 (EQ_RESOLVE (ASSUME :args (_let_306)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_306 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_538 (EQ_RESOLVE (ASSUME :args (_let_304)) (MACRO_SR_EQ_INTRO :args (_let_304 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_539 (EQ_RESOLVE (ASSUME :args (_let_303)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_303 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_540 (EQ_RESOLVE (ASSUME :args (_let_302)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_302 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_541 (EQ_RESOLVE (ASSUME :args (_let_301)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_301 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_542 (EQ_RESOLVE (ASSUME :args (_let_300)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_300 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_543 (EQ_RESOLVE (ASSUME :args (_let_296)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_296 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_544 (EQ_RESOLVE (ASSUME :args (_let_295)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_295 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_545 (EQ_RESOLVE (ASSUME :args (_let_294)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_294 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_546 (EQ_RESOLVE (ASSUME :args (_let_293)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_293 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_547 (EQ_RESOLVE (ASSUME :args (_let_292)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_292 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_548 (ASSUME :args (_let_291)))) (let ((_let_549 (EQ_RESOLVE (ASSUME :args (_let_290)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_290 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_550 (ASSUME :args (_let_289)))) (let ((_let_551 (EQ_RESOLVE (ASSUME :args (_let_288)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_288 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_552 (EQ_RESOLVE (ASSUME :args (_let_278)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_278 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_553 (EQ_RESOLVE (ASSUME :args (_let_277)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_277 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_554 (EQ_RESOLVE (ASSUME :args (_let_276)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_276 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_555 (EQ_RESOLVE (ASSUME :args (_let_275)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_275 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_556 (EQ_RESOLVE (ASSUME :args (_let_274)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_274 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_557 (EQ_RESOLVE (ASSUME :args (_let_273)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_273 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_558 (EQ_RESOLVE (ASSUME :args (_let_272)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_272 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_559 (EQ_RESOLVE (ASSUME :args (_let_271)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_271 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_560 (EQ_RESOLVE (ASSUME :args (_let_270)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_270 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_561 (ASSUME :args (_let_269)))) (let ((_let_562 (ASSUME :args (_let_268)))) (let ((_let_563 (EQ_RESOLVE (ASSUME :args (_let_267)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_267 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_564 (EQ_RESOLVE (ASSUME :args (_let_266)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_266 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_565 (EQ_RESOLVE (ASSUME :args (_let_265)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_265 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_566 (EQ_RESOLVE (ASSUME :args (_let_264)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_264 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_567 (EQ_RESOLVE (ASSUME :args (_let_263)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_263 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_568 (EQ_RESOLVE (ASSUME :args (_let_262)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_262 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_569 (EQ_RESOLVE (ASSUME :args (_let_261)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_261 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_570 (EQ_RESOLVE (ASSUME :args (_let_260)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_260 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_571 (EQ_RESOLVE (ASSUME :args (_let_252)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_252 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_572 (EQ_RESOLVE (ASSUME :args (_let_251)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_251 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_573 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_250)) (MACRO_SR_EQ_INTRO :args (_let_250 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.sgn_sgn_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_real X)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) X)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_574 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_249)) (MACRO_SR_EQ_INTRO :args (_let_249 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.sgn_sgn_int (lambda ((X tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int X)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) X)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_575 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_248)) (MACRO_SR_EQ_INTRO :args (_let_248 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.sgn_sgn_Code_integer (lambda ((X tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= tptp.zero_z3403309356797280102nteger X)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) X)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_576 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_247)) (MACRO_SR_EQ_INTRO :args (_let_247 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.sgn_sgn_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_rat X)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_577 (EQ_RESOLVE (ASSUME :args (_let_246)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_246 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_578 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_245)) (MACRO_SR_EQ_INTRO :args (_let_245 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A32 tptp.product_prod_int_int)) (let ((_let_1 (= tptp.zero_zero_int A22))) (or (not (or (not _let_1) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A1))))) (not (or _let_1 (forall ((Q5 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int))) (not (= A1 (@ (@ tptp.times_times_int Q5) A22))))))) (not (forall ((R5 tptp.int) (Q5 tptp.int)) (or (not (= A32 (@ (@ tptp.product_Pair_int_int Q5) R5))) (not (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int A22))) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int A22))) (not (= A1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) A22)) R5)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_579 (EQ_RESOLVE (ASSUME :args (_let_244)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_244 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_580 (EQ_RESOLVE (ASSUME :args (_let_243)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_243 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_581 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_242)) (MACRO_SR_EQ_INTRO :args (_let_242 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.modulo_modulo_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L2))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int L2)) K3) (@ (@ (@ tptp.if_int (= _let_3 (@ tptp.sgn_sgn_int K3))) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K3))))) _let_2)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_582 (ASSUME :args (_let_241)))) (let ((_let_583 (ASSUME :args (_let_240)))) (let ((_let_584 (EQ_RESOLVE (ASSUME :args (_let_238)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_238 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_585 (EQ_RESOLVE (ASSUME :args (_let_237)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_237 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_586 (ASSUME :args (_let_235)))) (let ((_let_587 (EQ_RESOLVE (ASSUME :args (_let_225)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_225 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_588 (ASSUME :args (_let_218)))) (let ((_let_589 (ASSUME :args (_let_217)))) (let ((_let_590 (EQ_RESOLVE (ASSUME :args (_let_211)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_211 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_591 (EQ_RESOLVE (SYMM (ASSUME :args (_let_210))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.pi _let_209) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_592 (EQ_RESOLVE (ASSUME :args (_let_205)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_205 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_593 (EQ_RESOLVE (ASSUME :args (_let_204)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_204 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_594 (EQ_RESOLVE (ASSUME :args (_let_203)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_203 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_595 (EQ_RESOLVE (ASSUME :args (_let_202)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_202 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_596 (EQ_RESOLVE (ASSUME :args (_let_201)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_201 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_597 (EQ_RESOLVE (ASSUME :args (_let_200)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_200 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_598 (EQ_RESOLVE (ASSUME :args (_let_199)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_199 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_599 (EQ_RESOLVE (ASSUME :args (_let_198)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_198 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_600 (EQ_RESOLVE (ASSUME :args (_let_197)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_197 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_601 (EQ_RESOLVE (ASSUME :args (_let_196)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_196 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_602 (EQ_RESOLVE (ASSUME :args (_let_195)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_195 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_603 (EQ_RESOLVE (SYMM (ASSUME :args (_let_191))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.imaginary_unit _let_190) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_604 (ASSUME :args (_let_183)))) (let ((_let_605 (ASSUME :args (_let_182)))) (let ((_let_606 (EQ_RESOLVE (ASSUME :args (_let_181)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_181 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_607 (EQ_RESOLVE (ASSUME :args (_let_179)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_179 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_608 (EQ_RESOLVE (ASSUME :args (_let_178)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_178 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_609 (EQ_RESOLVE (ASSUME :args (_let_177)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_177 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_610 (EQ_RESOLVE (ASSUME :args (_let_173)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_173 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_611 (EQ_RESOLVE (ASSUME :args (_let_172)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_172 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_612 (EQ_RESOLVE (ASSUME :args (_let_171)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_171 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_613 (ASSUME :args (_let_170)))) (let ((_let_614 (EQ_RESOLVE (ASSUME :args (_let_169)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_169 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_615 (EQ_RESOLVE (ASSUME :args (_let_168)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_168 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_616 (EQ_RESOLVE (ASSUME :args (_let_167)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_167 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_617 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_166)) (MACRO_SR_EQ_INTRO :args (_let_166 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo4055970368930404560y_real (lambda ((X3 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (not (forall ((M8 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_188844 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M8))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_188844)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X3 M6)) (@ X3 BOUND_VARIABLE_188844)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3))))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_618 (ASSUME :args (_let_165)))) (let ((_let_619 (ASSUME :args (_let_164)))) (let ((_let_620 (ASSUME :args (_let_163)))) (let ((_let_621 (ASSUME :args (_let_162)))) (let ((_let_622 (ASSUME :args (_let_161)))) (let ((_let_623 (ASSUME :args (_let_160)))) (let ((_let_624 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_159)) (MACRO_SR_EQ_INTRO :args (_let_159 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_complex2 (lambda ((Xs3 tptp.list_complex)) (@ tptp.collect_complex (lambda ((Uu3 tptp.complex)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_complex Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_625 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_158)) (MACRO_SR_EQ_INTRO :args (_let_158 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_real2 (lambda ((Xs3 tptp.list_real)) (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_real Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_real Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_626 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_157)) (MACRO_SR_EQ_INTRO :args (_let_157 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_list_nat2 (lambda ((Xs3 tptp.list_list_nat)) (@ tptp.collect_list_nat (lambda ((Uu3 tptp.list_nat)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_list_nat Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3023201423986296836st_nat Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_627 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_156)) (MACRO_SR_EQ_INTRO :args (_let_156 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_VEBT_VEBT2 (lambda ((Xs3 tptp.list_VEBT_VEBT)) (@ tptp.collect_VEBT_VEBT (lambda ((Uu3 tptp.vEBT_VEBT)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_VEBT_VEBT Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_628 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_155)) (MACRO_SR_EQ_INTRO :args (_let_155 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_o2 (lambda ((Xs3 tptp.list_o)) (@ tptp.collect_o (lambda ((Uu3 Bool)) (not (forall ((I3 tptp.nat)) (or (= (@ (@ tptp.nth_o Xs3) I3) (not Uu3)) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_629 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_154)) (MACRO_SR_EQ_INTRO :args (_let_154 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_nat2 (lambda ((Xs3 tptp.list_nat)) (@ tptp.collect_nat (lambda ((Uu3 tptp.nat)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_nat Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_630 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_153)) (MACRO_SR_EQ_INTRO :args (_let_153 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.set_int2 (lambda ((Xs3 tptp.list_int)) (@ tptp.collect_int (lambda ((Uu3 tptp.int)) (not (forall ((I3 tptp.nat)) (or (not (= Uu3 (@ (@ tptp.nth_int Xs3) I3))) (not (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs3)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_631 (EQ_RESOLVE (ASSUME :args (_let_152)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_152 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_632 (EQ_RESOLVE (ASSUME :args (_let_151)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_151 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_633 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_150)) (MACRO_SR_EQ_INTRO :args (_let_150 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.comm_s4028243227959126397er_rat (lambda ((A3 tptp.rat) (N tptp.nat)) (@ (@ (@ tptp.if_rat (= tptp.zero_zero_nat N)) 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 N) tptp.one_one_nat)) tptp.one_one_rat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_634 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_149)) (MACRO_SR_EQ_INTRO :args (_let_149 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.comm_s2602460028002588243omplex (lambda ((A3 tptp.complex) (N tptp.nat)) (@ (@ (@ tptp.if_complex (= tptp.zero_zero_nat N)) 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 N) tptp.one_one_nat)) tptp.one_one_complex)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_635 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_148)) (MACRO_SR_EQ_INTRO :args (_let_148 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.comm_s7457072308508201937r_real (lambda ((A3 tptp.real) (N tptp.nat)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N)) 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 N) tptp.one_one_nat)) tptp.one_one_real)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_636 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_147)) (MACRO_SR_EQ_INTRO :args (_let_147 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.comm_s4660882817536571857er_int (lambda ((A3 tptp.int) (N tptp.nat)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_nat N)) 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 N) tptp.one_one_nat)) tptp.one_one_int)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_637 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_146)) (MACRO_SR_EQ_INTRO :args (_let_146 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.comm_s4663373288045622133er_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= tptp.zero_zero_nat N)) 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 N) tptp.one_one_nat)) tptp.one_one_nat)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_638 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_145)) (MACRO_SR_EQ_INTRO :args (_let_145 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo6517432010174082258omplex (lambda ((X3 (-> tptp.nat tptp.complex))) (forall ((E3 tptp.real)) (or (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3)) (not (forall ((M8 tptp.nat)) (not (forall ((M6 tptp.nat) (BOUND_VARIABLE_189514 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M8))) (or (not (@ _let_1 M6)) (not (@ _let_1 BOUND_VARIABLE_189514)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X3 M6)) (@ X3 BOUND_VARIABLE_189514)))) E3))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_639 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_144)) (MACRO_SR_EQ_INTRO :args (_let_144 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.csqrt (lambda ((Z5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z5))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z5))) (let ((_let_4 (@ tptp.im Z5))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= tptp.zero_zero_real _let_4)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_640 (EQ_RESOLVE (ASSUME :args (_let_143)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_143 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_641 (EQ_RESOLVE (ASSUME :args (_let_142)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_142 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_642 (EQ_RESOLVE (ASSUME :args (_let_134)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_134 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_643 (EQ_RESOLVE (ASSUME :args (_let_133)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_133 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_644 (EQ_RESOLVE (ASSUME :args (_let_132)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_132 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_645 (EQ_RESOLVE (ASSUME :args (_let_131)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_131 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_646 (EQ_RESOLVE (ASSUME :args (_let_130)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_130 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_647 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_129)) (MACRO_SR_EQ_INTRO :args (_let_129 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo6980174941875973593q_real (lambda ((X3 (-> tptp.nat tptp.real))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_real (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_real (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_648 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_128)) (MACRO_SR_EQ_INTRO :args (_let_128 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo3100542954746470799et_int (lambda ((X3 (-> tptp.nat tptp.set_int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_set_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_set_int (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_649 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_127)) (MACRO_SR_EQ_INTRO :args (_let_127 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo4267028734544971653eq_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_rat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_rat (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_650 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_126)) (MACRO_SR_EQ_INTRO :args (_let_126 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo1459490580787246023eq_num (lambda ((X3 (-> tptp.nat tptp.num))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_num (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_num (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_651 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_125)) (MACRO_SR_EQ_INTRO :args (_let_125 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo4902158794631467389eq_nat (lambda ((X3 (-> tptp.nat tptp.nat))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_nat (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_nat (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_652 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_124)) (MACRO_SR_EQ_INTRO :args (_let_124 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.topolo4899668324122417113eq_int (lambda ((X3 (-> tptp.nat tptp.int))) (or (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_int (@ X3 M6)) (@ X3 N)))) (forall ((M6 tptp.nat) (N tptp.nat)) (or (not (@ (@ tptp.ord_less_eq_nat M6) N)) (@ (@ tptp.ord_less_eq_int (@ X3 N)) (@ X3 M6))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_653 (EQ_RESOLVE (ASSUME :args (_let_123)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_123 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_654 (EQ_RESOLVE (ASSUME :args (_let_122)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_122 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_655 (EQ_RESOLVE (ASSUME :args (_let_121)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_121 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_656 (EQ_RESOLVE (ASSUME :args (_let_120)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_120 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_657 (EQ_RESOLVE (ASSUME :args (_let_119)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_119 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_658 (EQ_RESOLVE (ASSUME :args (_let_118)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_118 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_659 (EQ_RESOLVE (ASSUME :args (_let_117)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_117 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_660 (EQ_RESOLVE (ASSUME :args (_let_116)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_116 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_661 (EQ_RESOLVE (ASSUME :args (_let_115)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_115 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_662 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_114)) (MACRO_SR_EQ_INTRO :args (_let_114 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.arg (lambda ((Z5 tptp.complex)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_complex Z5)) 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))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_663 (EQ_RESOLVE (ASSUME :args (_let_113)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_113 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_664 (EQ_RESOLVE (ASSUME :args (_let_112)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_112 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_665 (EQ_RESOLVE (ASSUME :args (_let_111)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_111 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_666 (ASSUME :args (_let_110)))) (let ((_let_667 (ASSUME :args (_let_109)))) (let ((_let_668 (EQ_RESOLVE (ASSUME :args (_let_108)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_108 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_669 (EQ_RESOLVE (ASSUME :args (_let_107)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_107 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_670 (EQ_RESOLVE (ASSUME :args (_let_106)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_106 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_671 (EQ_RESOLVE (ASSUME :args (_let_105)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_105 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_672 (EQ_RESOLVE (ASSUME :args (_let_104)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_104 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_673 (EQ_RESOLVE (ASSUME :args (_let_103)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_103 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_674 (ASSUME :args (_let_102)))) (let ((_let_675 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_101)) (MACRO_SR_EQ_INTRO :args (_let_101 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.arctan (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_real X) _let_1) (= Y5 (@ tptp.tan_real X)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_676 (EQ_RESOLVE (ASSUME :args (_let_100)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_100 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_677 (EQ_RESOLVE (ASSUME :args (_let_99)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_99 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_678 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_97)) (MACRO_SR_EQ_INTRO :args (_let_97 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.arcsin (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (@ (@ tptp.ord_less_eq_real X) _let_1) (= Y5 (@ tptp.sin_real X)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_679 (EQ_RESOLVE (ASSUME :args (_let_96)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_96 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_680 (EQ_RESOLVE (ASSUME :args (_let_95)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_95 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_681 (EQ_RESOLVE (ASSUME :args (_let_93)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_93 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_682 (EQ_RESOLVE (ASSUME :args (_let_92)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_92 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_683 (EQ_RESOLVE (ASSUME :args (_let_91)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_91 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_684 (ASSUME :args (_let_89)))) (let ((_let_685 (EQ_RESOLVE (ASSUME :args (_let_86)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_86 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_686 (EQ_RESOLVE (ASSUME :args (_let_84)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_84 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_687 (EQ_RESOLVE (ASSUME :args (_let_83)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_83 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_688 (EQ_RESOLVE (ASSUME :args (_let_82)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_82 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_689 (EQ_RESOLVE (ASSUME :args (_let_81)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_81 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_690 (EQ_RESOLVE (ASSUME :args (_let_80)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_80 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_691 (ASSUME :args (_let_79)))) (let ((_let_692 (EQ_RESOLVE (ASSUME :args (_let_78)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_78 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_693 (EQ_RESOLVE (ASSUME :args (_let_77)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_77 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_694 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_76)) (MACRO_SR_EQ_INTRO :args (_let_76 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (not (forall ((M6 tptp.nat)) (not (forall ((X tptp.nat)) (or (not (@ (@ tptp.member_nat X) N9)) (@ (@ tptp.ord_less_eq_nat X) M6)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_695 (EQ_RESOLVE (ASSUME :args (_let_75)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_75 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_696 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_74)) (MACRO_SR_EQ_INTRO :args (_let_74 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.adjust_mod (lambda ((L2 tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= tptp.zero_zero_int R5)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L2) R5)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_697 (EQ_RESOLVE (SYMM (ASSUME :args (_let_73))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.bot_bot_set_nat _let_72) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_698 (SYMM (ASSUME :args (_let_71))))) (let ((_let_699 (EQ_RESOLVE (SYMM (ASSUME :args (_let_70))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.zero_zero_nat tptp.bot_bot_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_700 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_69)) (MACRO_SR_EQ_INTRO :args (_let_69 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.normalize (lambda ((P5 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P5))) (let ((_let_2 (@ tptp.product_fst_int_int P5))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= tptp.zero_zero_int _let_1)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_701 (ASSUME :args (_let_68)))) (let ((_let_702 (EQ_RESOLVE (ASSUME :args (_let_67)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_67 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_703 (EQ_RESOLVE (ASSUME :args (_let_66)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_66 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_704 (EQ_RESOLVE (ASSUME :args (_let_65)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_65 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_705 (EQ_RESOLVE (ASSUME :args (_let_64)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_64 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_706 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_63)) (MACRO_SR_EQ_INTRO :args (_let_63 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.complete_Sup_Sup_int (lambda ((X3 tptp.set_int)) (@ tptp.the_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) X3) (forall ((Y5 tptp.int)) (or (not (@ (@ tptp.member_int Y5) X3)) (@ (@ tptp.ord_less_eq_int Y5) X)))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_707 (SYMM (ASSUME :args (_let_62))))) (let ((_let_708 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_61)) (MACRO_SR_EQ_INTRO :args (_let_61 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat M6)))) (@ (@ (@ tptp.if_option_num (= tptp.zero_zero_nat _let_1)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_709 (SYMM (ASSUME :args (_let_60))))) (let ((_let_710 (SYMM (ASSUME :args (_let_59))))) (let ((_let_711 (SYMM (ASSUME :args (_let_58))))) (let ((_let_712 (SYMM (ASSUME :args (_let_57))))) (let ((_let_713 (ASSUME :args (_let_56)))) (let ((_let_714 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_54)) (MACRO_SR_EQ_INTRO :args (_let_54 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.field_5140801741446780682s_real (@ tptp.collect_real (lambda ((Uu3 tptp.real)) (not (forall ((I3 tptp.int) (N tptp.nat)) (or (not (= Uu3 (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real I3)) (@ tptp.semiri5074537144036343181t_real N)))) (= tptp.zero_zero_nat N))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_715 (ASSUME :args (_let_53)))) (let ((_let_716 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_52)) (MACRO_SR_EQ_INTRO :args (_let_52 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (not (forall ((K3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ tptp.set_ord_atMost_int K3))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_717 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_49)) (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.root (lambda ((N tptp.nat) (X tptp.real)) (@ (@ (@ tptp.if_real (= tptp.zero_zero_nat N)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N)))) X)))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_718 (EQ_RESOLVE (ASSUME :args (_let_48)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_48 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_719 (ASSUME :args (_let_47)))) (let ((_let_720 (ASSUME :args (_let_46)))) (let ((_let_721 (ASSUME :args (_let_45)))) (let ((_let_722 (EQ_RESOLVE (ASSUME :args (_let_44)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_44 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_723 (EQ_RESOLVE (ASSUME :args (_let_43)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_43 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_724 (EQ_RESOLVE (ASSUME :args (_let_42)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_42 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_725 (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_726 (EQ_RESOLVE (SYMM (ASSUME :args (_let_28))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.top_top_set_nat _let_27) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_727 (EQ_RESOLVE (ASSUME :args (_let_17)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_17 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_728 (EQ_RESOLVE (ASSUME :args (_let_16)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_16 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_729 (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_14 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_730 (ASSUME :args (_let_13)))) (let ((_let_731 (ASSUME :args (_let_12)))) (let ((_let_732 (EQ_RESOLVE (ASSUME :args (_let_11)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_11 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_733 (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_10 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_734 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_735 (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_8 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_736 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= tptp.zero_zero_int R5))))))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_737 (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_6 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_738 (EQ_RESOLVE (SYMM (ASSUME :args (_let_5))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args ((= tptp.id_nat tptp.semiri1316708129612266289at_nat) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_739 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_4)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482) :args (_let_4 SB_DEFAULT SBA_FIXPOINT))) _let_738 _let_737 _let_736 _let_735 _let_734 _let_733 _let_732 _let_731 _let_730 _let_729 _let_728 _let_727 _let_726 _let_725 _let_724 _let_723 _let_722 _let_721 _let_720 _let_719 _let_718 _let_717 _let_716 _let_715 _let_714 _let_713 _let_712 _let_711 _let_710 _let_709 _let_708 _let_707 _let_706 _let_705 _let_704 _let_703 _let_702 _let_701 _let_700 _let_699 _let_698 _let_697 _let_696 _let_695 _let_694 _let_693 _let_692 _let_691 _let_690 _let_689 _let_688 _let_687 _let_686 _let_685 _let_684 _let_683 _let_682 _let_681 _let_680 _let_679 _let_678 _let_677 _let_676 _let_675 _let_674 _let_673 _let_672 _let_671 _let_670 _let_669 _let_668 _let_667 _let_666 _let_665 _let_664 _let_663 _let_662 _let_661 _let_660 _let_659 _let_658 _let_657 _let_656 _let_655 _let_654 _let_653 _let_652 _let_651 _let_650 _let_649 _let_648 _let_647 _let_646 _let_645 _let_644 _let_643 _let_642 _let_641 _let_640 _let_639 _let_638 _let_637 _let_636 _let_635 _let_634 _let_633 _let_632 _let_631 _let_630 _let_629 _let_628 _let_627 _let_626 _let_625 _let_624 _let_623 _let_622 _let_621 _let_620 _let_619 _let_618 _let_617 _let_616 _let_615 _let_614 _let_613 _let_612 _let_611 _let_610 _let_609 _let_608 _let_607 _let_606 _let_605 _let_604 _let_603 _let_602 _let_601 _let_600 _let_599 _let_598 _let_597 _let_596 _let_595 _let_594 _let_593 _let_592 _let_591 _let_590 _let_589 _let_588 _let_587 _let_586 _let_585 _let_584 _let_583 _let_582 _let_581 _let_580 _let_579 _let_578 _let_577 _let_576 _let_575 _let_574 _let_573 _let_572 _let_571 _let_570 _let_569 _let_568 _let_567 _let_566 _let_565 _let_564 _let_563 _let_562 _let_561 _let_560 _let_559 _let_558 _let_557 _let_556 _let_555 _let_554 _let_553 _let_552 _let_551 _let_550 _let_549 _let_548 _let_547 _let_546 _let_545 _let_544 _let_543 _let_542 _let_541 _let_540 _let_539 _let_538 _let_537 _let_536 _let_535 _let_534 _let_533 _let_532 _let_531 _let_530 _let_529 _let_528 _let_527 _let_526 _let_525 _let_524 _let_523 _let_522 _let_521 _let_520 _let_519 _let_518 _let_517 _let_516 _let_515 _let_514 _let_513 _let_512 _let_511 _let_510 _let_509 _let_508 _let_507 _let_506 _let_505 _let_504 _let_503 _let_502 _let_501 _let_500 _let_499 _let_498 _let_497 _let_496 _let_495 _let_494 _let_493 _let_492 _let_491 _let_490 _let_489 _let_488 _let_487 _let_486 _let_485 _let_484 _let_483 _let_482))) (let ((_let_740 (EQ_RESOLVE (ASSUME :args (_let_3)) (TRANS (MACRO_SR_EQ_INTRO _let_739 :args (_let_3 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (or _let_481 _let_480)) _let_475))) (PREPROCESS :args ((= _let_475 (not (or _let_464 _let_456))))))))) (let ((_let_741 (@ tptp.power_power_nat _let_233))) (let ((_let_742 (@ _let_741 (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ (@ _let_468 _let_470) _let_466)) (@ (@ _let_468 _let_233) _let_466)))))) (let ((_let_743 (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ (@ _let_468 tptp.x) _let_466)) (@ (@ _let_468 _let_742) _let_466))))) (let ((_let_744 (@ tptp.minus_minus_nat tptp.x))) (let ((_let_745 (@ _let_744 (@ (@ tptp.times_times_nat _let_743) _let_742)))) (let ((_let_746 (@ _let_441 _let_743))) (let ((_let_747 (@ (@ tptp.vEBT_V5719532721284313246member _let_746) _let_745))) (let ((_let_748 (=> _let_747 _let_474))) (let ((_let_749 (@ _let_741 (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ (@ _let_476 _let_478) _let_466)) (@ (@ _let_476 _let_233) _let_466)))))) (let ((_let_750 (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ (@ _let_476 tptp.x) _let_466)) (@ (@ _let_476 _let_749) _let_466))))) (let ((_let_751 (@ _let_744 (@ (@ tptp.times_times_nat _let_750) _let_749)))) (let ((_let_752 (@ _let_441 _let_750))) (let ((_let_753 (@ (@ tptp.vEBT_V5719532721284313246member _let_752) _let_751))) (let ((_let_754 (@ (@ tptp.vEBT_VEBT_membermima _let_746) _let_745))) (let ((_let_755 (or _let_754 _let_747))) (let ((_let_756 (@ (@ tptp.vEBT_VEBT_membermima _let_752) _let_751))) (let ((_let_757 (=> _let_754 _let_473))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (NOT_OR_ELIM _let_740 :args (1)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_446)) (TRANS (MACRO_SR_EQ_INTRO _let_739 :args (_let_446 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> _let_756 _let_480) _let_757))) (PREPROCESS :args ((= _let_757 (=> _let_462 _let_456))))))) :args ((or _let_456 (not _let_462)))) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (ASSUME :args (_let_445)) (TRANS (MACRO_SR_EQ_INTRO _let_739 :args (_let_445 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (or _let_756 _let_753) _let_755))) (PREPROCESS :args ((= _let_755 (or _let_462 _let_463)))))) :args ((or _let_463 _let_462))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_447)) (TRANS (MACRO_SR_EQ_INTRO _let_739 :args (_let_447 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> _let_753 _let_481) _let_748))) (PREPROCESS :args ((= _let_748 (=> _let_463 _let_464))))))) :args ((or _let_464 _let_465))) (NOT_OR_ELIM _let_740 :args (0)) :args (_let_465 true _let_464)) :args (_let_462 true _let_463)) :args (_let_456 false _let_462)) :args (false false _let_456)) :args (_let_448 (@ _let_397 tptp.deg) (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)))) (=> (= tptp.summary _let_1) _let_2) (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m) (@ (@ tptp.vEBT_invar_vebt _let_1) tptp.n) (@ (@ tptp.ord_less_nat tptp.x) _let_436) _let_447 _let_446 (@ (@ tptp.ord_less_nat _let_440) _let_433) _let_445 (@ (@ tptp.vEBT_V8194947554948674370ptions _let_442) _let_439) (forall ((X2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.info) tptp.deg) tptp.treeList) tptp.summary))) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X2) tptp.na) (=> (= X2 _let_1) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) tptp.x)))))) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I)))) _let_437 (@ (@ tptp.ord_less_nat tptp.ma) _let_436) _let_435 (forall ((Ma tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N2)) (@ _let_1 M))))) (=> _let_431 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))) _let_434 (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) _let_433) _let_432 (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (not _let_431) (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 ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) tptp.na) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I)) (@ (@ tptp.vEBT_VEBT_low X2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) X2) (@ (@ tptp.ord_less_eq_nat X2) tptp.ma)))))))) (= _let_391 _let_335) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat) _let_283) (= (@ _let_175 tptp.one_one_complex) _let_193) (= _let_392 _let_32) _let_424 (= _let_388 _let_232) (forall ((B tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))) (forall ((B tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))) (forall ((B tptp.nat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))) (forall ((B tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X4) Y))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num tptp.one) N2))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_rat N2) tptp.one_one_rat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat N2) tptp.one_on7984719198319812577d_enat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N2) tptp.one_one_complex) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real N2) tptp.one_one_real) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat N2) tptp.one_one_nat) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int N2) tptp.one_one_int) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_on7984719198319812577d_enat (@ tptp.numera1916890842035813515d_enat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N2)) (= tptp.one N2))) (forall ((N2 tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N2)) (= tptp.one N2))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_2 (@ _let_1 M))) (@ _let_1 N2)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((X4 tptp.nat)) (=> (forall ((N3 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N3) N3)))) (not (forall ((N3 tptp.nat)) (not (= X4 (@ (@ tptp.plus_plus_nat N3) (@ tptp.suc N3)))))))) (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ tptp.set_real2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N2))))) (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) (@ tptp.set_complex2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N2))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X5) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ P (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N2))))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N2))))) (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N2 tptp.nat)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N2))))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N2))))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N2 tptp.nat)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (@ P X5))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera1916890842035813515d_enat M) (@ tptp.numera1916890842035813515d_enat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N2) tptp.one_one_rat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N2) tptp.one_one_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N2) tptp.one_one_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N2) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N2) tptp.one_one_complex)) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2)))) (forall ((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.extended_enat)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))) (forall ((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 ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A2))) A2)) (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A2))) A2)) (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A2))) A2)) (forall ((A2 tptp.set_list_nat)) (= (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (@ (@ tptp.member_list_nat X) A2))) A2)) (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A2))) A2)) (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X tptp.int)) (@ (@ tptp.member_int X) 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 ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N2) tptp.one))) (forall ((N2 tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N2) tptp.one)))) (forall ((B tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))) (forall ((B tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))) (forall ((B tptp.nat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))) (forall ((B tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ tptp.suc (@ tptp.suc N2)))) (= (@ tptp.suc tptp.one_one_nat) _let_50) (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 ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N2) (@ (@ tptp.plus_plus_num N2) tptp.one))) (@ _let_333 tptp.one_one_real) (@ _let_332 tptp.one_one_rat) (@ _let_398 tptp.one_one_nat) (@ _let_331 tptp.one_one_int) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N2)) M)) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N2) K)))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((V tptp.num) (N2 tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.one_on7984719198319812577d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N2))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N2)))))) (forall ((A tptp.rat) (N2 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 N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N2) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((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 ((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 ((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 ((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))))))))) (not (@ _let_330 tptp.one_one_real)) (not (@ _let_328 tptp.one_one_rat)) (not (@ _let_397 tptp.one_one_nat)) (not (@ _let_329 tptp.one_one_int)) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N2) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N2) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.one_one_rat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.one_on7984719198319812577d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.one_one_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.one_one_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.one_one_int))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X4))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X4))) (= (@ (@ tptp.plus_p3455044024723400733d_enat tptp.one_on7984719198319812577d_enat) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X4))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X4))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X4))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X4))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) _let_430 _let_429 _let_428 _let_427 _let_425 _let_426 (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N2) (@ _let_1 (@ (@ tptp.power_power_complex A) N2))))) _let_425 (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N2)) (@ _let_1 N4)))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((A tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) _let_50) tptp.one_one_rat) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_50) tptp.one_one_nat) (= (@ (@ tptp.power_power_real tptp.one_one_real) _let_50) tptp.one_one_real) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_50) tptp.one_one_int) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) _let_50) tptp.one_one_complex) _let_424 (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N2))) (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) _let_19) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ tptp.suc (@ _let_1 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N2) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N2)) (= M N2))) (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 ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))) (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit0 N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N2)) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)))) (forall ((P (-> tptp.extended_enat Bool)) (N2 tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N2))) (forall ((X4 tptp.num)) (= (@ (@ tptp.ord_less_eq_num X4) tptp.one) (= X4 tptp.one))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X4) (@ tptp.suc Y)) (= X4 Y))) (forall ((N2 tptp.nat)) (not (= N2 (@ tptp.suc N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (= M N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) M) (not (= M N2)))) (forall ((S tptp.nat) (T2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T2) (not (= S T2)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) N2))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N2))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N2))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_nat Y) X4)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) N2)) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= M N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat N2) 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 ((X4 tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X4) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X4 Y)))) (forall ((X4 tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X4) (@ tptp.size_size_list_o Y))) (not (= X4 Y)))) (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X4) (@ tptp.size_size_list_nat Y))) (not (= X4 Y)))) (forall ((X4 tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X4) (@ tptp.size_size_list_int Y))) (not (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X4) (@ tptp.size_size_num Y))) (not (= X4 Y)))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K) (=> (not (= K (@ tptp.suc I2))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J2) (not (= K (@ tptp.suc J2)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N2) (=> (not (= _let_1 N2)) (@ (@ tptp.ord_less_nat _let_1) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N2)) (=> (not (@ _let_1 N2)) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P N2) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (or (@ _let_1 N2) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N2)) (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P N2) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P I3)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) M) (exists ((M3 tptp.nat)) (and (= M (@ tptp.suc M3)) (@ (@ tptp.ord_less_nat N2) M3))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ tptp.suc I2)) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (@ (@ P I4) (@ tptp.suc I4))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K2) (=> (@ _let_1 J2) (=> (@ (@ P J2) K2) (@ _let_1 K2))))))) (@ (@ P I2) J))))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (forall ((I4 tptp.nat)) (=> (= J (@ tptp.suc I4)) (@ P I4))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J) (=> (@ P (@ tptp.suc I4)) (@ P I4)))) (@ P I2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N2))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N2 M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N2)) (= M _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N2) (@ _let_1 (@ tptp.suc N2))))) (forall ((N2 tptp.nat) (M4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M4) (exists ((M5 tptp.nat)) (= M4 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N2) (= M _let_1)))))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) M))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N2))) (forall ((M tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (R (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (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) N2)))))) (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N2)))) _let_423 (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (= tptp.ord_less_eq_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_nat M6) N) (= M6 N)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N2) (= M N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (not (= M N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((F (-> tptp.nat tptp.nat)) (I2 tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ F I2)) (@ F J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) K) (@ (@ tptp.ord_less_nat I2) K))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) J)) I2))) (forall ((J tptp.nat) (I2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I2)) I2))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K tptp.nat) (L tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (not (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (@ (@ tptp.ord_less_eq_nat K) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat M) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N2) (@ (@ tptp.ord_less_eq_nat K) N2))) (forall ((K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L) (exists ((N3 tptp.nat)) (= L (@ (@ tptp.plus_plus_nat K) N3))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((I2 tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I2))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) _let_422 (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_real (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_rat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_num (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_nat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N2) N5) (@ (@ tptp.ord_less_int (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N2)) (@ F M)) (@ (@ tptp.ord_less_nat N2) M)))) (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N2)) (@ F N5))))) (forall ((F (-> tptp.nat tptp.set_int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.rat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.num)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N2))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N2) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)))) (= tptp.ord_less_nat (lambda ((N tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) __flatten_var_0))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc M)) (= N2 M)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P J) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P (@ tptp.suc N3)) (@ P N3))))) (@ P I2))))) (forall ((I2 tptp.nat) (J tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ P I2) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) N3) (=> (@ (@ tptp.ord_less_nat N3) J) (=> (@ P N3) (@ P (@ tptp.suc N3)))))) (@ P J))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (forall ((Q2 tptp.nat)) (not (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q2)))))))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) M)))) (forall ((I2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I2) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I2)))) (= tptp.ord_less_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M6) K3)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K2)))))) (forall ((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))))) _let_421 (= _let_389 tptp.suc) (= tptp.suc _let_389) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X4))) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X4))) (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 ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.one_one_Code_integer) A)) (forall ((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) (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_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_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 ((N2 tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N2)) (@ tptp.set_real2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N2)) (@ tptp.set_complex2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s5460976970255530739at_nat Xs)) (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.nth_Pr7617993195940197384at_nat Xs) N2)) (@ tptp.set_Pr5648618587558075414at_nat Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N2)) (@ tptp.set_VEBT_VEBT2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N2)) (@ tptp.set_o2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N2)) (@ tptp.set_nat2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N2)) (@ tptp.set_int2 Xs)))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))) (forall ((N2 tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Xs)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (@ P X5))) (@ P (@ (@ tptp.nth_o Xs) N2))))) (forall ((N2 tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))) (forall ((N2 tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N2) (@ 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) N2))))) (forall ((X4 tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X4) (@ 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) X4))))) (forall ((X4 tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I3) X4))))) (forall ((X4 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X4) (@ 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) X4))))) (forall ((X4 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X4) (@ 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) X4))))) (forall ((X4 Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X4) (@ 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) X4))))) (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X4) (@ 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) X4))))) (forall ((X4 tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X4) (@ 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) X4))))) (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (X4 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 X4) (@ tptp.set_real2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X4 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I4)))) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (P (-> tptp.product_prod_nat_nat Bool)) (X4 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 X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ P X4)))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (X4 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 X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X4 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 X4) (@ tptp.set_o2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (X4 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 X4) (@ tptp.set_nat2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (X4 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 X4) (@ tptp.set_int2 Xs)) (@ P X4)))) (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X))) (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 ((X Bool)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X))) (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 ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (@ P X))) (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 ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (@ P X))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I3)))))) (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)) (=> (@ (@ 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)) (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 ((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 ((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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X4) N3))))) _let_420 (forall ((S2 tptp.set_real)) (=> (exists ((X2 tptp.real)) (@ (@ tptp.member_real X2) S2)) (=> (exists ((Z3 tptp.real)) (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real X5) Z3)))) (exists ((Y3 tptp.real)) (and (forall ((X2 tptp.real)) (=> (@ (@ tptp.member_real X2) S2) (@ (@ tptp.ord_less_eq_real X2) Y3))) (forall ((Z3 tptp.real)) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real X5) Z3))) (@ (@ tptp.ord_less_eq_real Y3) Z3)))))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_real Y) X4)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_rat Y) X4)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (= X4 Y)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_int Y) X4)))) (forall ((X2 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X2) X_12))) (forall ((X2 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X2) X_12))) (forall ((X2 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X2))) (forall ((X2 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X2))) (forall ((X4 tptp.complex)) (= (= tptp.one_one_complex X4) (= X4 tptp.one_one_complex))) (forall ((X4 tptp.real)) (= (= tptp.one_one_real X4) (= X4 tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (= tptp.one_one_rat X4) (= X4 tptp.one_one_rat))) (forall ((X4 tptp.nat)) (= (= tptp.one_one_nat X4) (= X4 tptp.one_one_nat))) (forall ((X4 tptp.int)) (= (= tptp.one_one_int X4) (= X4 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) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_real I2) K) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_rat I2) K) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_nat I2) K) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (= K L)) (= (@ (@ tptp.plus_plus_int I2) K) (@ (@ tptp.plus_plus_int J) L)))) (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 ((Xs tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B3) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ _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 ((X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ _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 ((X tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X))) (=> (@ _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 ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X))) (=> (@ _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 ((X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ _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 ((X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B3)))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_o)) (= (@ tptp.size_size_list_o Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs2) N2))) (forall ((N2 tptp.nat)) (exists ((Xs2 tptp.list_int)) (= (@ tptp.size_size_list_int Xs2) N2))) (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) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (= K L)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (= K L)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (= K L)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (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) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (= K L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (= K L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (= K L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (= K L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (= I2 J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (= I2 J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (= I2 J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (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)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))) (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs2 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs2 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs2 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs2 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs2)) (@ P Ys2))) (@ P Xs2))) (@ P Xs))) (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) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_real I2) J) (@ (@ tptp.ord_less_eq_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I2) J) (@ (@ tptp.ord_less_eq_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I2) J) (@ (@ tptp.ord_less_eq_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_int I2) J) (@ (@ tptp.ord_less_eq_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (forall ((I2 tptp.real) (J tptp.real) (K tptp.real) (L tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I2) J) (@ (@ tptp.ord_less_real K) L)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I2) K)) (@ (@ tptp.plus_plus_real J) L)))) (forall ((I2 tptp.rat) (J tptp.rat) (K tptp.rat) (L tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I2) J) (@ (@ tptp.ord_less_rat K) L)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I2) K)) (@ (@ tptp.plus_plus_rat J) L)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_nat K) L)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ (@ tptp.plus_plus_nat J) L)))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int) (L tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I2) J) (@ (@ tptp.ord_less_int K) L)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I2) K)) (@ (@ tptp.plus_plus_int J) L)))) (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)) (@ (@ 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))) (= (lambda ((Y6 tptp.list_VEBT_VEBT) (Z4 tptp.list_VEBT_VEBT)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (= (@ (@ tptp.nth_VEBT_VEBT Xs3) I3) (@ (@ tptp.nth_VEBT_VEBT Ys3) I3))))))) (= (lambda ((Y6 tptp.list_o) (Z4 tptp.list_o)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) (@ tptp.size_size_list_o Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_o Xs3)) (= (@ (@ tptp.nth_o Xs3) I3) (@ (@ tptp.nth_o Ys3) I3))))))) (= (lambda ((Y6 tptp.list_nat) (Z4 tptp.list_nat)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) (@ tptp.size_size_list_nat Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_nat Xs3)) (= (@ (@ tptp.nth_nat Xs3) I3) (@ (@ tptp.nth_nat Ys3) I3))))))) (= (lambda ((Y6 tptp.list_int) (Z4 tptp.list_int)) (= Y6 Z4)) (lambda ((Xs3 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) (@ tptp.size_size_list_int Ys3)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.size_size_list_int Xs3)) (= (@ (@ tptp.nth_int Xs3) I3) (@ (@ tptp.nth_int Ys3) I3))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.vEBT_VEBT)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_VEBT_VEBT Xs3) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 Bool)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_o Xs3) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.nat)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_nat Xs3) I3)))))))) (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (exists ((X3 tptp.int)) (@ (@ P I3) X3)))) (exists ((Xs3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs3) K) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) K) (@ (@ P I3) (@ (@ tptp.nth_int Xs3) I3)))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs Ys)))) (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs Ys)))) (= 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))) _let_419 (forall ((N2 tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N2)) X4))) _let_418 (forall ((N2 tptp.nat) (X4 tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N2)) X4))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X5) X_12))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))) (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) _let_335) (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) _let_193) (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) _let_32) (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) _let_232) (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L)))) (forall ((K tptp.num) (L tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L)))) (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T2) D) (@ (@ tptp.vEBT_invar_vebt T2) D))) _let_417 (forall ((T2 tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) D) (@ (@ tptp.vEBT_VEBT_valid T2) D))) (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 ((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) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat M) N2) M))) (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) _let_416 _let_415 _let_414 _let_416 _let_415 _let_414 (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 ((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) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N2)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N2)) B))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N2)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N2)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N2)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) B))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) M)) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))) (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)) (N2 tptp.nat) (P2 tptp.nat) (M tptp.nat)) (=> (@ P N2) (=> (@ (@ tptp.ord_less_nat N2) 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) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N2))) N2)) _let_413 _let_412 _let_411 (forall ((X4 tptp.num)) (= (@ (@ tptp.pow X4) tptp.one) X4)) (forall ((P (-> tptp.nat Bool)) (X4 tptp.nat) (M7 tptp.nat)) (=> (@ P X4) (=> (forall ((X5 tptp.nat)) (=> (@ P X5) (@ (@ tptp.ord_less_eq_nat X5) M7))) (not (forall ((M5 tptp.nat)) (=> (@ P M5) (not (forall ((X2 tptp.nat)) (=> (@ P X2) (@ (@ tptp.ord_less_eq_nat X2) M5)))))))))) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N2))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)))) _let_2))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N2)) N2))) (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 ((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_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_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_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 ((X22 tptp.num) (Y2 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y2)) (= X22 Y2))) (forall ((X4 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X4) X4)) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) X4)) (forall ((X4 tptp.num)) (@ (@ tptp.ord_less_eq_num X4) X4)) (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat X4) X4)) (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_eq_int X4) X4)) (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 ((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 ((Xs tptp.list_VEBT_VEBT)) (= (@ tptp.size_s8217280938318005548T_VEBT (@ tptp.subseqs_VEBT_VEBT Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_s6755466524823107622T_VEBT Xs)))) (forall ((Xs tptp.list_o)) (= (@ tptp.size_s2710708370519433104list_o (@ tptp.subseqs_o Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_o Xs)))) (forall ((Xs tptp.list_nat)) (= (@ tptp.size_s3023201423986296836st_nat (@ tptp.subseqs_nat Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_nat Xs)))) (forall ((Xs tptp.list_int)) (= (@ tptp.size_s533118279054570080st_int (@ tptp.subseqs_int Xs)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.size_size_list_int Xs)))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N2)) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_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) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((T2 tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T2) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) _let_410 (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))) (forall ((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 ((X4 tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X4) Y)) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 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.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.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 ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((C tptp.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 ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))) (forall ((A tptp.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.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (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.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((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.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.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 ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)) (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) (N2 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N2) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (= (@ 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) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N2 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N2) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))) (forall ((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 ((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.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) (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) (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 (@ (@ 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 ((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.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= 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.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (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.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.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))) (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 ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.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.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((A tptp.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.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))) (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))) (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger A) A) tptp.one_one_Code_integer))) (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.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N2)) tptp.zero_zero_rat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N2)) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N2)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N2)) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N2)) tptp.zero_zero_complex)) (forall ((K tptp.num)) (= (@ (@ tptp.power_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.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 ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (@ _let_1 M) (@ _let_1 N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) tptp.one_one_nat) (= N2 tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N2) _let_1))) (forall ((X4 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X4) M) _let_1) (or (= M tptp.zero_zero_nat) (= X4 _let_1))))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X4) N2)) (or (@ _let_1 X4) (= N2 tptp.zero_zero_nat))))) (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (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_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.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 ((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) (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) (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 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 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 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 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)) (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)) (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)) (= (@ (@ 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)) (= (@ (@ 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) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat N2) M)))))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (@ (@ tptp.ord_less_eq_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (@ (@ tptp.ord_less_eq_rat A) B))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.ord_less_eq_nat A) B))))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.ord_less_eq_int A) B))))))) (forall ((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))) _let_408 _let_406 _let_404 _let_408 _let_406 _let_404 (forall ((B tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((B tptp.rat) (M tptp.nat) (N2 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 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((B tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((B tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat N2) M)))))) (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X4 Y))))))) (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X4 Y))))))) (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X4) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X4 Y))))))) (forall ((X4 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 X4) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X4 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 ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_set_real 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_set_nat 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_less_set_complex 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_set_int 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_le7866589430770878221at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((X4 tptp.complex)) (= (= tptp.zero_zero_complex X4) (= X4 tptp.zero_zero_complex))) (forall ((X4 tptp.real)) (= (= tptp.zero_zero_real X4) (= X4 tptp.zero_zero_real))) (forall ((X4 tptp.rat)) (= (= tptp.zero_zero_rat X4) (= X4 tptp.zero_zero_rat))) (forall ((X4 tptp.nat)) (= (= tptp.zero_zero_nat X4) (= X4 tptp.zero_zero_nat))) (forall ((X4 tptp.int)) (= (= tptp.zero_zero_int X4) (= X4 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 ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X4 tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X4) (or (= X4 Mi) (= X4 Ma)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N2) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N2) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N2) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2) tptp.zero_zero_complex))) (forall ((X4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X4)) (@ _let_228 tptp.zero_zero_real) (@ _let_323 tptp.zero_zero_rat) (@ _let_400 tptp.zero_zero_nat) _let_372 (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (not (@ _let_229 tptp.zero_zero_real)) (not (@ _let_312 tptp.zero_zero_rat)) (not (@ _let_378 tptp.zero_zero_nat)) _let_371 (forall ((D1 tptp.real) (D2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ _let_1 D1) (@ _let_1 D2)))))))) (forall ((D1 tptp.rat) (D2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D2) (exists ((E tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ _let_1 D1) (@ _let_1 D2)))))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_z5237406670263579293d_enat (@ tptp.numera1916890842035813515d_enat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N2)))) (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) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N2) tptp.zero_zero_rat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N2) tptp.zero_zero_nat)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N2) tptp.zero_zero_real)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N2) tptp.zero_zero_int)))) (forall ((A tptp.complex) (N2 tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N2) tptp.zero_zero_complex)))) (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat) (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (=> (not (= X4 (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X4 (@ tptp.suc (@ tptp.suc Va2))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (exists ((M5 tptp.nat)) (= N2 (@ 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) (N2 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) N2))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N2)))) (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)) (N2 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 N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (not (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat N2) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N2) tptp.zero_zero_nat) (= N2 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 ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N2)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N2) M) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N2) N2)) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N2) (@ (@ tptp.power_power_real B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N2) (@ (@ tptp.power_power_rat B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N2) (@ (@ tptp.power_power_nat B) N2)) (= A B))))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N2) (@ (@ tptp.power_power_int B) N2)) (= A B))))))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat N2)) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N2))) _let_403 _let_402 _let_401 _let_399 _let_403 _let_402 _let_401 _let_399 (not (@ _let_333 tptp.zero_zero_real)) (not (@ _let_332 tptp.zero_zero_rat)) (not (@ _let_398 tptp.zero_zero_nat)) (not (@ _let_331 tptp.zero_zero_int)) (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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X4) Y) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X4) Y) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))) (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X4) Y) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X4) Y) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X4) Y) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X4) Y) tptp.zero_zero_nat) (and (= X4 tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X4) Y) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))) (not (@ _let_330 tptp.zero_zero_real)) (not (@ _let_328 tptp.zero_zero_rat)) (not (@ _let_397 tptp.zero_zero_nat)) (not (@ _let_329 tptp.zero_zero_int)) _let_396 _let_395 _let_394 _let_393 _let_396 _let_395 _let_394 _let_393 (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))) (forall ((A tptp.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)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C3 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C3)) (= C3 tptp.zero_zero_nat)))))) (forall ((A tptp.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 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.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)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X4) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) 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.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)) (@ (@ tptp.divide_divide_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.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))) (forall ((A tptp.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)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) 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 ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((A tptp.rat) (B tptp.rat) (N2 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) N2)) (@ (@ tptp.power_power_rat B) N2))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((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 ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))) (forall ((A tptp.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 ((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)) (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)) (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) (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) (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) (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) (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 ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) 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 X4) Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Y))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N2))))) (forall ((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 ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))) (forall ((A tptp.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 ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (or (@ P tptp.zero_zero_nat) (exists ((I3 tptp.nat)) (and (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M6 tptp.nat)) (= N2 (@ tptp.suc M6))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ tptp.suc N2)) (@ P I3))) (and (@ P tptp.zero_zero_nat) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) N2) (@ P (@ tptp.suc I3))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((M5 tptp.nat)) (= N2 (@ tptp.suc M5))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N2)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N2) _let_1) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (or (and (= M _let_1) (= N2 tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N2 _let_1)))))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K2) (not (@ P I)))) (@ P K2)))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K2) (= (@ (@ tptp.plus_plus_nat I2) K2) J))))) (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ tptp.divide_divide_nat B3) N2))))))) (= tptp.one_one_nat _let_230) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N2) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N2) (= N2 tptp.zero_zero_nat)))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I2) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (let ((_let_3 (= _let_1 N2))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))) (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))) (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (= (@ (@ tptp.ord_less_eq_set_int X4) Y) (= X4 Y)))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (= (@ (@ tptp.ord_less_eq_rat X4) Y) (= X4 Y)))) (forall ((Y tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (= (@ (@ tptp.ord_less_eq_num X4) Y) (= X4 Y)))) (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (= (@ (@ tptp.ord_less_eq_nat X4) Y) (= X4 Y)))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (= (@ (@ tptp.ord_less_eq_int X4) Y) (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (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)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_eq_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_eq_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_int Y) X4))) (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 ((X4 tptp.set_int) (Y tptp.set_int)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_set_int X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_rat X4) Y))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_num X4) Y))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_nat X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (= X4 Y) (@ (@ tptp.ord_less_eq_int X4) Y))) (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)) (=> (@ (@ tptp.ord_less_eq_num X5) Y3) (@ (@ tptp.ord_less_eq_rat (@ F X5)) (@ F Y3)))) (@ (@ tptp.ord_less_eq_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_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))))) (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))))) (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))))) (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))))) (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))))) (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))))))) (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (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 ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))) (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))) (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))) (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (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.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)))) (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 ((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)))) (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (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 ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))) (= (lambda ((Y6 tptp.num) (Z4 tptp.num)) (= Y6 Z4)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))) (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))) (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))) (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)))) (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (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 ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (= X4 Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (= X4 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (= X4 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) (=> (= 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 ((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)))) (= (lambda ((Y6 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(not _let_2)))))))))))))))))) (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 ((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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (@ (@ tptp.ord_less_real Y) X4)))) (forall ((X4 tptp.rat) (Y 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(=> (@ (@ tptp.ord_less_int X4) Y) (not (@ (@ tptp.ord_less_int Y) X4)))) (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 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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 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tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))) (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))))) (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))))) (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))))) (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))))) (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))))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N tptp.nat)) (and (@ P4 N) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N) (not (@ P4 M6)))))))) (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 ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))) (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))) (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_real Y) X4)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_rat Y) X4)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_num Y) X4)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_nat Y) X4)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (=> (not (= X4 Y)) (@ (@ tptp.ord_less_int Y) X4)))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X4)) (= (not (@ (@ tptp.ord_less_real X4) Y)) (= X4 Y)))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X4)) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (= X4 Y)))) (forall ((Y tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X4)) (= (not (@ (@ tptp.ord_less_num X4) Y)) (= X4 Y)))) (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X4)) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (= X4 Y)))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X4)) (= (not (@ (@ tptp.ord_less_int X4) Y)) (= X4 Y)))) (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))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_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_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))) (forall ((A tptp.rat) (B tptp.rat) (C tptp.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)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))) (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (not (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (not (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (not (= X4 Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (not (= X4 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (not (= X4 Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real X4) Z2) (@ (@ tptp.ord_less_real Z2) Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (exists ((Z2 tptp.rat)) (and (@ (@ tptp.ord_less_rat X4) Z2) (@ (@ tptp.ord_less_rat Z2) Y))))) (forall ((X4 tptp.real)) (exists ((X_12 tptp.real)) (@ (@ tptp.ord_less_real X4) X_12))) (forall ((X4 tptp.rat)) (exists ((X_12 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_12))) (forall ((X4 tptp.nat)) (exists ((X_12 tptp.nat)) (@ (@ tptp.ord_less_nat X4) X_12))) (forall ((X4 tptp.int)) (exists ((X_12 tptp.int)) (@ (@ tptp.ord_less_int X4) X_12))) (forall ((X4 tptp.real)) (exists ((Y3 tptp.real)) (@ (@ tptp.ord_less_real Y3) X4))) (forall ((X4 tptp.rat)) (exists ((Y3 tptp.rat)) (@ (@ tptp.ord_less_rat Y3) X4))) (forall ((X4 tptp.int)) (exists ((Y3 tptp.int)) (@ (@ tptp.ord_less_int Y3) X4))) (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)) (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 ((X4 tptp.real) (Y tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real Y) E)))) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat Y) E)))) (@ (@ tptp.ord_less_eq_rat X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) Y)) tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X4) Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) 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 ((X4 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))) (forall ((X4 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))) (forall ((X4 tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((X4 tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (=> (@ (@ tptp.ord_less_rat X4) 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 X4) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))) (forall ((Y tptp.real) (X4 tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X4) 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 X4) Z)) (@ (@ tptp.divide_divide_real Y) W))))))) (forall ((Y tptp.rat) (X4 tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X4) 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 X4) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger A) B)))))) (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))) (@ _let_229 _let_392) (@ _let_312 _let_391) (@ _let_378 _let_390) (@ _let_313 _let_388) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.one_one_real)))) (forall ((A tptp.rat) (N2 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) N2)) tptp.one_one_rat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int)))) (forall ((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 ((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.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.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.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ 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) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N2))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((A tptp.rat) (N2 tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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) (N2 tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))) (forall ((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 ((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 ((A2 tptp.set_real) (B3 tptp.set_real) (X4 tptp.real)) (let ((_let_1 (@ tptp.member_real X4))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X4))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X4 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X4))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat) (X4 tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat X4))) (=> (@ (@ tptp.ord_le3146513528884898305at_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X4 tptp.int)) (let ((_let_1 (@ tptp.member_int X4))) (=> (@ (@ tptp.ord_less_eq_set_int 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_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_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)))))) _let_387 _let_386 _let_385 _let_384 _let_383 (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_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((T tptp.real)) (let ((_let_1 (@ tptp.member_real T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T tptp.nat)) (let ((_let_1 (@ tptp.member_nat T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((T tptp.complex)) (let ((_let_1 (@ tptp.member_complex T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (forall ((T tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.member8440522571783428010at_nat T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T tptp.int)) (let ((_let_1 (@ tptp.member_int T))) (=> (@ _let_1 A6) (@ _let_1 B6)))))) (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) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))) (= (lambda ((Y6 tptp.set_int) (Z4 tptp.set_int)) (= Y6 Z4)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))) (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X tptp.complex)) (=> (@ P X) (@ Q X))))) (forall ((P (-> tptp.real Bool)) (Q (-> tptp.real Bool))) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real P)) (@ tptp.collect_real Q)) (forall ((X tptp.real)) (=> (@ P X) (@ Q X))))) (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 ((X tptp.list_nat)) (=> (@ P X) (@ Q X))))) (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)) (forall ((X tptp.nat)) (=> (@ P X) (@ Q X))))) (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)) (forall ((X tptp.int)) (=> (@ P X) (@ Q X))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C4) (@ (@ tptp.ord_less_set_int A2) C4)))) _let_382 (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))) (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))) (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))))) (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int))) (forall ((N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)) (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)) (= _let_381 _let_230) (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P N2) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K2 tptp.nat)) (and (@ (@ tptp.ord_less_nat K2) N2) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K2) (not (@ P I)))) (@ P (@ tptp.suc K2))))))) (forall ((X4 tptp.real) (Xs tptp.list_real)) (=> (@ (@ tptp.member_real X4) (@ tptp.set_real2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_real Xs)))) (forall ((X4 tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))) (forall ((X4 tptp.product_prod_nat_nat) (Xs tptp.list_P6011104703257516679at_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s5460976970255530739at_nat Xs)))) (forall ((X4 tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s6755466524823107622T_VEBT Xs)))) (forall ((X4 Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X4) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))) (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_nat Xs)))) (forall ((X4 tptp.int) (Xs tptp.list_int)) (=> (@ (@ tptp.member_int X4) (@ tptp.set_int2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_int Xs)))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ 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 N2))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N2) K)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N2)) (and (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M)))))) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I2) (@ _let_1 (@ (@ tptp.power_power_nat I2) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N2)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N2) M) (= N2 tptp.one_one_nat)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) M)))) (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))) (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 ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) A)))) (forall ((A tptp.rat) (N2 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 N2))) A)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) A)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N2))) tptp.one_one_real)))) (forall ((A tptp.rat) (N2 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 N2))) tptp.one_one_rat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N2))) tptp.one_one_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N2))) tptp.one_one_int)))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N2))))))) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) _let_50) tptp.zero_zero_rat) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_50) tptp.zero_zero_nat) (= (@ _let_137 _let_50) tptp.zero_zero_real) (= (@ _let_136 _let_50) tptp.zero_zero_int) (= (@ _let_135 _let_50) tptp.zero_zero_complex) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_real A) N2)))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_rat A) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ _let_1 (@ (@ tptp.power_power_int A) N2)))))) (= _let_50 _let_231) (forall ((A2 tptp.nat) (B3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N2)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N2) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N2))))) (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 (@ (@ 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 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))) (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 ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X4) Y))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X4) Y))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X4) Y))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X4) Y))))) (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))) (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))) (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 Y))))))) (forall ((X4 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 X4) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= X4 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 ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 N2) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 N2) tptp.zero_zero_int))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N2 tptp.zero_zero_nat) (= N2 (@ tptp.suc tptp.zero_zero_nat))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X4) Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X4) Y))))) (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X4) Y))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X4) Y))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (or (@ (@ tptp.ord_less_real X4) Y) (= X4 Y)))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (or (@ (@ tptp.ord_less_set_int X4) Y) (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (or (@ (@ tptp.ord_less_rat X4) Y) (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (or (@ (@ tptp.ord_less_num X4) Y) (= X4 Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (or (@ (@ tptp.ord_less_nat X4) Y) (= X4 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (or (@ (@ tptp.ord_less_int X4) Y) (= X4 Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_real Y) X4))) (forall ((X4 tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X4) Y) (@ (@ tptp.ord_less_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X4) Y) (@ (@ tptp.ord_less_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_int Y) X4))) (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 ((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.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.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 ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))) (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X4) Z)))) (forall ((X4 tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X4) Z)))) (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X4) Z)))) (forall ((X4 tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X4) Z)))) (forall ((X4 tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X4) Z)))) (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X4) Z)))) (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 ((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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int X4) Y) (@ (@ tptp.ord_less_eq_set_int X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (@ (@ tptp.ord_less_eq_rat X4) Y))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Y) (@ (@ tptp.ord_less_eq_num X4) Y))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ (@ tptp.ord_less_eq_nat X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Y) (@ (@ tptp.ord_less_eq_int X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_eq_real Y) X4))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))) (forall ((X4 tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X4) Y)) (@ (@ tptp.ord_less_real Y) X4))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X4) Y)) (@ (@ tptp.ord_less_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X4) Y)) (@ (@ tptp.ord_less_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X4) Y)) (@ (@ tptp.ord_less_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X4) Y)) (@ (@ tptp.ord_less_int Y) X4))) (= tptp.ord_less_real (lambda ((X tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y5) (not (= X Y5))))) (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y5) (not (= X Y5))))) _let_380 _let_379 (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (not (= X Y5))))) (= tptp.ord_less_int (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (not (= X Y5))))) (= tptp.ord_less_eq_real (lambda ((X tptp.real) (Y5 tptp.real)) (or (@ (@ tptp.ord_less_real X) Y5) (= X Y5)))) (= tptp.ord_less_eq_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X) Y5) (= X Y5)))) (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y5) (= X Y5)))) (= tptp.ord_less_eq_num (lambda ((X tptp.num) (Y5 tptp.num)) (or (@ (@ tptp.ord_less_num X) Y5) (= X Y5)))) (= tptp.ord_less_eq_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y5) (= X Y5)))) (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Y5 tptp.int)) (or (@ (@ tptp.ord_less_int X) Y5) (= X Y5)))) (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))) (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))) (= 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 ((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)))) (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))))) (= 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))))) (= 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)))) (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X4) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X4) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X4) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X4) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))) (= 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 ((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))))) (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)))) (= 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))))) (= 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)))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X4)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X4)) (@ (@ tptp.ord_less_rat X4) Y))) (forall ((Y tptp.num) (X4 tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X4)) (@ (@ tptp.ord_less_num X4) Y))) (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X4)) (@ (@ tptp.ord_less_nat X4) Y))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X4)) (@ (@ tptp.ord_less_int X4) Y))) (= tptp.ord_less_real (lambda ((X tptp.real) (Y5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X) Y5) (not (@ (@ tptp.ord_less_eq_real Y5) X))))) (= tptp.ord_less_set_int (lambda ((X tptp.set_int) (Y5 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X) Y5) (not (@ (@ tptp.ord_less_eq_set_int Y5) X))))) (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X) Y5) (not (@ (@ tptp.ord_less_eq_rat Y5) X))))) (= tptp.ord_less_num (lambda ((X tptp.num) (Y5 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X) Y5) (not (@ (@ tptp.ord_less_eq_num Y5) X))))) (= tptp.ord_less_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X) Y5) (not (@ (@ tptp.ord_less_eq_nat Y5) X))))) (= tptp.ord_less_int (lambda ((X tptp.int) (Y5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X) Y5) (not (@ (@ tptp.ord_less_eq_int Y5) X))))) (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))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (= (not (@ (@ tptp.ord_less_real X4) Y)) (= X4 Y)))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (= (not (@ (@ tptp.ord_less_set_int X4) Y)) (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (= (not (@ (@ tptp.ord_less_rat X4) Y)) (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X4) Y) (= (not (@ (@ tptp.ord_less_num X4) Y)) (= X4 Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X4) Y) (= (not (@ (@ tptp.ord_less_nat X4) Y)) (= X4 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (= (not (@ (@ tptp.ord_less_int X4) Y)) (= X4 Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (= (@ (@ tptp.ord_less_eq_real X4) Y) (= X4 Y)))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (not (@ (@ tptp.ord_less_set_int X4) Y)) (= (@ (@ tptp.ord_less_eq_set_int X4) Y) (= X4 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (= (@ (@ tptp.ord_less_eq_rat X4) Y) (= X4 Y)))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (= (@ (@ tptp.ord_less_eq_num X4) Y) (= X4 Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (= (@ (@ tptp.ord_less_eq_nat X4) Y) (= X4 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (= (@ (@ tptp.ord_less_eq_int X4) Y) (= X4 Y)))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X4) Y)) (@ (@ tptp.ord_less_eq_real Y) X4))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X4) Y)) (@ (@ tptp.ord_less_eq_rat Y) X4))) (forall ((X4 tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X4) Y)) (@ (@ tptp.ord_less_eq_num Y) X4))) (forall ((X4 tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X4) Y)) (@ (@ tptp.ord_less_eq_nat Y) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X4) Y)) (@ (@ tptp.ord_less_eq_int Y) X4))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (not (@ (@ tptp.ord_less_real X4) Y)))) (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) X4) (not (@ (@ tptp.ord_less_set_int X4) Y)))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (not (@ (@ tptp.ord_less_rat X4) Y)))) (forall ((Y tptp.num) (X4 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X4) (not (@ (@ tptp.ord_less_num X4) Y)))) (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (not (@ (@ tptp.ord_less_nat X4) Y)))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X4) (not (@ (@ tptp.ord_less_int X4) Y)))) (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))) (forall ((TreeList2 tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X5) N2))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N2) (=> (= Deg (@ (@ tptp.plus_plus_nat N2) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_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) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N2))) (forall ((X5 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X5) N2) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X5) N2))) (and (@ (@ tptp.ord_less_nat Mi) X5) (@ (@ tptp.ord_less_eq_nat X5) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))) (forall ((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)))) (= 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 ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N) _let_1)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (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))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) N) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N)) (= A22 (@ (@ tptp.plus_plus_nat N) N)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _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))) N)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X) N))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N tptp.nat) (Summary2 tptp.vEBT_VEBT) (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))))) (let ((_let_3 (@ tptp.suc N))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) A22) TreeList) Summary2)) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X) N))) (@ (@ tptp.vEBT_invar_vebt Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N) _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 N))) (= (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I3)))) (=> _let_1 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ _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 N))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low Ma2) N))) (forall ((X tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X) N) I3) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I3)) (@ (@ tptp.vEBT_VEBT_low X) N))) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))))) (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) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 Summary3) X_1))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 Summary3) X_1))) (not (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _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 Ma3) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary3 tptp.vEBT_VEBT) (M5 tptp.nat) (Deg2 tptp.nat) (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))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) Deg2) TreeList3) Summary3)) (=> (= A23 Deg2) (=> (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X2) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary3) 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I)))) (=> (=> _let_1 (forall ((X2 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X2) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X2) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (=> (@ (@ tptp.ord_less_nat Ma3) (@ _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 Ma3) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low Ma3) N3))) (forall ((X2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X2) N3) I) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I)) (@ (@ tptp.vEBT_VEBT_low X2) N3))) (and (@ (@ tptp.ord_less_nat Mi3) X2) (@ (@ tptp.ord_less_eq_nat X2) Ma3)))))))))))))))))))))))))))))) (forall ((P (-> tptp.nat Bool)) (N2 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 N2))))) (forall ((X4 tptp.option4927543243414619207at_nat)) (= (forall ((Y5 tptp.product_prod_nat_nat)) (not (= X4 (@ tptp.some_P7363390416028606310at_nat Y5)))) (= X4 tptp.none_P5556105721700978146at_nat))) (forall ((X4 tptp.option_num)) (= (forall ((Y5 tptp.num)) (not (= X4 (@ tptp.some_num Y5)))) (= X4 tptp.none_num))) (forall ((X4 tptp.option4927543243414619207at_nat)) (= (not (= X4 tptp.none_P5556105721700978146at_nat)) (exists ((Y5 tptp.product_prod_nat_nat)) (= X4 (@ tptp.some_P7363390416028606310at_nat Y5))))) (forall ((X4 tptp.option_num)) (= (not (= X4 tptp.none_num)) (exists ((Y5 tptp.num)) (= X4 (@ tptp.some_num Y5))))) (@ _let_378 _let_50) (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 ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.divide_divide_int K) L) tptp.zero_zero_int)))) (forall ((X21 Bool) (X222 Bool) (Y21 Bool) (Y22 Bool)) (= (= (@ (@ tptp.vEBT_Leaf X21) X222) (@ (@ tptp.vEBT_Leaf Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N2) (not (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)) (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))) (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))) (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (=> (= (@ (@ tptp.modulo_modulo_int A2) N2) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ tptp.divide_divide_int B3) N2))))))) (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 ((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 ((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 ((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 ((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 ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N2)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N2) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N2))))) (forall ((X4 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X4) K)) X4)))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L) K) (=> (@ _let_1 L) (@ _let_1 (@ (@ tptp.divide_divide_int K) L)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L)) (or (= K tptp.zero_zero_int) (= L tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))))) (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 ((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 ((Uu Bool) (Uv Bool) (Uw tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.vEBT_Leaf Uu) Uv)) Uw))) (forall ((N2 tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N2) tptp.zero_z5237406670263579293d_enat))) (forall ((N2 tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N2)) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N2) tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) (@ tptp.suc N2)) A))))) (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) _let_377) (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X5) (= (@ (@ tptp.power_power_real X5) N2) A) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y4) (= (@ (@ tptp.power_power_real Y4) N2) A)) (= Y4 X5)))))))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) N2) A)))))) (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int))) (= (@ tptp.vEBT_vebt_buildup _let_230) _let_377) (forall ((A Bool) (B Bool) (X4 tptp.nat)) (let ((_let_1 (= X4 tptp.one_one_nat))) (let ((_let_2 (= X4 tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X4) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) N3)) Y))))) (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))) (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))) (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))) (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))) (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))) (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))) (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))) (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))) (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X6 tptp.option4927543243414619207at_nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X)))))) (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X6 tptp.option_num)) (@ P3 X6))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X tptp.num)) (@ P4 (@ tptp.some_num X)))))) (forall ((X4 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= X4 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X4) Y)))) _let_1))))) (forall ((X4 tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.num)) (=> (= X4 (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X4) Y)))) _let_1))))) (forall ((X4 tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.product_prod_nat_nat)) (=> (= X4 (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X4) Y)))) _let_1))))) (forall ((X4 tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X4) Y))) (=> (=> (= X4 tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= X4 (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X4) Y)))) _let_1))))) (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) _let_230) (= (@ tptp.size_size_option_num tptp.none_num) _let_230) (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 ((Q3 tptp.nat) (R3 tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q3) R3)) (= R3 tptp.zero_zero_nat))) (forall ((Q3 tptp.int) (R3 tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q3) R3)) (= R3 tptp.zero_zero_int))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (=> (forall ((M5 tptp.nat)) (@ (@ P M5) tptp.zero_zero_nat)) (=> (forall ((M5 tptp.nat) (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) N2)))) (forall ((X4 (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X4) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X4 X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((X4 (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X4) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X4 X22)) (@ tptp.suc tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))) (forall ((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 ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))) (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 ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((U tptp.real) (X4 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 X4) Y)) (=> (@ _let_2 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((U tptp.rat) (X4 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 X4) Y)) (=> (@ _let_2 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)) (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N2) N2)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= M N2) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N2) K)) (or (= M N2) (= K tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N2) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N2)) (and (= M tptp.one_one_nat) (= N2 tptp.one_one_nat)))) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.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.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((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.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))) (forall ((A tptp.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.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N2)) (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))) (forall ((V tptp.num) (W tptp.num) (Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat W)) Z)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ (@ tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))) (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N2) (@ tptp.bit0 N2))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))) (forall ((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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N2) _let_1) (and (= M _let_1) (= N2 _let_1))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (= M _let_1) (= N2 _let_1))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))) (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((X4 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X4) X4))) (= X4 tptp.zero_zero_real))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N2))))) (forall ((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))) _let_376 _let_375 _let_374 (= (@ 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 ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N2)))))))) (forall ((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) _let_373 (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))) (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.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((C tptp.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.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((C tptp.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.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))) (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))) (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))) (forall ((C tptp.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.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))) (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))) (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (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.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((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 ((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.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) A))) (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 ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((C tptp.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.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))) (forall ((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 ((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.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) 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)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))) (forall ((C tptp.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.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger A) B)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_z3403309356797280102nteger))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger A) B)))))))) (forall ((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.extended_enat) (B tptp.extended_enat) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat V))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat A) B)) _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat A) _let_1)) (@ (@ tptp.times_7803423173614009249d_enat B) _let_1))))) (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))) (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))) (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))) (forall ((V tptp.num) (B tptp.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.extended_enat) (C tptp.extended_enat)) (let ((_let_1 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat V)))) (= (@ _let_1 (@ (@ tptp.plus_p3455044024723400733d_enat B) C)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((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.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.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))) (forall ((A tptp.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.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))) (forall ((A tptp.code_integer) (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) (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.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) (@ (@ tptp.times_times_complex C) A))) (@ _let_1 B)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))) (forall ((A tptp.code_integer) (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.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.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex C) A)) B)) (@ _let_1 B)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))) (forall ((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) (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 ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))) (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))) (forall ((A tptp.nat) (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 ((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 ((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 ((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 ((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.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((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 ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) M)) N2) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N2)) N2) M))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N2) (@ tptp.zero_n2687167440665602831ol_nat (not (= N2 _let_1)))))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N2)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N2) K)))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((K tptp.nat) (N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N2)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((N2 tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) K)) M))) N2) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N2))) (forall ((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_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.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.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((B tptp.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 ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))) (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))) (forall ((A tptp.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 ((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 ((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 ((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) (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.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))) (forall ((A tptp.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 ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.plus_p5714425477246183910nteger C) (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((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 ((A tptp.complex) (M tptp.num) (N2 tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.real) (M tptp.num) (N2 tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N2))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))) B)))) (forall ((A tptp.complex) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.real) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.nat) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((A tptp.int) (M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N2))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N2)))))) (forall ((K tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) _let_1) tptp.one_one_nat)))) (forall ((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) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) K)))) (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L) (= (@ (@ tptp.modulo_modulo_int K) L) K)))) (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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N2))) (@ _let_1 N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N2)) (not (@ _let_1 N2))))) (forall ((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 ((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 ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)) (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)) (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N2)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N2) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))) (forall ((A tptp.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.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))))) (forall ((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) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))) (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.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 ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n356916108424825756nteger (= N2 tptp.zero_zero_nat)))) (forall ((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 ((Z tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N2) (@ (@ tptp.ord_less_eq_int Z) N2)))) (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)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N2) K)) (and (=> (= K tptp.zero_zero_int) (@ P N2)) (=> (@ (@ 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) (= N2 (@ (@ 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) (= N2 (@ (@ 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) (Q4 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) Q4)) R4)) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q4)))))) (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)))))) (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 ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.modulo_modulo_int A) B) R3))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N2) tptp.one_one_int) (and (= M tptp.one_one_int) (= N2 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 ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L)) (or (@ (@ tptp.dvd_dvd_int L) K) (and (= L tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))))) (forall ((B tptp.int) (Q3 tptp.int) (R3 tptp.int) (B4 tptp.int) (Q4 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) Q4)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R4) B4) (=> (@ _let_1 R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q3) Q4)))))))))) (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 ((B tptp.int) (Q3 tptp.int) (R3 tptp.int) (B4 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q4)) R4))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R3) 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 Q4) Q3))))))))) (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) (Q4 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R4)) (@ (@ tptp.plus_plus_int (@ _let_1 Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R4) (=> (@ (@ tptp.ord_less_int R4) B) (=> (@ (@ tptp.ord_less_int R3) B) (@ (@ tptp.ord_less_eq_int Q4) Q3))))))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L)) tptp.zero_zero_int))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L)))) (forall ((B tptp.int) (Q4 tptp.int) (R4 tptp.int) (Q3 tptp.int) (R3 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 Q4)) R4)) (@ (@ tptp.plus_plus_int (@ _let_2 Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ _let_1 R3) (=> (@ _let_1 R4) (@ (@ tptp.ord_less_eq_int Q3) Q4)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L) _let_1))))) (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 ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_int M) N2) (=> (@ (@ tptp.dvd_dvd_int N2) M) (= M N2))))))) (forall ((A tptp.int) (X4 tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X4) (= A X4) (@ (@ tptp.ord_less_eq_int X4) A))) _let_372 (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q2 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q2))))) (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q5))))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L)) L))) (forall ((L tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N2) (not (@ (@ tptp.dvd_dvd_int N2) M))))) _let_371 (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N2) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N2 tptp.zero_z5237406670263579293d_enat)))) (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)) (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 ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))) (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))) (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (=> (@ (@ tptp.dvd_dvd_nat N2) M) (= M N2)))) (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X4 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 X4) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X4) (@ (@ 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 ((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 ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K2 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K2))))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (not (forall ((K2 tptp.complex)) (not (= A (@ (@ tptp.times_times_complex B) K2))))))) (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K2 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K2))))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K2 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K2))))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K2 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K2))))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))) (forall ((A tptp.complex) (B tptp.complex) (K tptp.complex)) (=> (= A (@ (@ tptp.times_times_complex B) K)) (@ (@ tptp.dvd_dvd_complex B) A))) (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))) (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))) (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))) _let_370 _let_369 _let_368 _let_367 _let_366 (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n1201886186963655149omplex (and P Q)) (@ (@ tptp.times_times_complex (@ tptp.zero_n1201886186963655149omplex P)) (@ tptp.zero_n1201886186963655149omplex Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))) (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))) (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))) (forall ((A tptp.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 ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P2) (@ tptp.zero_n2687167440665602831ol_nat Q3)) (= P2 Q3))) (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P2) (@ tptp.zero_n2684676970156552555ol_int Q3)) (= P2 Q3))) (forall ((P2 Bool) (Q3 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P2) (@ tptp.zero_n356916108424825756nteger Q3)) (= P2 Q3))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex A) C))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex A) B))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex A) B) (=> (@ (@ tptp.dvd_dvd_complex C) D) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) D))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))) (= tptp.times_times_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.times_times_complex B2) A3))) (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real 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.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) B)) C) (@ (@ tptp.dvd_dvd_complex B) C))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) (@ (@ tptp.times_times_complex B) A))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))) (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))) (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))) (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (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 ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C3 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C3)))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C3 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C3)))))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C3 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C3)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))) (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))) (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.dvd_dvd_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N2))))) (= 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)))) _let_365 (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 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 ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))) (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))) (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))) (forall ((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 ((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.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))) (forall ((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 ((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.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) N2)))) (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) N2)))) (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)))) (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)))) (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)))) (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.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.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))))) (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.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))) (forall ((A tptp.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.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))) (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))) (forall ((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.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.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 ((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.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.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 ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)) (forall ((A tptp.rat) (E2 tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E2)) C))) (forall ((A tptp.complex) (E2 tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) C)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) E2)) C))) (forall ((A tptp.real) (E2 tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E2)) C))) (forall ((A tptp.nat) (E2 tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E2)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E2)) C))) (forall ((A tptp.int) (E2 tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E2)) 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.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N2)))))) (forall ((K tptp.int) (M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N2)))))) (forall ((K tptp.code_integer) (M tptp.code_integer) (N2 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N2)))))) (forall ((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.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))) (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) W)) (@ (@ tptp.times_times_real Y) Z)))) (forall ((X4 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) W)) (@ (@ tptp.times_times_complex Y) Z)))) (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) W)))) (forall ((X4 tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex Y) W)))) (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) N2))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) N2))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X4) N2))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))) (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X4) N2))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X4) Y) (@ _let_2 X4)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N2)) (@ (@ tptp.power_power_complex B) N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2)))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N2)))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_real (@ _let_1 M)) N2)))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_int (@ _let_1 M)) N2)))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N2)))) (forall ((X4 tptp.produc3368934014287244435at_num)) (not (forall ((F2 (-> tptp.nat tptp.num tptp.num)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.num)) (not (= X4 (@ (@ tptp.produc851828971589881931at_num F2) (@ (@ tptp.produc1195630363706982562at_num A5) (@ (@ tptp.product_Pair_nat_num B5) Acc)))))))) (forall ((X4 tptp.produc4471711990508489141at_nat)) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat) (Acc tptp.nat)) (not (= X4 (@ (@ tptp.produc3209952032786966637at_nat F2) (@ (@ tptp.produc487386426758144856at_nat A5) (@ (@ tptp.product_Pair_nat_nat B5) Acc)))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N2)) (or (= K tptp.zero_zero_nat) (= M N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I2)) (@ _let_1 J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) L))))) (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))) (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 ((I2 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I2) J)) U)) K))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat N2) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N2) N2)) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N2) Q3)) (@ (@ tptp.divide_divide_nat (@ _let_1 N2)) Q3)))) (forall ((A2 tptp.int) (N2 tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N2)) N2)) (@ (@ tptp.modulo_modulo_int A2) N2)))) (forall ((P (-> tptp.int Bool)) (N2 tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N2) 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) (= N2 (@ (@ 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ P I3))))))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R3) (= (@ (@ tptp.divide_divide_int A) B) Q3))))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q3)) R3)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (= (@ (@ tptp.divide_divide_int A) B) Q3))))) (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))) (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N2) K)) (@ (@ tptp.modulo_modulo_int N2) 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) (= N2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I3)) J3))) (@ (@ P I3) J3)))))) (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 ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ (@ tptp.dvd_dvd_nat M) N2) (@ _let_1 M))))) (forall ((M tptp.extended_enat) (N2 tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N2)) (and (@ _let_1 M) (@ _let_1 N2))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))) (forall ((A tptp.nat) (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) (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.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))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N2) M)) M) (= N2 tptp.one_one_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N2)) M) (= N2 tptp.one_one_nat)))) (forall ((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 ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))) (forall ((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)) (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 ((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))))) (= tptp.zero_n1201886186963655149omplex (lambda ((P5 Bool)) (@ (@ (@ tptp.if_complex P5) tptp.one_one_complex) tptp.zero_zero_complex))) (= tptp.zero_n3304061248610475627l_real (lambda ((P5 Bool)) (@ (@ (@ tptp.if_real P5) tptp.one_one_real) tptp.zero_zero_real))) (= tptp.zero_n2052037380579107095ol_rat (lambda ((P5 Bool)) (@ (@ (@ tptp.if_rat P5) tptp.one_one_rat) tptp.zero_zero_rat))) _let_364 _let_363 (= tptp.zero_n356916108424825756nteger (lambda ((P5 Bool)) (@ (@ (@ tptp.if_Code_integer P5) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)) (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)) (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)) (forall ((B tptp.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 ((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.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))) (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))) (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))) (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))) (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))) (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))) (forall ((B tptp.nat) (A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N2)) (@ (@ tptp.power_power_nat B) N2))))) (forall ((B tptp.int) (A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N2) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (forall ((B tptp.code_integer) (A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N2) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))) (forall ((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 ((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 ((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))))) (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)) (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) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.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)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))) (forall ((A tptp.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)))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))) (forall ((A tptp.real) (B tptp.real)) (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) (=> (@ (@ 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 (@ (@ 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)) (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((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)) (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 ((X4 tptp.code_integer) (Y tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X4) N2)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))) (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) M))))) (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) M))))) (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) M))))) (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X4) Y) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) M))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))) (forall ((A tptp.nat) (N2 tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))) (forall ((A tptp.real) (N2 tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))) (forall ((A tptp.int) (N2 tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))) (forall ((A tptp.complex) (N2 tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N2)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N2))))) (forall ((M tptp.real) (N2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_real M) N2)))))) (forall ((M tptp.rat) (N2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_rat M) N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.times_times_int M) N2)))))) (forall ((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 ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))) (forall ((C tptp.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.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))) (forall ((C tptp.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.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))) (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))) (forall ((C tptp.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.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))) (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))) (forall ((A tptp.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 ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((B tptp.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 ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))) (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X4) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X4) Z) (@ (@ tptp.times_times_rat W) Y)))))) (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X4) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X4) Z) (@ (@ tptp.times_times_real W) Y)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X4) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X4) Z) (@ (@ tptp.times_times_complex W) Y)))))) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat A) (@ tptp.numera1916890842035813515d_enat tptp.one)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)) (forall ((A tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat tptp.one)) A) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (not (@ (@ tptp.dvd_dvd_nat N2) M))))) (forall ((A tptp.nat) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L)))))) (forall ((A tptp.int) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L)))))) (forall ((A tptp.code_integer) (K tptp.num) (L tptp.num)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ tptp.numera6620942414471956472nteger K))) (@ tptp.numera6620942414471956472nteger L)) (@ _let_1 (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num K) L)))))) (forall ((X4 tptp.rat) (Y tptp.rat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X4) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_rat Y) N2)) tptp.one_one_rat))) (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X4) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)) tptp.one_one_complex))) (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X4) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)) tptp.one_one_real))) (forall ((X4 tptp.nat) (Y tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X4) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X4) N2)) (@ (@ tptp.power_power_nat Y) N2)) tptp.one_one_nat))) (forall ((X4 tptp.int) (Y tptp.int) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_int X4) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)) tptp.one_one_int))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ _let_1 N2))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ _let_1 N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ _let_1 N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ _let_1 N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) A)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) A)))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) A)))) (forall ((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 ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2)))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_nat M) N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N2)) (= M N2))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I2)) (@ _let_1 J)))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I2) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N2) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N2)) (or (= N2 tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I2) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N2)) I2))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2)) M)) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2))) M)) (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q2 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q2))))) (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X4) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (= (@ (@ tptp.plus_plus_nat X4) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))) (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 ((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 ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) Deg3))))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N2))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N2))) _let_2))))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.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) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N2)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N2)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N2 tptp.zero_zero_nat)))) (forall ((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) (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_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) (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)) (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) (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 ((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)) (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 ((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 ((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_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 ((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 ((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) (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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X4)) X4)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X4)) X4)))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X4)) X4)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Y)) X4)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Y)) X4)))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Y)) X4)))))) (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 ((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 ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X4 tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X4 tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X4 tptp.zero_zero_int) (= Y tptp.zero_zero_int)))) (forall ((X4 tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))) (forall ((X4 tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))) (forall ((X4 tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X4 tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X4 tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X4 tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))) (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 ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))) (forall ((B tptp.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 ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X4) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X4) Y))))) (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X4) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X4) Y))))) (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X4) Y)) Z)))) (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X4) Y)) Z)))) (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 ((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) (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) (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) (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) (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) (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) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))) (forall ((A tptp.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 ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))) (forall ((B tptp.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 ((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 ((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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((B tptp.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 ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))) (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) Y)) Z)))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) Y)) Z)))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X4) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.real) (Z tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X4) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.times_times_rat Z) Y))) Y)))) (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X4) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real Z) Y))) Y)))) (forall ((Y tptp.complex) (X4 tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.times_times_complex Z) Y))) Y)))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) 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.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))) (forall ((Z tptp.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 ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N2)))))) (forall ((A tptp.rat) (N2 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) N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N2)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_nat K) N2)))) (forall ((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 ((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 ((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.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)) (= 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) (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 ((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)) (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 ((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 ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat M) N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat N2) M))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N2)) (not (@ (@ tptp.dvd_dvd_nat N2) M)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q3)) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N2) Q3))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.divide_divide_nat M) N2))))) (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat Q3) S3))))))))) (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (not (forall ((S3 tptp.nat)) (not (= N2 (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q3) S3))))))))) (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X4) N2) (@ (@ tptp.modulo_modulo_nat Y) N2)) (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (exists ((Q2 tptp.nat)) (= X4 (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N2) Q2))))))) (forall ((A2 tptp.nat) (N2 tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N2)) N2)) (@ (@ tptp.modulo_modulo_nat A2) N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N2))) (= (@ _let_1 (@ _let_2 Q3)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N2)) Q3))) (@ _let_1 N2)))))) (@ _let_362 tptp.zero_z3403309356797280102nteger) (@ _let_361 tptp.zero_zero_nat) (@ _let_360 tptp.zero_zero_int) (not (@ _let_362 tptp.one_one_Code_integer)) (not (@ _let_361 tptp.one_one_nat)) (not (@ _let_360 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)))))) (= (lambda ((Y6 tptp.nat) (Z4 tptp.nat)) (= Y6 Z4)) (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 ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (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))))))) (= (lambda ((Y6 tptp.code_integer) (Z4 tptp.code_integer)) (= Y6 Z4)) (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))))))) (forall ((X4 tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X4))) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_Code_integer X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((X4 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X4))) (=> (not (= X4 tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_nat X4) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((X4 tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (=> (not (= X4 tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N2)) (or (@ (@ tptp.dvd_dvd_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((N2 tptp.nat) (X4 tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X4) (@ (@ tptp.power_8256067586552552935nteger X4) N2)))) (forall ((N2 tptp.nat) (X4 tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X4) (@ (@ tptp.power_power_rat X4) N2)))) (forall ((N2 tptp.nat) (X4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X4) (@ (@ tptp.power_power_nat X4) N2)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X4) (@ (@ tptp.power_power_real X4) N2)))) (forall ((N2 tptp.nat) (X4 tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X4) (@ (@ tptp.power_power_int X4) N2)))) (forall ((N2 tptp.nat) (X4 tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= X4 tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X4) (@ (@ tptp.power_power_complex X4) N2)))) (forall ((X4 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) X4)) Y)))) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 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) X4)) Y)))) (@ (@ tptp.ord_less_eq_rat X4) 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) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X4) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X4) Y))))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X4) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X4) Y))))) (forall ((Y tptp.real) (X4 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X4) Y)) Z)))) (forall ((Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X4) 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 ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_rat V) Y))) A)))))))) (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_int V) Y))) A)))))))) (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 ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((B tptp.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 ((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 ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (=> (@ (@ 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) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))) (forall ((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.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))) (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat Z) (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))) (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))) (forall ((Z tptp.extended_enat)) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_p3455044024723400733d_enat Z) Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X4) X4)) X4)) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X4) X4)) X4)) X4))) (forall ((X4 tptp.nat)) (= (@ (@ tptp.power_power_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X4) X4)) X4)) X4))) (forall ((X4 tptp.int)) (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X4) X4)) X4)) X4))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N2))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_nat (@ _let_2 N2)) _let_1))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_real (@ _let_2 N2)) _let_1))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_int (@ _let_2 N2)) _let_1))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N2)) (@ (@ tptp.power_power_complex (@ _let_2 N2)) _let_1))))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I2))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I2) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))) (forall ((N2 tptp.nat) (Q3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q3)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q3))) (= (@ (@ tptp.divide_divide_nat M) N2) Q3))))) (forall ((Q3 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q3) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N2) Q3)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q3)) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.divide_divide_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N2)) N2))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P I3))))))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (= N2 tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N2)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I3 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N2) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) I3)) J3)) (@ P J3))))))))) (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X5)))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (Ux2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)) Ux2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3)) X5)))))))) (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 ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat B) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_real V) Y))) A)))))))) (forall ((X4 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 X4) 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) X4)) (@ (@ tptp.times_times_rat V) Y))) A)))))))) (forall ((X4 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 X4) 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) X4)) (@ (@ 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 ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((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 ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.ord_less_eq_nat M) N2))))) (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) _let_2))))) (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N2 tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N2)) (or (and (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N2))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q5)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N2))) M) tptp.one_one_nat))) (forall ((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 ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N2)))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.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))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (@ _let_1 A))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))) (forall ((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 ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y)))))) (forall ((X4 tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_8040749407984259932d_enat (@ (@ tptp.plus_p3455044024723400733d_enat X4) Y)) _let_2) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.power_8040749407984259932d_enat X4) _let_2)) (@ (@ tptp.power_8040749407984259932d_enat Y) _let_2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat _let_1)) X4)) Y)))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y)))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y)))))) (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X4) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X4) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X4)) Y))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y)))))) (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((A tptp.rat) (N2 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))) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((P (-> tptp.nat Bool)) (N2 tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((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 N2))))) (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.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.rat) (N2 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))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N2)) (or (= N2 tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))) (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((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 ((X4 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)) X4)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))) (forall ((X4 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)) X4)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))) (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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))) (forall ((A tptp.rat) (N2 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))) N2)))) (@ _let_1 A)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ _let_1 A)))) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_real))) (forall ((A tptp.rat) (N2 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))) N2)))) tptp.zero_zero_rat))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) tptp.zero_zero_int))) (forall ((X4 tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (Uw2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) Uw2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT) (Uz2 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)) Uz2)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2)) X5)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc)) X5)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X5 tptp.nat)) (not (= X4 (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd)) X5)))))))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N2)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (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) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))) (forall ((M tptp.code_integer) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))) (forall ((M tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))) (forall ((M tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X4))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))) (forall ((X4 (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X4) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))) (forall ((X4 (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X4) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))) (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 ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N2) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))) (forall ((X4 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 X4) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X4) (@ _let_2 Y)) (= X4 Y)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger tptp.zero_zero_nat) A) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))) (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))) (forall ((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 ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.plus_plus_int X2) (@ (@ tptp.times_times_int K) D))))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))))))) (forall ((P (-> tptp.code_integer Bool)) (L tptp.code_integer)) (= (exists ((X tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L) X))) (exists ((X tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L) (@ (@ tptp.plus_p5714425477246183910nteger X) tptp.zero_z3403309356797280102nteger)) (@ P X))))) (forall ((P (-> tptp.rat Bool)) (L tptp.rat)) (= (exists ((X tptp.rat)) (@ P (@ (@ tptp.times_times_rat L) X))) (exists ((X tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L) (@ (@ tptp.plus_plus_rat X) tptp.zero_zero_rat)) (@ P X))))) (forall ((P (-> tptp.complex Bool)) (L tptp.complex)) (= (exists ((X tptp.complex)) (@ P (@ (@ tptp.times_times_complex L) X))) (exists ((X tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L) (@ (@ tptp.plus_plus_complex X) tptp.zero_zero_complex)) (@ P X))))) (forall ((P (-> tptp.real Bool)) (L tptp.real)) (= (exists ((X tptp.real)) (@ P (@ (@ tptp.times_times_real L) X))) (exists ((X tptp.real)) (and (@ (@ tptp.dvd_dvd_real L) (@ (@ tptp.plus_plus_real X) tptp.zero_zero_real)) (@ P X))))) (forall ((P (-> tptp.nat Bool)) (L tptp.nat)) (= (exists ((X tptp.nat)) (@ P (@ (@ tptp.times_times_nat L) X))) (exists ((X tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L) (@ (@ tptp.plus_plus_nat X) tptp.zero_zero_nat)) (@ P X))))) (forall ((P (-> tptp.int Bool)) (L tptp.int)) (= (exists ((X tptp.int)) (@ P (@ (@ tptp.times_times_int L) X))) (exists ((X tptp.int)) (and (@ (@ tptp.dvd_dvd_int L) (@ (@ tptp.plus_plus_int X) tptp.zero_zero_int)) (@ P X))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N2) K)) K)) (forall ((K tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N2) K))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (@ (@ tptp.ord_less_real T2) X2)))))) (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (@ (@ tptp.ord_less_rat T2) X2)))))) (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (@ (@ tptp.ord_less_num T2) X2)))))) (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (@ (@ tptp.ord_less_nat T2) X2)))))) (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (@ (@ tptp.ord_less_int T2) X2)))))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X2))) (=> (@ _let_1 Z2) (@ _let_1 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(@ P6 X5))))) (=> (exists ((Z3 tptp.num)) (forall ((X5 tptp.num)) (=> (@ (@ tptp.ord_less_num Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))) (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.nat)) (forall ((X5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))) (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ Q X5) (@ Q6 X5))))) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (= (and (@ P X2) (@ Q X2)) (and (@ P6 X2) (@ Q6 X2))))))))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (not (@ (@ tptp.ord_less_eq_real T2) X2)))))) (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (not (@ (@ tptp.ord_less_eq_rat T2) X2)))))) (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (not (@ (@ tptp.ord_less_eq_num T2) X2)))))) (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (not (@ (@ tptp.ord_less_eq_nat T2) X2)))))) (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (not (@ (@ tptp.ord_less_eq_int T2) X2)))))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real X2) Z2) (@ (@ tptp.ord_less_eq_real X2) T2))))) (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X2) Z2) (@ (@ tptp.ord_less_eq_rat X2) T2))))) (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num X2) Z2) (@ (@ tptp.ord_less_eq_num X2) T2))))) (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X2) Z2) (@ (@ tptp.ord_less_eq_nat X2) T2))))) (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int X2) Z2) (@ (@ tptp.ord_less_eq_int X2) T2))))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (@ (@ tptp.ord_less_eq_real T2) X2))))) (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (@ (@ tptp.ord_less_eq_rat T2) X2))))) (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (@ (@ tptp.ord_less_eq_num T2) X2))))) (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (@ (@ tptp.ord_less_eq_nat T2) X2))))) (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (@ (@ tptp.ord_less_eq_int T2) X2))))) (forall ((T2 tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z2) X2) (not (@ (@ tptp.ord_less_eq_real X2) T2)))))) (forall ((T2 tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z2) X2) (not (@ (@ tptp.ord_less_eq_rat X2) T2)))))) (forall ((T2 tptp.num)) (exists ((Z2 tptp.num)) (forall ((X2 tptp.num)) (=> (@ (@ tptp.ord_less_num Z2) X2) (not (@ (@ tptp.ord_less_eq_num X2) T2)))))) (forall ((T2 tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z2) X2) (not (@ (@ tptp.ord_less_eq_nat X2) T2)))))) (forall ((T2 tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (=> (@ (@ tptp.ord_less_int Z2) X2) (not (@ (@ tptp.ord_less_eq_int X2) T2)))))) (forall ((X4 tptp.nat)) (=> (not (= X4 tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X4 (@ tptp.suc N3))))))) (forall ((X4 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X4 X7) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X4) P) (=> _let_2 P6))))))) (forall ((X4 tptp.int) (X7 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X7))) (=> (= X4 X7) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X4) P) (and _let_2 P6))))))) (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 ((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 ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S))))) (=> (@ (@ tptp.ord_less_real X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S))))) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S))))) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S))))) (=> (@ (@ tptp.ord_less_int X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S)))) (=> (@ (@ tptp.ord_less_rat X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int X2) Z2) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S))))) (=> (@ (@ tptp.ord_less_real Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S))))) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S))))) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S))))) (=> (@ (@ tptp.ord_less_int Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z2 tptp.code_integer)) (forall ((X2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X2) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.real) (S tptp.real)) (exists ((Z2 tptp.real)) (forall ((X2 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X2) S)))) (=> (@ (@ tptp.ord_less_real Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z2 tptp.rat)) (forall ((X2 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X2) S)))) (=> (@ (@ tptp.ord_less_rat Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z2 tptp.nat)) (forall ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X2) S)))) (=> (@ (@ tptp.ord_less_nat Z2) X2) (= _let_1 _let_1)))))) (forall ((D tptp.int) (S tptp.int)) (exists ((Z2 tptp.int)) (forall ((X2 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X2) S)))) (=> (@ (@ tptp.ord_less_int Z2) X2) (= _let_1 _let_1)))))) (forall ((Xs tptp.list_list_VEBT_VEBT) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X5) (@ tptp.set_list_VEBT_VEBT2 Xs)) (= (@ tptp.size_s6755466524823107622T_VEBT X5) N2))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ tptp.concat_VEBT_VEBT Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s8217280938318005548T_VEBT Xs)) N2)))) (forall ((Xs tptp.list_list_o) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_o)) (=> (@ (@ tptp.member_list_o X5) (@ tptp.set_list_o2 Xs)) (= (@ tptp.size_size_list_o X5) N2))) (= (@ tptp.size_size_list_o (@ tptp.concat_o Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s2710708370519433104list_o Xs)) N2)))) (forall ((Xs tptp.list_list_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X5) (@ tptp.set_list_nat2 Xs)) (= (@ tptp.size_size_list_nat X5) N2))) (= (@ tptp.size_size_list_nat (@ tptp.concat_nat Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s3023201423986296836st_nat Xs)) N2)))) (forall ((Xs tptp.list_list_int) (N2 tptp.nat)) (=> (forall ((X5 tptp.list_int)) (=> (@ (@ tptp.member_list_int X5) (@ tptp.set_list_int2 Xs)) (= (@ tptp.size_size_list_int X5) N2))) (= (@ tptp.size_size_list_int (@ tptp.concat_int Xs)) (@ (@ tptp.times_times_nat (@ tptp.size_s533118279054570080st_int Xs)) N2)))) (forall ((Z tptp.real) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))) (forall ((Z tptp.rat) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))))) (forall ((Z tptp.int) (X4 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 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X4) Y))))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X4) Y)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X4) Y)))) (forall ((Z tptp.int) (X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X4) Y)))) (forall ((N2 tptp.nat) (Xs tptp.list_num) (Ys tptp.list_num)) (let ((_let_1 (@ tptp.size_size_list_num Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_num Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6456567536196504476um_num (@ (@ tptp.product_num_num Xs) Ys)) N2) (@ (@ tptp.product_Pair_num_num (@ (@ tptp.nth_num Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_num Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_Code_integer) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s3445333598471063425nteger Xs)) _let_1)) (= (@ (@ tptp.nth_Pr8522763379788166057eger_o (@ (@ tptp.produc3607205314601156340eger_o Xs) Ys)) N2) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.nth_Code_integer Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N2) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N2) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N2) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) N2) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) N2) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) (forall ((N2 tptp.nat) (Xs tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys)) N2) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N2) _let_1))))))) _let_359 (forall ((B tptp.int) (A tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q3))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R3)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R3)))))))))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys)))) (forall ((Xs tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))) (forall ((Xs tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N2)) _let_1)))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R4)) (= R3 R4))))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int) (Q4 tptp.int) (R4 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R4)) (= Q3 Q4))))) (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) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (= (@ (@ tptp.divide_divide_int K) L) Q3))) (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (= (@ (@ tptp.modulo_modulo_int K) L) R3))) (forall ((L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q3) L)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int))))) (forall ((K tptp.int) (L tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L)) (@ (@ tptp.modulo_modulo_int K) L)))) (forall ((K tptp.int) (L tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L))) (= (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L) Q3)) R3)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (@ (@ tptp.ord_less_int R3) L))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int R3) tptp.zero_zero_int))) (=> (not _let_2) (= Q3 tptp.zero_zero_int)))))))))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X4) Y)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X4) Y)))) (forall ((Z tptp.int) (X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X4) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X4) Y)))) (forall ((Q3 tptp.int) (R3 tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q3) R3)) (@ (@ tptp.plus_plus_int Q3) (@ tptp.zero_n2684676970156552555ol_int (not (= R3 tptp.zero_zero_int)))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N2)) K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N2) (@ (@ tptp.divide_divide_int K) _let_1)) L)))))) (forall ((B tptp.int) (A tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q3))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R3)) (@ (@ (@ 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 R3)) tptp.one_one_int)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))))))) (forall ((N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N2)) (@ tptp.nat_set_decode X4)) (@ (@ tptp.member_nat N2) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((X4 tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X4)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4)))) (forall ((R3 tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R3))) (=> (not (= R3 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 ((R3 tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R3))) (=> (not (= R3 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 ((R3 tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R3))) (=> (not (= R3 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 ((R3 tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R3))) (=> (not (= R3 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 ((R3 tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R3))) (=> (not (= R3 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 ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N2))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N2) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N2) M)))))))))))) (forall ((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.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.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.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.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.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)) (forall ((A tptp.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 ((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.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 ((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)) 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.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 ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N2)) K))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((I2 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat I2) N2) (= (@ _let_1 (@ _let_1 I2)) I2)))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L) L)) (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 (@ (@ 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))) (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))) (= (@ _let_342 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_344 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_341 tptp.one_one_rat) tptp.zero_zero_rat) (= (@ _let_343 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 ((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.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((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.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))) (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))) (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))) (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((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 ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N2) K) L)) (@ _let_1 L)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N2) K) L)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) I2) (@ (@ tptp.minus_minus_nat (@ tptp.suc J)) (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I2) (@ tptp.suc (@ (@ tptp.minus_minus_nat J) K))) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I2) K)) (@ tptp.suc J))))) (forall ((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 ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) N2))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))) (forall ((N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (or (@ (@ tptp.ord_less_nat M) N2) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N2)) tptp.one_one_Code_integer)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N2)) tptp.one_one_nat)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N2)) tptp.one_one_int)) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N2) _let_1)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((A tptp.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 ((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 ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I2))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((A tptp.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))))) (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) (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 ((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)))) (= (lambda ((Y6 tptp.complex) (Z4 tptp.complex)) (= Y6 Z4)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))) (= (lambda ((Y6 tptp.real) (Z4 tptp.real)) (= Y6 Z4)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))) (= (lambda ((Y6 tptp.rat) (Z4 tptp.rat)) (= Y6 Z4)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))) (= (lambda ((Y6 tptp.int) (Z4 tptp.int)) (= Y6 Z4)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))) (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.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 ((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)) (=> (@ (@ 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 ((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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((B tptp.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.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) C)) A) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex B) A)) (@ (@ tptp.times_times_complex C) A)))) (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))) (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))) (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))) (forall ((A tptp.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.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))) (forall ((A tptp.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 ((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) (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 ((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)) (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) (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)) (= (@ (@ 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)) (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 ((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))) (= (@ (@ 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 ((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 ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))) (forall ((X4 tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))) (forall ((X4 tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))) (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))) (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 ((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) (N2 tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N2) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N2) M) tptp.zero_zero_nat) (= M N2)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((A 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 ((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) (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)) (@ (@ 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 ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N2) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N2)) (@ _let_1 M))))))) (forall ((J tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N2)) K))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N2) K)) (= M N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_eq_nat M) N2)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N2) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ _let_1 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N2) L)))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) M)) (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))) (forall ((M tptp.nat) (N2 tptp.nat) (L tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) (@ _let_1 M))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)) (@ (@ tptp.minus_minus_nat M) N2)))) (forall ((M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) M)) N2) M)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) N2) M)) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N2)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N2) K)))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))))) (forall ((N2 tptp.nat) (K tptp.int) (M tptp.nat) (L tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N2) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L) R3)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 L)) R3)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (= 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))) (= 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 ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))) (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N2) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N2) K)) J)))))))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N2) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N2) K)) J)))))))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N2) K)) J)))))))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N2) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N2) K)) J)))))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))) (forall ((I2 tptp.real) (K tptp.real) (N2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I2) K)) N2) (@ (@ tptp.ord_less_eq_real I2) (@ (@ tptp.minus_minus_real N2) K)))) (forall ((I2 tptp.rat) (K tptp.rat) (N2 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I2) K)) N2) (@ (@ tptp.ord_less_eq_rat I2) (@ (@ tptp.minus_minus_rat N2) K)))) (forall ((I2 tptp.nat) (K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) N2) (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat N2) K)))) (forall ((I2 tptp.int) (K tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I2) K)) N2) (@ (@ tptp.ord_less_eq_int I2) (@ (@ tptp.minus_minus_int N2) K)))) (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))) (forall ((A tptp.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 ((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) (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 ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_rat X4) Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) X4)) (@ (@ tptp.times_times_complex Y) Y)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_complex X4) Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real X4) Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) Y)) (@ (@ tptp.minus_minus_int X4) Y)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))) (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) D)) (= C (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex B) A)) E2)) D)))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C) D))) (forall ((A tptp.complex) (E2 tptp.complex) (C tptp.complex) (B tptp.complex) (D tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) E2)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex B) E2)) D)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) E2)) C) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C) D))) (forall ((X4 tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (= (@ (@ 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 X4) A)) B))))) (forall ((X4 tptp.complex) (Y tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X4))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 Y)) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.plus_plus_complex (@ _let_1 (@ (@ tptp.minus_minus_complex Y) B))) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) A)) B))))) (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (= (@ (@ 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 X4) A)) B))))) (forall ((X4 tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (= (@ (@ 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 X4) 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 ((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 ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ tptp.suc M))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N2) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N2))) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N2) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N2)) M))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N2))))) (forall ((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 ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.ord_less_nat M) N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N2) (@ (@ tptp.plus_plus_nat N2) M)) tptp.zero_zero_nat)) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I2) K)) J))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat M) N2)) M))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.minus_minus_nat J) I2) K) (= J (@ (@ tptp.plus_plus_nat K) I2))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I2)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I2)))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I2) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I2) K)) J)))) (forall ((J tptp.nat) (K tptp.nat) (I2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I2) K)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N2)))) (forall ((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 ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (or (@ (@ tptp.ord_less_nat N2) M) (@ _let_1 N2))))) (forall ((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.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 M)))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ _let_1 N2)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))) (= tptp.modulo_modulo_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M6) N)) M6) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M6) N)) N)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.modulo_modulo_nat M) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N2))))))) (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))) (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))) (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))) (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))) (forall ((A tptp.rat) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))) (forall ((A tptp.int) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E2)) C)) D))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E2)) C)) D))) (forall ((A tptp.real) (E2 tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E2)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))) (forall ((A tptp.rat) (E2 tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E2)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E2)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E2)) D)))) (forall ((A tptp.int) (E2 tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E2)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E2)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E2)) D)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X4) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X4) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) Y)) Z)))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) Y)) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X4) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) Y)) Z)))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))) (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))) (forall ((Y tptp.complex) (Z tptp.complex) (X4 tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) 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 ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) X4)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X4) X4)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X4) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) X4)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))) (forall ((X4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X4) X4)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X4) tptp.one_one_int)))) (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X2) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2)))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat K4) D4))) T2)))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D4))) T2)))))))) (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D4))) T2)))))))) (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X2) T2))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D4))) T2)))))))) (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T2 tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X2 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X2) T2)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X2) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T2))))))) (forall ((D tptp.rat) (D4 tptp.rat) (T2 tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X2 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X2) (@ (@ tptp.times_times_rat K4) D4))) T2))))))) (forall ((D tptp.complex) (D4 tptp.complex) (T2 tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex D) D4) (forall ((X2 tptp.complex) (K4 tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex D))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.minus_minus_complex X2) (@ (@ tptp.times_times_complex K4) D4))) T2))))))) (forall ((D tptp.real) (D4 tptp.real) (T2 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X2 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X2) (@ (@ tptp.times_times_real K4) D4))) T2))))))) (forall ((D tptp.int) (D4 tptp.int) (T2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X2 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X2) T2)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K4) D4))) T2))))))) (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 ((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.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.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 ((N2 tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I2))) N2))) (forall ((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 ((D5 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D5)) (@ P D5)))))) (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 ((D5 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D5)) (not (@ P D5)))))))) (forall ((K tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) K)) I2) (@ (@ tptp.ord_less_nat J) (@ (@ tptp.plus_plus_nat I2) K))))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M) N2)))) (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D))))) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (exists ((X_1 tptp.int)) (@ P6 X_1)) (exists ((X_12 tptp.int)) (@ P X_12))))))) (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 ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P1 X5))))) (=> (exists ((X_1 tptp.int)) (@ P1 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 ((N2 tptp.nat) (M tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q3) (@ (@ tptp.modulo_modulo_nat N2) Q3)) (@ (@ tptp.dvd_dvd_nat Q3) (@ (@ tptp.minus_minus_nat M) N2))))) _let_358 (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))) (forall ((Y tptp.rat) (Z tptp.rat) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X4) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))) (forall ((Y tptp.real) (Z tptp.real) (X4 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 X4) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X4) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X4) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X4)) _let_1)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X4)) _let_1)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X4) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X4)) _let_1)))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X4) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X4)) _let_1)))) (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= N2 (@ tptp.suc (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N2) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (@ (@ tptp.ord_less_nat M) N2)) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M6) N) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))) (= tptp.plus_plus_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))) (forall ((J tptp.nat) (I2 tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I2) J)) U)) M)) N2)))) (forall ((I2 tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I2) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N2)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I2)) U)) N2))))) (= tptp.times_times_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)) N))))) (forall ((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 ((X2 tptp.int)) (=> (@ P X2) (@ P (@ (@ tptp.minus_minus_int X2) (@ (@ tptp.times_times_int K) D))))))))) (forall ((Q3 tptp.nat) (N2 tptp.nat) (R3 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R3) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q3))) (=> (@ _let_3 N2) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N2) Q3)) (@ _let_2 (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.minus_minus_nat _let_1) Q3)))))))))) (forall ((R3 tptp.nat) (N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R3) N2) (=> (@ (@ tptp.ord_less_eq_nat R3) M) (=> (@ (@ tptp.dvd_dvd_nat N2) (@ (@ tptp.minus_minus_nat M) R3)) (= (@ (@ tptp.modulo_modulo_nat M) N2) R3))))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.modulo_modulo_int K) L) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L)) L))))) (forall ((U tptp.real) (V tptp.real) (R3 tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_eq_real R3) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.minus_minus_real V) U))) S))) V))))) (forall ((U tptp.rat) (V tptp.rat) (R3 tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (=> (@ (@ tptp.ord_less_eq_rat R3) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R3) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N2) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) tptp.zero_zero_int))))) (forall ((A tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((A tptp.code_integer) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (let ((_let_2 (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 M)) (@ _let_1 N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N2) M))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M))))))))))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= tptp.power_power_rat (lambda ((P5 tptp.rat) (M6 tptp.nat)) (@ (@ (@ tptp.if_rat (= M6 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P5) (@ (@ tptp.power_power_rat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_complex (lambda ((P5 tptp.complex) (M6 tptp.nat)) (@ (@ (@ tptp.if_complex (= M6 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P5) (@ (@ tptp.power_power_complex P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_real (lambda ((P5 tptp.real) (M6 tptp.nat)) (@ (@ (@ tptp.if_real (= M6 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P5) (@ (@ tptp.power_power_real P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_nat (lambda ((P5 tptp.nat) (M6 tptp.nat)) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P5) (@ (@ tptp.power_power_nat P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (= tptp.power_power_int (lambda ((P5 tptp.int) (M6 tptp.nat)) (@ (@ (@ tptp.if_int (= M6 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P5) (@ (@ tptp.power_power_int P5) (@ (@ tptp.minus_minus_nat M6) tptp.one_one_nat)))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) A) (@ _let_1 N2))))) (forall ((K tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N2)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat M) N2) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N2)) N2)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))) (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))) (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L) (=> (@ (@ tptp.ord_less_eq_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L)) L)) tptp.one_one_int))))) (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 ((W tptp.rat) (Y tptp.rat) (X4 tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X4))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))) (forall ((W tptp.complex) (Y tptp.complex) (X4 tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex X4))) (let ((_let_2 (@ tptp.times_times_complex W))) (= (= (@ (@ tptp.plus_plus_complex (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_complex (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))) (forall ((W tptp.real) (Y tptp.real) (X4 tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X4))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))) (forall ((W tptp.nat) (Y tptp.nat) (X4 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X4))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))) (forall ((W tptp.int) (Y tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X4))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X4) (= Y Z)))))) (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.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex B))) (let ((_let_2 (@ tptp.times_times_complex A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_complex (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X4) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X4)) Y)))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X4) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) Y)))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) Y)))))) (forall ((X4 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 X4) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X4) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X4)) Y)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))) (forall ((M tptp.nat) (N2 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) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)))) _let_2)))))) (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 ((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 ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N2))) (@ (@ tptp.ord_less_eq_nat M) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) _let_3)) _let_2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N2))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N2)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N2) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N2))))))) (forall ((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 ((L tptp.num) (R3 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L) (@ (@ tptp.product_Pair_nat_nat Q3) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.int) (Q3 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L) (@ (@ tptp.product_Pair_int_int Q3) R3)))) (let ((_let_3 (@ tptp.numeral_numeral_int L))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R3))))))))) (forall ((L tptp.num) (R3 tptp.code_integer) (Q3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q3))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L) (@ (@ tptp.produc1086072967326762835nteger Q3) R3)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R3) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R3))))))))) (= tptp.bit_ri6519982836138164636nteger (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N 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 (= N tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))) (= tptp.bit_se1745604003318907178nteger (lambda ((N tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)) (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int 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 ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int 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 ((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 ((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 ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N2)) (= M N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N2)) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N2)) (= M N2))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ _let_1 Y)) Y))) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N2) tptp.zero_z5237406670263579293d_enat)) (forall ((N2 tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N2) tptp.zero_z5237406670263579293d_enat) N2)) (forall ((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))) (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int) (= (@ 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 ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))) (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int 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))) (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (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.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))) (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.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))) (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 ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))) (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))) (forall ((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) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= M N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= M N2))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))) (forall ((A tptp.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.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))) (forall ((A tptp.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.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))) (forall ((A tptp.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.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.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.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)) (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.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int 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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real Y)) (@ _let_1 Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X4))) (= (@ _let_1 (@ tptp.uminus_uminus_int Y)) (@ _let_1 Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X4))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X4))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X4))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X4)) Y) (@ (@ tptp.dvd_dvd_real X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X4)) Y) (@ (@ tptp.dvd_dvd_int X4) Y))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X4)) Y) (@ (@ tptp.dvd_dvd_complex X4) Y))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X4)) Y) (@ (@ tptp.dvd_dvd_Code_integer X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X4)) Y) (@ (@ tptp.dvd_dvd_rat X4) Y))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (not (= tptp.one (@ tptp.bit1 N2)))) (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X4) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X4 A))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) X4) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) A) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) A) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.zero_zero_nat) A) A)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.zero_zero_int) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.zero_zero_nat) A)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.zero_zero_int) A)) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.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.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.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.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.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.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.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.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ 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_let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (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.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))) (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))) (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))) (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))) (forall ((X4 tptp.real)) (= (@ (@ tptp.divide_divide_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X4))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.divide_divide_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X4))) (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))) (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N2)) (= tptp.zero_zero_nat N2))) (forall ((N2 tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= tptp.zero_zero_nat N2))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri4216267220026989637d_enat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera1916890842035813515d_enat N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N2)) (@ tptp.numera6690914467698888265omplex N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_real N2))) (forall ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((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 ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((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 ((N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N2) tptp.one_one_complex) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N2) tptp.one_one_rat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N2) tptp.one_one_real) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N2) tptp.one_one_int) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N2) tptp.one_one_nat) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N2)) (= N2 tptp.one_one_nat))) (forall ((N2 tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N2)) (= N2 tptp.one_one_nat))) (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex) (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat) (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real) _let_305 (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) tptp.one_one_int) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) tptp.one_one_nat) tptp.one_one_nat)) (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) tptp.one_one_int) tptp.one_one_int)) (forall ((L tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) tptp.one_one_nat) tptp.one_one_nat)) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X4) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X4) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X4) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X4) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X4 (@ (@ tptp.power_power_nat B) W)))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X4)) (= (@ (@ tptp.power_power_nat B) W) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X4)) (= (@ (@ tptp.power_power_nat B) W) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X4)) (= (@ (@ tptp.power_power_nat B) W) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X4)) (= (@ (@ tptp.power_power_nat B) W) X4))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N2)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N2) _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) _let_1) _let_1))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N2)) (@ tptp.bit0 (@ _let_1 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N2))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))) (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))))) (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real 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))) (= (@ _let_357 _let_24) tptp.zero_zero_real) (= (@ _let_356 _let_255) tptp.zero_zero_int) (= (@ _let_175 _let_189) tptp.zero_zero_complex) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) _let_254) tptp.zero_z3403309356797280102nteger) (= (@ _let_355 _let_253) tptp.zero_zero_rat) (= (@ _let_354 tptp.one_one_real) tptp.zero_zero_real) (= (@ _let_353 tptp.one_one_int) tptp.zero_zero_int) (= (@ _let_352 tptp.one_one_complex) tptp.zero_zero_complex) (= (@ _let_351 tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) (= (@ _let_350 tptp.one_one_rat) tptp.zero_zero_rat) (= (@ _let_349 _let_24) tptp.zero_zero_real) (= (@ _let_348 _let_255) tptp.zero_zero_int) (= (@ _let_347 _let_189) tptp.zero_zero_complex) (= (@ _let_346 _let_254) tptp.zero_z3403309356797280102nteger) (= (@ _let_345 _let_253) tptp.zero_zero_rat) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (= N2 tptp.one))) (forall ((N2 tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (= N2 tptp.one))) (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 ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)))) (= (@ _let_1 (@ _let_1 A)) A))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))) (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 ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))) (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))) (forall ((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) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N2)))) (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 ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.bit1 N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N2) 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) (N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) tptp.one)))) (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))) (forall ((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.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.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.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))) (forall ((V tptp.num) (W tptp.num) (Y tptp.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) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_eq_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ (@ tptp.ord_less_num N2) M))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N2)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.ord_less_eq_num M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((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 ((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 ((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)))) (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_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))) (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))) (forall ((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 ((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 ((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 ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((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)))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y))))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 X4)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 X4)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((X4 tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat B) W)))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((B tptp.nat) (W tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X4))) (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri4216267220026989637d_enat Y) (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))) (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))) (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))) (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)))) (forall ((Y tptp.nat) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_8040749407984259932d_enat (@ tptp.numera1916890842035813515d_enat X4)) N2) (@ tptp.semiri4216267220026989637d_enat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))) (forall ((N2 tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N2) (@ tptp.numeral_numeral_nat W)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N2))) (forall ((N2 tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N2)) M))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (= (@ _let_354 _let_24) _let_338) (= (@ _let_353 _let_255) _let_256) (= (@ _let_352 _let_189) _let_337) (= (@ _let_351 _let_254) _let_257) (= (@ _let_350 _let_253) _let_336) (= (@ _let_349 tptp.one_one_real) _let_338) (= (@ _let_348 tptp.one_one_int) _let_256) (= (@ _let_347 tptp.one_one_complex) _let_337) (= (@ _let_346 tptp.one_one_Code_integer) _let_257) (= (@ _let_345 tptp.one_one_rat) _let_336) (= (@ _let_344 _let_24) _let_32) (= (@ _let_343 _let_255) _let_232) (= (@ _let_342 _let_189) _let_193) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) _let_254) _let_55) (= (@ _let_341 _let_253) _let_335) (= (@ (@ tptp.divide_divide_int _let_255) _let_232) _let_255) (= (@ (@ tptp.divide6298287555418463151nteger _let_254) _let_55) _let_254) _let_340 _let_339 _let_340 _let_339 (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X4)) N2)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (= N2 tptp.zero_zero_nat)))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X4)) N2)) (or (@ _let_1 X4) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.power_power_int A) N2)))) (forall ((N2 tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.power_power_complex A) N2)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N2))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N2))))) (forall ((N2 tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N2))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N2))))) (forall ((N2 tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N2))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A)) (or (= N2 tptp.zero_zero_nat) (@ _let_1 A))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N2)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))) (forall ((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))))) (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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))) (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.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 ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N2)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (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.neg_numeral_dbl_real _let_24) _let_338) (= (@ tptp.neg_numeral_dbl_int _let_255) _let_256) (= (@ tptp.neg_nu7009210354673126013omplex _let_189) _let_337) (= (@ tptp.neg_nu8804712462038260780nteger _let_254) _let_257) (= (@ tptp.neg_numeral_dbl_rat _let_253) _let_336) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_real)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_complex)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_Code_integer)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_rat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2) tptp.one_one_real))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2) tptp.one_one_int))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2) tptp.one_one_Code_integer))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2) tptp.one_one_rat))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_int _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_complex _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N2) _let_1)))) (forall ((N2 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))) N2)) (= (@ (@ tptp.power_power_rat _let_1) N2) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2)) (@ _let_1 N2)))) (forall ((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 ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_nat X4) _let_1)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X4)) _let_1) (@ (@ tptp.ord_less_eq_nat X4) _let_1)))) (forall ((X4 tptp.nat) (I2 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ (@ tptp.ord_less_eq_nat X4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I2)) N2)) (@ tptp.semiri5074537144036343181t_real X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I2)) N2)) (@ tptp.semiri681578069525770553at_rat X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X4)) (@ _let_1 X4)))) (forall ((I2 tptp.num) (N2 tptp.nat) (X4 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I2)) N2)) (@ tptp.semiri1314217659103216013at_int X4)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I2)) N2)) X4))) (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 ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat X4)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.numeral_numeral_int X4)) (@ tptp.numeral_numeral_int Y)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N2) M))) _let_1)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) _let_2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N2))) _let_1)))) (forall ((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 ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) _let_334 (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat B) C))))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int B) C))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat B2) A3))) (= tptp.bit_se6526347334894502574or_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int B2) A3))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se6528837805403552850or_nat M) N2)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se6528837805403552850or_nat M) N2)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))) (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se6528837805403552850or_nat B))) (let ((_let_2 (@ tptp.bit_se6528837805403552850or_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int B))) (let ((_let_2 (@ tptp.bit_se6526347334894502574or_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int 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)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int 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 ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X4) _let_1))))) (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X4) _let_1))))) (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X4) _let_1))))) (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1))))) (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X4) _let_1))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N2))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 A) (@ _let_1 B))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q3)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) Q3)))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M)) (forall ((X4 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))) (forall ((X4 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X4))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))) (forall ((X4 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X4))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X4))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.times_times_int K) L))))) (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.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) (@ 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_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((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 ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))) (forall ((A tptp.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.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.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 ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))) (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)))) (forall ((M tptp.num) (N2 tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N2)))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))) (forall ((A tptp.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.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))) (forall ((A tptp.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_real _let_24)) (not (= tptp.one_one_int _let_255)) (not (= tptp.one_one_complex _let_189)) (not (= tptp.one_one_Code_integer _let_254)) (not (= tptp.one_one_rat _let_253)) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((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.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))) (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))) (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))) (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))) (forall ((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.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))) (forall ((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 ((N2 tptp.nat) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))) (forall ((A tptp.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 ((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.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.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.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 ((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)) (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.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 ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ 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 C4) D4))))) (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ 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 C4) 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) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))) (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))) (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 ((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 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 ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2))))) (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))) (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (B3 tptp.set_Pr1261947904930325089at_nat)) (=> (@ (@ tptp.ord_le7866589430770878221at_nat A2) B3) (exists ((B5 tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat B5) (@ (@ tptp.minus_1356011639430497352at_nat B3) A2))))) (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2))))) (forall ((N2 tptp.nat) (K tptp.int) (L tptp.int) (R3 tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ tptp.bit_concat_bit N2))) (= (= (@ (@ _let_2 K) L) (@ (@ _let_2 R3) S)) (and (= (@ _let_1 K) (@ _let_1 R3)) (= L S)))))) (forall ((N2 tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N2))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) B)) (@ _let_1 B)))) (forall ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4))))) (forall ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4)))) tptp.one_one_real)) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N2))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N2)) tptp.zero_zero_nat))) (forall ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_3 (@ tptp.divide6298287555418463151nteger A))) (= (@ _let_3 (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_3 _let_2)) _let_1)))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real I2)) (@ tptp.semiri5074537144036343181t_real J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I2)) (@ tptp.semiri681578069525770553at_rat J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat I2)) (@ tptp.semiri1316708129612266289at_nat J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ _let_1 tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N2))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N2) M)) _let_2) _let_1) A))))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((M tptp.num) (N2 tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((M tptp.num) (N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N2))) (not (@ _let_333 _let_24)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) _let_254)) (not (@ _let_332 _let_253)) (not (@ _let_331 _let_255)) (@ _let_321 tptp.one_one_real) (@ _let_320 tptp.one_one_Code_integer) (@ _let_319 tptp.one_one_rat) (@ _let_318 tptp.one_one_int) (not (= tptp.zero_zero_real _let_24)) (not (= tptp.zero_zero_int _let_255)) (not (= tptp.zero_zero_complex _let_189)) (not (= tptp.zero_z3403309356797280102nteger _let_254)) (not (= tptp.zero_zero_rat _let_253)) (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))) (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))) (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))) (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))) (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))) (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))) (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))) (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)) (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)) (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)) (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))) (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))) (forall ((X4 tptp.product_prod_num_num)) (=> (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit0 N3))))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M5)) (@ tptp.bit1 N3))))) (=> (forall ((M5 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) tptp.one)))) (=> (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit0 N3))))) (not (forall ((M5 tptp.num) (N3 tptp.num)) (not (= X4 (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M5)) (@ tptp.bit1 N3))))))))))))))) (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)))))))) (@ _let_317 tptp.one_one_real) (@ _let_316 tptp.one_one_int) (@ _let_315 tptp.one_one_Code_integer) (@ _let_314 tptp.one_one_rat) (not (@ _let_330 _let_24)) (not (@ _let_329 _let_255)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) _let_254)) (not (@ _let_328 _let_253)) (forall ((W tptp.num) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real X4) (@ tptp.uminus_uminus_real _let_1))))) (forall ((W tptp.num) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X4)) (@ (@ tptp.times_times_int X4) (@ tptp.uminus_uminus_int _let_1))))) (forall ((W tptp.num) (X4 tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex X4) (@ tptp.uminus1482373934393186551omplex _let_1))))) (forall ((W tptp.num) (X4 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X4)) (@ (@ tptp.times_3573771949741848930nteger X4) (@ tptp.uminus1351360451143612070nteger _let_1))))) (forall ((W tptp.num) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat X4) (@ tptp.uminus_uminus_rat _let_1))))) (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 ((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 ((N2 tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_real N2) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N2) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((N2 tptp.num)) (not (= (@ tptp.numeral_numeral_rat N2) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X4 tptp.real)) (= (= (@ (@ tptp.times_times_real X4) X4) tptp.one_one_real) (or (= X4 tptp.one_one_real) (= X4 (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((X4 tptp.int)) (= (= (@ (@ tptp.times_times_int X4) X4) tptp.one_one_int) (or (= X4 tptp.one_one_int) (= X4 (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((X4 tptp.complex)) (= (= (@ (@ tptp.times_times_complex X4) X4) tptp.one_one_complex) (or (= X4 tptp.one_one_complex) (= X4 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X4) X4) tptp.one_one_Code_integer) (or (= X4 tptp.one_one_Code_integer) (= X4 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.times_times_rat X4) X4) tptp.one_one_rat) (or (= X4 tptp.one_one_rat) (= X4 (@ tptp.uminus_uminus_rat tptp.one_one_rat))))) (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.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.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_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))) _let_327 _let_326 _let_325 _let_324 (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real 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_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 ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)) (@ (@ tptp.dvd_dvd_nat M) N2))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N2) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))) (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))) (forall ((B tptp.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 ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))) (forall ((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 ((N2 tptp.nat) (X4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) X4))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real X4)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N2)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((U tptp.real) (X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X4) X4))) (forall ((D tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real D))))) (forall ((K tptp.int) (L tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L) tptp.zero_zero_int)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L)) tptp.zero_zero_int)) (not (= (@ _let_1 L) tptp.zero_zero_int))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4))) (@ (@ tptp.power_power_real (@ _let_1 X4)) N2))))) (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X4 tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X4))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N2)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) A)) (@ _let_1 A))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))))) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) tptp.zero_z3403309356797280102nteger)) (forall ((N2 tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) tptp.zero_zero_rat)) (not (@ _let_228 _let_24)) (not (@ _let_90 _let_254)) (not (@ _let_323 _let_253)) (not (@ _let_322 _let_255)) (@ _let_321 tptp.zero_zero_real) (@ _let_320 tptp.zero_z3403309356797280102nteger) (@ _let_319 tptp.zero_zero_rat) (@ _let_318 tptp.zero_zero_int) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))) (@ _let_317 tptp.zero_zero_real) (@ _let_316 tptp.zero_zero_int) (@ _let_315 tptp.zero_z3403309356797280102nteger) (@ _let_314 tptp.zero_zero_rat) (not (@ _let_229 _let_24)) (not (@ _let_313 _let_255)) (not (@ _let_85 _let_254)) (not (@ _let_312 _let_253)) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2))))) (forall ((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)) (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)) (@ (@ 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)) (@ (@ 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.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)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))) (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))) (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)) (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)) (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_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 ((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 ((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)) (=> (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 ((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.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))) (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))) (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))) (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))) (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))) (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))) (= (@ tptp.uminus_uminus_real _let_185) _let_24) (= (@ tptp.uminus_uminus_int _let_311) _let_255) (= (@ tptp.uminus1482373934393186551omplex _let_184) _let_189) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_254) (= (@ tptp.uminus_uminus_rat _let_310) _let_253) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ (@ tptp.power_power_int A) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ (@ tptp.power_power_complex A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ (@ tptp.power_power_rat A) N2)))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) _let_1))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) _let_1)))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q3))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) _let_1)))))) (forall ((M tptp.num) (Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q3))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) _let_1)))))) (forall ((X4 tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) _let_1) (@ (@ tptp.power_power_real X4) _let_1)))) (forall ((X4 tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X4)) _let_1) (@ (@ tptp.power_power_int X4) _let_1)))) (forall ((X4 tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) _let_1) (@ (@ tptp.power_power_complex X4) _let_1)))) (forall ((X4 tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X4)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)))) (forall ((X4 tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X4)) _let_1) (@ (@ tptp.power_power_rat X4) _let_1)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (forall ((Y4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X4)))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X4)) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X4)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X4) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X4)))) (forall ((X4 tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X4) D))) _let_1))))) (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 ((A tptp.code_integer) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N2))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.int) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((A tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger N2))) (forall ((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 ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (forall ((Z tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))) (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))) (forall ((Z tptp.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 ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3))) tptp.zero_zero_nat))) (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3))) tptp.zero_zero_int))) (forall ((N2 tptp.num) (Q3 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3))) tptp.zero_z3403309356797280102nteger))) (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 ((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) (X4 tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X4) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real Y) Z))) Z)))) (forall ((Z tptp.complex) (X4 tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X4) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex Y) Z))) Z)))) (forall ((Z tptp.rat) (X4 tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X4) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X4)) (@ (@ tptp.times_times_rat Y) Z))) Z)))) (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))) (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))) (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))) (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))) (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)))) (= (@ tptp.numeral_numeral_nat _let_212) (@ tptp.suc _let_231)) (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_se3222712562003087583nteger 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.bit_se6528837805403552850or_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.bit_se6526347334894502574or_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X4) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_real Y)))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X4) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_int Y)))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X4) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus1482373934393186551omplex Y)))))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus1351360451143612070nteger Y)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X4) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_rat Y)))))) (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri681578069525770553at_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri8010041392384452111omplex N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N2)))) (@ tptp.semiri5074537144036343181t_real N2)))) (= tptp.ord_less_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M6)))) (= tptp.ord_less_eq_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M6)) tptp.one_one_real)))) (forall ((A2 tptp.int) (B3 tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N2)) (@ (@ tptp.divide_divide_int A2) N2))))) (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 ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) _let_309 _let_308 _let_307 (forall ((N2 tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) M) M))) (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))) (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)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N2))))))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (forall ((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 ((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 ((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 ((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 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 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 ((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_se2923211474154528505it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.modulo_modulo_int K3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N2)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))) (forall ((Q3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q3)) tptp.zero_zero_nat)))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q3)) tptp.zero_zero_int)))) (forall ((M tptp.num) (Q3 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q3)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q3)) tptp.zero_z3403309356797280102nteger)))) (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))) (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))) (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))) (forall ((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 ((X4 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 C) (=> (forall ((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)) X4)) C))) (= X4 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N2))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N2))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N2))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N2))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((N2 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N2))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N2) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N2))) (forall ((U tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X4) _let_1)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) K))) (forall ((N2 tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N2) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L))))) (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 ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) M))) (forall ((A tptp.int) (B tptp.int) (Q3 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.if_int (= R3 tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q3))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q3) R3)) (=> (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) R3))))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) K))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))) (forall ((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 ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (=> (@ (@ tptp.ord_le3102999989581377725nteger X4) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (=> (@ (@ tptp.ord_less_eq_int X4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2))) (= (@ (@ 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))) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N2))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) _let_1))) (forall ((K tptp.int) (L tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L) (@ tptp.uminus_uminus_int tptp.one_one_int))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))) _let_306 (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) _let_1))) (forall ((N2 tptp.nat)) (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))) N2))) _let_1))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N2)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N2)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))) (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K2 tptp.int)) (=> (@ P K2) (=> (not (= K2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K2) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (= tptp.bit_se6528837805403552850or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M6)) (not (@ _let_2 N)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N2)) tptp.one_one_Code_integer))))))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N2)) tptp.one_one_int))))))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N2)) tptp.one_one_nat))))))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger A) tptp.one_one_Code_integer) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat A) tptp.one_one_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int A) tptp.one_one_int) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se3222712562003087583nteger tptp.one_one_Code_integer) A) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.zero_n356916108424825756nteger _let_1))) (@ tptp.zero_n356916108424825756nteger (not _let_1)))))) (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6528837805403552850or_nat tptp.one_one_nat) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A))) (= (@ (@ tptp.bit_se6526347334894502574or_int tptp.one_one_int) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) (@ tptp.zero_n2684676970156552555ol_int _let_1))) (@ tptp.zero_n2684676970156552555ol_int (not _let_1)))))) (forall ((K tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N2))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.bit_ri631733984087533419it_int N2) K))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))) (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) N2)))) (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 ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E2)))))) (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E2)))))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X4)) (@ tptp.uminus1532241313380277803et_int Y)) (@ (@ tptp.ord_less_eq_set_int Y) X4))) (= (@ tptp.neg_nu6075765906172075777c_real _let_24) (@ tptp.uminus_uminus_real _let_213)) (= (@ tptp.neg_nu3811975205180677377ec_int _let_255) (@ tptp.uminus_uminus_int _let_297)) (= (@ tptp.neg_nu6511756317524482435omplex _let_189) (@ tptp.uminus1482373934393186551omplex _let_298)) (= (@ tptp.neg_nu7757733837767384882nteger _let_254) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger _let_212))) (= (@ tptp.neg_nu3179335615603231917ec_rat _let_253) (@ tptp.uminus_uminus_rat _let_299)) (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (= (@ _let_1 K) (@ _let_1 L))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int))))) (forall ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) (@ tptp.semiri1314217659103216013at_int M))) (= (@ 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 ((N2 tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) (@ tptp.semiri1314217659103216013at_int M))) (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) _let_24) (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) _let_255) (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) _let_189) (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) _let_254) (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) _let_253) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))) (forall ((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)))) (forall ((N2 tptp.nat) (M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)))))) (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 ((N2 tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N2)) (@ tptp.numeral_numeral_int N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N2 tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))) (= 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) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)) (@ (@ tptp.ord_less_eq_nat M) N2))) (= tptp.ord_less_eq_nat (lambda ((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) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) tptp.zero_zero_int)) (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 ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N2))) Z))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1314217659103216013at_int M)))) (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))) _let_305 _let_304 (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 ((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 ((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)))))))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) tptp.zero_zero_int) (exists ((N3 tptp.nat)) (= X4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N3))))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)))) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))) (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))) (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z5 tptp.int)) (exists ((N tptp.nat)) (= Z5 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N))))))) (forall ((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)) (=> (@ (@ 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 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 ((I2 tptp.int) (J tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_int I2) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I2)) (@ _let_1 J)))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))) (forall ((P (-> tptp.int Bool)) (X4 tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X4) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X4) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X4)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X4) Y) (@ P tptp.zero_zero_int))))) _let_303 _let_302 _let_301 _let_300 (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) X4) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int X4)) Y))) (forall ((Y tptp.set_int) (X4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int Y) (@ tptp.uminus1532241313380277803et_int X4)) (@ (@ tptp.ord_less_eq_set_int X4) (@ tptp.uminus1532241313380277803et_int Y)))) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X4) Y) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int Y)) (@ tptp.uminus1532241313380277803et_int X4)))) (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)) _let_1)))))) (forall ((X4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real N3)))) (forall ((X4 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X4 tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X4) (@ tptp.semiri681578069525770553at_rat N3)))) (forall ((X4 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real N3)))) (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))))))) (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K3)) (not (@ _let_2 L2)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))) (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 ((D6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D6) (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)) D6)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X4))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X4))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit1 N2))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N2))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((H tptp.real) (Z tptp.real) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H))) (=> (not (= H tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N2)) (@ _let_4 N2))) H)) (@ _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 H)))))))))))) (forall ((H tptp.complex) (Z tptp.complex) (K5 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H))) (=> (not (= H tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N2)) (@ _let_3 N2))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H))))))))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) _let_299) (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) _let_298) (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) _let_213) (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) _let_297) (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat) (forall ((N2 tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N2) (@ tptp.numeral_numeral_nat K)) (= N2 (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N2)) (= (@ tptp.pred_numeral K) N2))) (= (@ 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) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))) (= (@ tptp.neg_nu8295874005876285629c_real _let_24) _let_24) (= (@ tptp.neg_nu5851722552734809277nc_int _let_255) _let_255) (= (@ tptp.neg_nu8557863876264182079omplex _let_189) _let_189) (= (@ tptp.neg_nu5831290666863070958nteger _let_254) _let_254) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_253) _let_253) (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N2) (@ tptp.pred_numeral K)))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N2))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.pred_numeral K)))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N2))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_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_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))) (forall ((K tptp.num)) (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) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N2)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N2)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N2) 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 ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N2))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))) (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))) (forall ((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_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))) (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))) (forall ((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 ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N2)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N2)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N2)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((P (-> tptp.num Bool)) (X4 tptp.num)) (=> (@ P tptp.one) (=> (forall ((X5 tptp.num)) (=> (@ P X5) (@ P (@ tptp.inc X5)))) (@ P X4)))) (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X4))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))) (= tptp.numeral_numeral_nat (lambda ((K3 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K3)))) (= (@ tptp.inc tptp.one) _let_19) (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X4)) (@ tptp.bit1 X4))) (forall ((X4 tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X4)) (@ tptp.bit0 (@ tptp.inc X4)))) (forall ((X4 tptp.num)) (= (@ (@ tptp.plus_plus_num X4) tptp.one) (@ tptp.inc X4))) (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X4))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X4)))) _let_296 (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X4)) tptp.one_one_rat))) (forall ((X4 tptp.num)) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.inc X4)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ tptp.numera1916890842035813515d_enat X4)) tptp.one_on7984719198319812577d_enat))) (forall ((X4 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X4)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X4)) tptp.one_one_complex))) (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X4)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X4)) tptp.one_one_real))) (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X4)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X4)) tptp.one_one_nat))) (forall ((X4 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X4)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X4)) tptp.one_one_int))) _let_295 _let_294 _let_293 _let_292 _let_291 (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))) _let_290 _let_289 (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= tptp.unique5055182867167087721od_nat (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M6))) (@ (@ tptp.unique5026877609467782581ep_nat N) (@ (@ tptp.unique5055182867167087721od_nat M6) (@ tptp.bit0 N)))))) (= tptp.unique5052692396658037445od_int (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M6))) (@ (@ tptp.unique5024387138958732305ep_int N) (@ (@ tptp.unique5052692396658037445od_int M6) (@ tptp.bit0 N)))))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M6) N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.unique4921790084139445826nteger N) (@ (@ tptp.unique3479559517661332726nteger M6) (@ tptp.bit0 N)))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (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 ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real) (= X4 tptp.zero_zero_complex))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X4)) (not (= X4 tptp.zero_zero_real)))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4)) (not (= X4 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 ((X4 tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.zero_zero_real))) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X4))) (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 ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N2))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N2))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X4)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y)))) (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))) (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))) (forall ((W tptp.real) (N2 tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N2) (@ (@ tptp.power_power_real Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))) (forall ((W tptp.complex) (N2 tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N2) (@ (@ tptp.power_power_complex Z) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))) (forall ((X4 tptp.real) (R3 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.times_times_real R3) S))))) (forall ((X4 tptp.complex) (R3 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y))) (@ (@ tptp.times_times_real R3) S))))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X4) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) E2))) (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) E2))) (forall ((X4 tptp.real) (R3 tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real R3) S))))) (forall ((X4 tptp.complex) (R3 tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) R3) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.plus_plus_real R3) S))))) (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 ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) E2))) (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) E2))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)))) (forall ((A tptp.real) (R3 tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R3) (=> (@ (@ 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 R3) S))))) (forall ((A tptp.complex) (R3 tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R3) (=> (@ (@ 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 R3) S))))) (forall ((X4 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 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 ((X4 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 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 ((X4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X4) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X4)) N2))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X4) N2))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X4)) N2))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y))))) (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 ((X4 tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 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 ((X4 tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X4))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 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 ((X4 tptp.real) (Y tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.real_V7735802525324610683m_real Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X4) Y))) E2))) (forall ((X4 tptp.complex) (Y tptp.complex) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y))) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X4) Y))) E2))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))) (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))) (forall ((W tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N2) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((W tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N2) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))) (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))) (forall ((X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X4) tptp.one_one_real))) (forall ((X4 tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X4) tptp.one_one_real))) (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 ((Z tptp.rat) (N2 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) N2))) (= (@ (@ 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) N2))) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) _let_2))) N2)))))))) (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.times_times_complex _let_2) Z)) _let_4) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s2602460028002588243omplex Z) N2))) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2))) N2)))))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_4 (@ (@ tptp.times_times_nat _let_3) N2))) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.times_times_real _let_2) Z)) _let_4) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat _let_3) _let_4))) (@ (@ tptp.comm_s7457072308508201937r_real Z) N2))) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) N2)))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N2)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) N2)))))) (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))) (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X4) (@ tptp.ln_ln_real Y)) (= X4 Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X4) 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)) (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))) (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (= (@ _let_1 (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (= (@ tptp.ln_ln_real X4) tptp.zero_zero_real) (= X4 tptp.one_one_real)))) (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))) (= (@ tptp.bitM tptp.one) tptp.one) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) X4))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s7457072308508201937r_real X4) N2))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4028243227959126397er_rat X4) N2))))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4663373288045622133er_nat X4) N2))))) (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.comm_s4660882817536571857er_int X4) N2))))) (forall ((A tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_complex)))))) (forall ((A tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_real)))))) (forall ((A tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (not (= (@ _let_1 M) tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (not (= (@ _let_1 N2) tptp.zero_zero_rat)))))) (forall ((A tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (=> (= (@ _let_1 N2) tptp.zero_zero_complex) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_complex))))) (forall ((A tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (=> (= (@ _let_1 N2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_real))))) (forall ((A tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (=> (= (@ _let_1 N2) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ _let_1 M) tptp.zero_zero_rat))))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N2)) (@ tptp.bit1 (@ tptp.bitM N2)))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (= (@ tptp.inc (@ tptp.bitM N2)) (@ tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (@ tptp.bitM (@ tptp.inc N2)) (@ tptp.bit1 N2))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) X4))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X4)) (=> (@ _let_1 X4) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X4)) tptp.zero_zero_real)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)))) (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.comm_s7457072308508201937r_real X4) N2)))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.comm_s4028243227959126397er_rat X4) N2)))) (forall ((X4 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X4) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.comm_s4663373288045622133er_nat X4) N2)))) (forall ((X4 tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.comm_s4660882817536571857er_int X4) N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s2602460028002588243omplex tptp.zero_zero_complex) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s7457072308508201937r_real tptp.zero_zero_real) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4028243227959126397er_rat tptp.zero_zero_rat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4663373288045622133er_nat tptp.zero_zero_nat) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.comm_s4660882817536571857er_int tptp.zero_zero_int) N2))) (let ((_let_2 (= N2 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N2))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N2)) (@ tptp.bit0 N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N2)) tptp.one) (@ tptp.bit0 N2))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X4) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (= (@ tptp.ln_ln_real X4) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (= X4 tptp.one_one_real)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_rat A) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex A) (@ tptp.suc N2)) (@ (@ tptp.times_times_complex A) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) tptp.one_one_complex)) N2)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real A) (@ tptp.suc N2)) (@ (@ tptp.times_times_real A) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4663373288045622133er_nat A) (@ tptp.suc N2)) (@ (@ tptp.times_times_nat A) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int A) (@ tptp.suc N2)) (@ (@ tptp.times_times_int A) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) N2)))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) (@ _let_1 N2))))) (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) (@ _let_1 N2))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) (@ _let_1 N2))))) (forall ((Z tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) (@ _let_1 N2))))) (forall ((Z tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) (@ _let_1 N2))))) (forall ((A tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2)))))) (forall ((A tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2)))))) (forall ((A tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.plus_plus_int A) (@ tptp.semiri1314217659103216013at_int N2)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat A))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.plus_plus_nat A) (@ tptp.semiri1316708129612266289at_nat N2)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real))) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int) (@ (@ tptp.ord_less_nat N2) K))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s2602460028002588243omplex A) N2) tptp.zero_zero_complex) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K3))))))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s4028243227959126397er_rat A) N2) tptp.zero_zero_rat) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K3))))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (= (@ (@ tptp.comm_s7457072308508201937r_real A) N2) tptp.zero_zero_real) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N2) (= A (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K3))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) K) tptp.zero_zero_complex)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) K) tptp.zero_z3403309356797280102nteger)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) K) tptp.zero_zero_rat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) K) tptp.zero_zero_real)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (not (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) K) tptp.zero_zero_int)))) (forall ((Z tptp.rat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat N2))) M))))) (forall ((Z tptp.complex) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex N2))) M))))) (forall ((Z tptp.real) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real N2))) M))))) (forall ((Z tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_int (@ _let_1 N2)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int N2))) M))))) (forall ((Z tptp.nat) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N2) M)) (@ (@ tptp.times_times_nat (@ _let_1 N2)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat N2))) M))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N2)))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real _let_32)) tptp.one_one_real) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2))) tptp.one_one_rat))) (forall ((N2 tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2))) tptp.one_one_complex))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N2))) tptp.one_one_real))) (forall ((N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N2)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) tptp.one_one_int))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X4)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) Y)) Y)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ln_ln_real X4))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.rat)) (let ((_let_1 (@ tptp.comm_s4028243227959126397er_rat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat Z) (@ tptp.semiri681578069525770553at_rat M))) (@ (@ tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.complex)) (let ((_let_1 (@ tptp.comm_s2602460028002588243omplex Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ tptp.semiri8010041392384452111omplex M))) (@ (@ tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.real)) (let ((_let_1 (@ tptp.comm_s7457072308508201937r_real Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ tptp.semiri5074537144036343181t_real M))) (@ (@ tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.int)) (let ((_let_1 (@ tptp.comm_s4660882817536571857er_int Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int Z) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.minus_minus_nat N2) M))))))) (forall ((M tptp.nat) (N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.comm_s4663373288045622133er_nat Z))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 N2) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.comm_s4663373288045622133er_nat (@ (@ tptp.plus_plus_nat Z) (@ tptp.semiri1316708129612266289at_nat M))) (@ (@ tptp.minus_minus_nat N2) M))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N2) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))) (forall ((K tptp.nat) (K6 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N2) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N2) _let_1))) (let ((_let_3 (@ tptp.binomial N2))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4))) (@ tptp.uminus_uminus_real X4))))) (forall ((R3 tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex R3))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex R3) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.comm_s2602460028002588243omplex _let_1) K)) (@ (@ tptp.times_times_complex R3) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) K))))) (forall ((R3 tptp.code_integer) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R3))) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.minus_8373710615458151222nteger R3) (@ tptp.semiri4939895301339042750nteger K))) (@ (@ tptp.comm_s8582702949713902594nteger _let_1) K)) (@ (@ tptp.times_3573771949741848930nteger R3) (@ (@ tptp.comm_s8582702949713902594nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) K))))) (forall ((R3 tptp.rat) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat R3))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat R3) (@ tptp.semiri681578069525770553at_rat K))) (@ (@ tptp.comm_s4028243227959126397er_rat _let_1) K)) (@ (@ tptp.times_times_rat R3) (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) K))))) (forall ((R3 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real R3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.comm_s7457072308508201937r_real _let_1) K)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) K))))) (forall ((R3 tptp.int) (K tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int R3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int R3) (@ tptp.semiri1314217659103216013at_int K))) (@ (@ tptp.comm_s4660882817536571857er_int _let_1) K)) (@ (@ tptp.times_times_int R3) (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) 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.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 ((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.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.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.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.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.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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.ord_less_eq_nat K) N2))) _let_288 (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) _let_1)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N2))) (= (@ (@ tptp.binomial (@ tptp.suc N2)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N2) K))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_1) N2) _let_1))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) N2) tptp.one_one_nat)) (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) (@ tptp.suc tptp.zero_zero_nat)) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.binomial N2) tptp.one_one_nat) N2)) (forall ((N2 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K) (= (@ (@ tptp.binomial N2) K) tptp.zero_zero_nat))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) K)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((M tptp.nat) (R3 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R3))) (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 ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) R3)) (@ (@ tptp.power_power_nat N2) R3)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N2) K)))) (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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.binomial N2))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K)) (@ (@ tptp.minus_minus_nat M) K)))))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N2) K))) _let_1))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N2))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) K))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri5074537144036343181t_real K))) K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.semiri681578069525770553at_rat K))) K)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K))))) (forall ((N2 tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N2) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N2) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N2) K)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))) (forall ((N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.binomial N2) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K3)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N))))))) (forall ((N2 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)) N2))) (= (@ 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)) N2))) (@ tptp.semiri773545260158071498ct_rat N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri5044797733671781792omplex _let_3) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex _let_2) _let_3)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) _let_2)) N2))) (@ tptp.semiri5044797733671781792omplex N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (let ((_let_3 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2))) (= (@ tptp.semiri2265585572941072030t_real _let_3) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real _let_2) _let_3)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) N2))) (@ tptp.semiri2265585572941072030t_real N2))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4))) X4))) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (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.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _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 ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) _let_287 (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex) _let_286 _let_285 _let_284 (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))) (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))) _let_287 _let_286 _let_285 _let_284 (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((A tptp.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.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.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))) _let_282 (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex) _let_281 _let_280 _let_279 (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.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.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int 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 ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int 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)) (= (@ (@ 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 ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))) (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.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ tptp.abs_abs_real _let_1) _let_1))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((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_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _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 ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X4) 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 ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))) (= (@ tptp.abs_abs_real _let_24) tptp.one_one_real) (= (@ tptp.abs_abs_int _let_255) tptp.one_one_int) (= (@ tptp.abs_abs_Code_integer _let_254) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_rat _let_253) tptp.one_one_rat) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N2)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N2)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N2)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N2)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)))) (= (@ 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.semiri1408675320244567234ct_nat tptp.zero_zero_nat) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real tptp.zero_zero_nat) tptp.one_one_real) (= (@ 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.semiri1408675320244567234ct_nat tptp.one_one_nat) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real tptp.one_one_nat) tptp.one_one_real) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (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) (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)) (=> (@ (@ 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 ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= (@ tptp.semiri5044797733671781792omplex _let_230) tptp.one_one_complex) (= (@ tptp.semiri773545260158071498ct_rat _let_230) tptp.one_one_rat) (= (@ tptp.semiri1406184849735516958ct_int _let_230) tptp.one_one_int) (= (@ tptp.semiri1408675320244567234ct_nat _let_230) tptp.one_one_nat) (= (@ tptp.semiri2265585572941072030t_real _let_230) tptp.one_one_real) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri5044797733671781792omplex _let_1) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ tptp.semiri5044797733671781792omplex N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1406184849735516958ct_int _let_1) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.semiri1406184849735516958ct_int N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri1408675320244567234ct_nat _let_1) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat _let_1)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.semiri2265585572941072030t_real _let_1) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real _let_1)) (@ tptp.semiri2265585572941072030t_real N2))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X4))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N2))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) (or (not (= A tptp.zero_zero_real)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2)) (or (not (= A tptp.zero_zero_rat)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2)) (or (not (= A tptp.zero_zero_int)) (= N2 tptp.zero_zero_nat)))) (forall ((A tptp.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.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))) (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 ((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.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))) (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))) (= (@ tptp.semiri4449623510593786356d_enat _let_50) _let_283) (= (@ tptp.semiri5044797733671781792omplex _let_50) _let_193) (= (@ tptp.semiri1406184849735516958ct_int _let_50) _let_232) (= (@ tptp.semiri1408675320244567234ct_nat _let_50) _let_50) (= (@ tptp.semiri2265585572941072030t_real _let_50) _let_32) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N2))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat W)) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N2)))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)))) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)))) (forall ((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.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))) (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 ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N2)))) (forall ((W tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N2)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N2))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.modulo_modulo_int A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) N2) (and (= N2 tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((M tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (forall ((M tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.numeral_numeral_nat M)) N2))) (= _let_1 _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.semiri1314217659103216013at_int M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.semiri1316708129612266289at_nat M)) N2) (@ (@ tptp.bit_se1148574629649215175it_nat M) N2))) (forall ((A tptp.int) (B tptp.int) (N2 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)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (=> (forall ((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)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))) (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.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer 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.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) _let_282 _let_281 _let_280 _let_279 (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)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ tptp.abs_abs_real X4) (@ tptp.abs_abs_real Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_real Y))))) (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.abs_abs_int X4) (@ tptp.abs_abs_int Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_int Y))))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X4) (@ tptp.abs_abs_Code_integer Y)) (or (= X4 Y) (= X4 (@ tptp.uminus1351360451143612070nteger Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X4) (@ tptp.abs_abs_rat Y)) (or (= X4 Y) (= X4 (@ tptp.uminus_uminus_rat Y))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))) (forall ((L tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L) K))) (forall ((L tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L) K))) (forall ((L tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L) K))) (forall ((L tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L) K))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) N2) (not (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int A) B)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2))))) (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se4203085406695923979it_int M) A)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (= M N2))))) (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (= M N2))))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) N2) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2))))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) N2) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) N2) (= N2 tptp.zero_zero_nat))) (forall ((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 ((N2 tptp.num)) (not (@ (@ tptp.bit_se1146084159140164899it_int tptp.one_one_int) (@ tptp.numeral_numeral_nat N2)))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N2)))) (forall ((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)) (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) (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 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 ((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 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.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 ((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 ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))) (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))) (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)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((M tptp.nat) (A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se2923211474154528505it_int M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((M tptp.nat) (A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) A)) N2) (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ tptp.zero_n356916108424825756nteger B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.zero_n2684676970156552555ol_int B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (forall ((B Bool) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.zero_n2687167440665602831ol_nat B)) N2) (and B (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat N2)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real N2)) tptp.zero_zero_real))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri773545260158071498ct_rat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.semiri773545260158071498ct_rat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.semiri1406184849735516958ct_int N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.semiri2265585572941072030t_real N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)) (= (@ (@ tptp.bit_ri631733984087533419it_int N2) A) (@ (@ tptp.bit_se2923211474154528505it_int N2) A)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (@ (@ tptp.dvd_dvd_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real M)))) _let_278 _let_277 _let_276 _let_275 _let_274 (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X4)) tptp.one_one_real)) (forall ((X4 tptp.real)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) E))) (= X4 tptp.zero_zero_real))) (forall ((X4 tptp.rat)) (=> (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) E))) (= X4 tptp.zero_zero_rat))) (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 ((X4 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X4) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X4) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X4))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X4) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X4))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X4) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X4))))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X4) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X4))))) (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 ((A tptp.code_integer) (N2 tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2))) (forall ((A tptp.rat) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X4)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X4) Y))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X4)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X4) Y))))) _let_273 _let_272 _let_271 _let_270 (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))) (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_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_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_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 ((X4 tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R3) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X4) (@ (@ tptp.ord_le3102999989581377725nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))) (forall ((X4 tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R3) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R3)) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real A) R3))))) (forall ((X4 tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R3) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R3)) X4) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat A) R3))))) (forall ((X4 tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R3) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R3)) X4) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.plus_plus_int A) R3))))) (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 ((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 ((X4 tptp.code_integer) (A tptp.code_integer) (R3 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) A))) R3) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R3)) X4) (@ (@ tptp.ord_le6747313008572928689nteger X4) (@ (@ tptp.plus_p5714425477246183910nteger A) R3))))) (forall ((X4 tptp.real) (A tptp.real) (R3 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) A))) R3) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R3)) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real A) R3))))) (forall ((X4 tptp.rat) (A tptp.rat) (R3 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) A))) R3) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R3)) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat A) R3))))) (forall ((X4 tptp.int) (A tptp.int) (R3 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) A))) R3) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R3)) X4) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.plus_plus_int A) R3))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (= tptp.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 ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_rat (@ tptp.semiri773545260158071498ct_rat M)) (@ tptp.semiri773545260158071498ct_rat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_int (@ tptp.semiri1406184849735516958ct_int M)) (@ tptp.semiri1406184849735516958ct_int N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N2) (@ (@ tptp.ord_less_real (@ tptp.semiri2265585572941072030t_real M)) (@ tptp.semiri2265585572941072030t_real N2))))) (forall ((A tptp.real) (X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) Y4))) D3) (and (@ (@ tptp.ord_less_real A) Y4) (@ (@ tptp.ord_less_real Y4) B))))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger N2))) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int N2))) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat N2))) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real N2))) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.plus_plus_nat K) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1406184849735516958ct_int M)) tptp.zero_zero_int))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri3624122377584611663nteger N2)) (@ tptp.semiri3624122377584611663nteger M)) tptp.zero_z3403309356797280102nteger))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat M)) tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri773545260158071498ct_rat N2)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1406184849735516958ct_int N2)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat N2) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat N2) N2)))) (forall ((X4 tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X4 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 X4) U)) Y))) V)))) _let_269 _let_268 (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X4))) (forall ((X4 tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X4)))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4)))) (forall ((X4 tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X4)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N2))) (=> (@ (@ tptp.ord_less_nat N2) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N2)))))))) (forall ((R3 tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R3) N2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) R3)))) (@ (@ tptp.power_power_nat N2) R3)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.binomial N2) K)) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((N2 tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N2) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))) (forall ((A tptp.real) (X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4) 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 ((M tptp.nat) (K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L)) N2) (or (and (@ (@ tptp.ord_less_nat N2) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) (@ (@ tptp.minus_minus_nat N2) M)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri3624122377584611663nteger K)) (@ tptp.semiri3624122377584611663nteger (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri3624122377584611663nteger N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.semiri1406184849735516958ct_int K)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri1408675320244567234ct_nat N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((K tptp.num)) (= (@ tptp.semiri4449623510593786356d_enat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat K)) (@ tptp.semiri4449623510593786356d_enat (@ tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (@ tptp.semiri5044797733671781792omplex (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.semiri5044797733671781792omplex (@ tptp.pred_numeral K))))) (forall ((K tptp.num)) (= (@ tptp.semiri1406184849735516958ct_int (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int K)) (@ tptp.semiri1406184849735516958ct_int (@ tptp.pred_numeral K))))) (forall ((K tptp.num)) (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 ((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))))) (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N) K3) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K3) N)))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((N2 tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc N2)) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc N2)) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N2))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)))))) (forall ((A tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (not (@ (@ tptp.dvd_dvd_int _let_1) A)))))) (forall ((A tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (not (@ (@ tptp.dvd_dvd_nat _let_1) A)))))) (forall ((A tptp.code_integer)) (=> (forall ((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 ((X4 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 X4)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))) (forall ((X4 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 X4)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))) (forall ((X4 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 X4)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))) (forall ((X4 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 X4)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))) (forall ((X4 tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X4) tptp.one_one_Code_integer))) (forall ((X4 tptp.rat)) (= (= (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X4) tptp.one_one_rat))) (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X4) tptp.one_one_real))) (forall ((X4 tptp.int)) (= (= (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X4) tptp.one_one_int))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N2) (@ (@ tptp.power_8256067586552552935nteger A) N2)))) (forall ((N2 tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N2) (@ (@ tptp.power_power_rat A) N2)))) (forall ((N2 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2) (@ (@ tptp.power_power_real A) N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N2) (@ (@ tptp.power_power_int A) N2)))) (forall ((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 ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.binomial N2) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) K))))))) _let_267 _let_266 _let_265 (forall ((Y tptp.code_integer) (X4 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 X4) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) Y))))) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) Y))))) (forall ((Y tptp.rat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) Y))))) (forall ((Y tptp.int) (X4 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) Y))))) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))) (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat))) (forall ((X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger B) N2))))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real B) N2))))) (forall ((N2 tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ 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) N2)) (@ (@ tptp.power_power_rat B) N2))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int B) N2))))) (= tptp.bit_se1146084159140164899it_int (lambda ((K3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K3) (@ (@ tptp.power_power_int _let_1) N))))))) (= 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.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.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.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)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri5044797733671781792omplex N2) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1406184849735516958ct_int N2) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.semiri1406184849735516958ct_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri1408675320244567234ct_nat N2) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.semiri2265585572941072030t_real N2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) N2) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2)) (@ tptp.semiri5044797733671781792omplex N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s8582702949713902594nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.semiri4939895301339042750nteger N2))) N2) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N2)) (@ tptp.semiri3624122377584611663nteger N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat N2))) N2) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N2)) (@ tptp.semiri773545260158071498ct_rat N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N2))) N2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N2)) (@ tptp.semiri1406184849735516958ct_int N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) N2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real N2)))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K)) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K))))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_complex (@ tptp.semiri5044797733671781792omplex K)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri5044797733671781792omplex N2)) (@ tptp.semiri5044797733671781792omplex (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ (@ tptp.times_times_real (@ tptp.semiri2265585572941072030t_real K)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K))) (@ (@ tptp.divide_divide_real (@ tptp.semiri2265585572941072030t_real N2)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se9216721137139052372nteger A) N2) (or (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.minus_8373710615458151222nteger A) tptp.one_one_Code_integer)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.nat) (N2 tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (= (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (or (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.minus_minus_nat A) tptp.one_one_nat)) N2) (= N2 tptp.zero_zero_nat))))) (forall ((A tptp.code_integer) (B tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se9216721137139052372nteger A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.plus_p5714425477246183910nteger A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se9216721137139052372nteger _let_2) N2))))))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.plus_plus_int A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N2))))))))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) B))) (let ((_let_3 (= N2 tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) (@ tptp.suc J2)))) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.plus_plus_nat A) _let_2)) N2) (and (=> _let_3 (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (not _let_3) (@ (@ tptp.bit_se1148574629649215175it_nat _let_2) N2))))))))) (= tptp.bit_se9216721137139052372nteger (lambda ((A3 tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ tptp.divide6298287555418463151nteger A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_int _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.divide_divide_int A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (not (@ (@ tptp.dvd_dvd_nat _let_1) A3))) (=> (not _let_2) (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.divide_divide_nat A3) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))))) _let_264 _let_263 (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (@ (@ tptp.bit_se2923211474154528505it_int N2) K)))) (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X4 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 X4)) (@ (@ tptp.power_8256067586552552935nteger X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.real tptp.real Bool)) (X4 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 X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.rat tptp.rat Bool)) (X4 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 X4)) (@ (@ tptp.power_power_rat X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((P (-> tptp.int tptp.int Bool)) (X4 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 X4)) (@ (@ tptp.power_power_int X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) _let_262 (= tptp.binomial (lambda ((N tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) K3))) (let ((_let_2 (@ tptp.ord_less_nat N))) (@ (@ (@ tptp.if_nat (@ _let_2 K3)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K3))) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K3)))))))) _let_261 (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X4)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X4)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1)))))))))) (= tptp.semiri1406184849735516958ct_int (lambda ((N tptp.nat)) (@ tptp.semiri1314217659103216013at_int (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (= tptp.semiri1408675320244567234ct_nat (lambda ((N tptp.nat)) (@ tptp.semiri1316708129612266289at_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (= tptp.semiri2265585572941072030t_real (lambda ((N tptp.nat)) (@ tptp.semiri5074537144036343181t_real (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) tptp.one_one_nat)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.arctan X4)) (@ tptp.arctan Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X4)) (@ tptp.arctan Y)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N2)))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X4) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X4)) (@ tptp.abs_abs_int Y))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.sin_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.cos_coeff N2)) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((N2 tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N2)))) (= tptp.abs_abs_int (lambda ((I3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I3)) I3))) (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 ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L))) (@ tptp.abs_abs_int L)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ tptp.cos_coeff _let_1) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real (@ tptp.sin_coeff N2))) (@ tptp.semiri5074537144036343181t_real _let_1))))) (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Xa tptp.nat) (Xb tptp.nat) (Xc tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.set_fo2584398358068434914at_nat X4))) (let ((_let_2 (@ (@ tptp.ord_less_nat Xb) Xa))) (=> (= (@ (@ (@ _let_1 Xa) Xb) Xc) Y) (and (=> _let_2 (= Y Xc)) (=> (not _let_2) (= Y (@ (@ (@ _let_1 (@ (@ tptp.plus_plus_nat Xa) tptp.one_one_nat)) Xb) (@ (@ X4 Xa) 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 ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L))) (@ _let_2 (@ _let_1 L)))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L))))) (= tptp.bit_se1148574629649215175it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M6) (@ (@ tptp.power_power_nat _let_1) N))))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N2)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K)))))))) (forall ((D tptp.int) (Z tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Z))) tptp.one_one_int)) D))))) (forall ((D tptp.int) (X4 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X4))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))) (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 ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N2)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N2) (= (@ F I4) K))))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X4)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X4) Y)))))))) (= tptp.bit_se6526347334894502574or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K3 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L2)) (@ (@ (@ tptp.if_int (= L2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K3)) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 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 L2) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N2)))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N2)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N2)))))) (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N2)))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))) _let_1)))))))))))))))) (forall ((L tptp.int) (K tptp.int) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N2))) (let ((_let_2 (@ tptp.sgn_sgn_int L))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N2))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N2 tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N2) M)))))))))))))))))) _let_260 (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 tptp.zero_zero_int) (= L2 tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K3 _let_2)) L2) (@ (@ (@ tptp.if_int (= L2 _let_2)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_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) (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)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ tptp.sgn_sgn_int _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.sgn_sgn_real _let_1) _let_1))) (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.sgn_sgn_complex A))) (= (@ tptp.sgn_sgn_complex _let_1) _let_1))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ tptp.sgn_sgn_Code_integer _let_1) _let_1))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.sgn_sgn_rat _let_1) _let_1))) (forall ((X4 tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4)) (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.bit_ri7919022796975470100ot_int X4) (@ tptp.bit_ri7919022796975470100ot_int Y)) (= X4 Y))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ _let_1 N2)))) (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A tptp.int)) (= (@ (@ tptp.bit_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 ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X4) tptp.zero_zero_int)) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) tptp.zero_zero_int) tptp.zero_zero_int)) (= (@ tptp.sgn_sgn_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_complex tptp.zero_zero_complex) tptp.zero_zero_complex) (= (@ tptp.sgn_sgn_real tptp.zero_zero_real) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_rat tptp.zero_zero_rat) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_int tptp.zero_zero_int) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int tptp.one_one_int) tptp.one_one_int) _let_259 _let_258 (= (@ tptp.sgn_sgn_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer) (= (@ tptp.sgn_sgn_rat tptp.one_one_rat) tptp.one_one_rat) _let_259 _let_258 (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))) (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real (@ tptp.sgn_sgn_real A)))) (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ tptp.sgn_sgn_int A)))) (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex (@ tptp.sgn_sgn_complex A)))) (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ tptp.sgn_sgn_Code_integer A)))) (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.sgn_sgn_rat A)))) (forall ((A tptp.code_integer) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N2)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.sgn_sgn_Code_integer A)) N2))) (forall ((A tptp.rat) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.power_power_rat A) N2)) (@ (@ tptp.power_power_rat (@ tptp.sgn_sgn_rat A)) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.power_power_real A) N2)) (@ (@ tptp.power_power_real (@ tptp.sgn_sgn_real A)) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.power_power_int A) N2)) (@ (@ tptp.power_power_int (@ tptp.sgn_sgn_int A)) N2))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) Y) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int X4) Y)))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int X4))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int Y)) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 Y))))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.sgn_sgn_Code_integer A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sgn_sgn_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.sgn_sgn_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.sgn_sgn_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (= (@ _let_1 (@ tptp.sgn_sgn_Code_integer A)) (@ _let_1 A)))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real A)) (@ _let_1 A)))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.sgn_sgn_rat A)) (@ _let_1 A)))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.sgn_sgn_int A)) (@ _let_1 A)))) (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4)) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) X4)) (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 ((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.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (= (@ (@ tptp.divide_divide_rat A) _let_1) (@ (@ tptp.times_times_rat A) _let_1)))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (= (@ (@ tptp.divide_divide_real A) _let_1) (@ (@ tptp.times_times_real A) _let_1)))) (= (@ 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 ((N2 tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N2) tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N2) tptp.zero_zero_int) (= N2 tptp.zero_zero_nat))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) tptp.zero_zero_int)) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) tptp.zero_zero_int)) (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real X4) tptp.one_one_real) (= X4 tptp.zero_zero_real))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.sgn_sgn_real A) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.sgn_sgn_int A) tptp.one_one_int))) (= (@ tptp.bit_ri7632146776885996613nteger _let_254) tptp.zero_z3403309356797280102nteger) (= (@ tptp.bit_ri7919022796975470100ot_int _let_255) tptp.zero_zero_int) (= (@ tptp.bit_ri7632146776885996613nteger tptp.zero_z3403309356797280102nteger) _let_254) (= _let_87 _let_255) (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 ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) tptp.one_one_int) tptp.one_one_int)) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) tptp.one_one_nat) tptp.one_one_nat)) (forall ((A tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) tptp.one_one_Code_integer))) (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) tptp.one_one_real))) (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) tptp.one_one_rat))) (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) tptp.one_one_int))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat)))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real)))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int)))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger)))))) (= (@ tptp.bit_se2002935070580805687sk_nat _let_230) tptp.one_one_nat) (= (@ tptp.bit_se2000444600071755411sk_int _let_230) tptp.one_one_int) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X4) (@ tptp.bit_ri7632146776885996613nteger X4))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X4) (@ tptp.bit_ri7919022796975470100ot_int X4))) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger X4))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int X4))) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger (@ tptp.bit_ri7632146776885996613nteger X4)) X4) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.bit_ri7919022796975470100ot_int X4)) X4) (@ tptp.uminus_uminus_int tptp.one_one_int))) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.bit_se3222712562003087583nteger X4) (@ tptp.bit_ri7632146776885996613nteger X4)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (forall ((X4 tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int X4) (@ tptp.bit_ri7919022796975470100ot_int X4)) (@ tptp.uminus_uminus_int tptp.one_one_int))) (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.abs_abs_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))) (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.abs_abs_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))) (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.abs_abs_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))) (forall ((A tptp.int)) (= (@ tptp.sgn_sgn_int (@ tptp.abs_abs_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.abs_abs_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))) (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.zero_n1201886186963655149omplex (not (= A tptp.zero_zero_complex))))) (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)) (@ tptp.zero_n3304061248610475627l_real (not (= A tptp.zero_zero_real))))) (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.zero_n2052037380579107095ol_rat (not (= A tptp.zero_zero_rat))))) (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)) (@ tptp.zero_n2684676970156552555ol_int (not (= A tptp.zero_zero_int))))) (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.zero_n356916108424825756nteger (not (= A tptp.zero_z3403309356797280102nteger))))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((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 ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4))) (forall ((X4 tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X4)) X4) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))) (forall ((N2 tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N2))) (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2)))) (forall ((N2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int (@ tptp.inc N2)))) (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 ((X4 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) tptp.one_one_nat) tptp.zero_zero_nat)) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)))) (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7632146776885996613nteger A)) (not (@ _let_1 A))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (not (@ _let_1 A))))) (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.zero_n2052037380579107095ol_rat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.zero_n3304061248610475627l_real (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_int (@ tptp.semiri1314217659103216013at_int N2)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.sgn_sgn_Code_integer (@ tptp.semiri4939895301339042750nteger N2)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int)) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.one_one_int) tptp.one_one_int)) (= (@ tptp.bit_ri7632146776885996613nteger tptp.one_one_Code_integer) _let_257) (= _let_88 _let_256) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.zero_zero_int)) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) tptp.zero_zero_int)) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_int Y)))))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ 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 X4)) (@ tptp.numeral_numeral_nat Y)))))) (forall ((B tptp.int) (A tptp.int)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.bit_se1146084159140164899it_int B) N3) (@ (@ tptp.bit_se1146084159140164899it_int A) N3))) (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.bit_ri7919022796975470100ot_int B))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X4))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X4)))) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X4))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X4)))) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) _let_88) tptp.zero_zero_int) (= tptp.bit_se2923211474154528505it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N)))) (= tptp.bit_se2925701944663578781it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N)))) (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))))) (= 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 ((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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N2))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))) (forall ((N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N2)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N2)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.complex)) (= (= (@ tptp.sgn_sgn_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.sgn_sgn_Code_integer B)))) (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.sgn_sgn_rat B)))) (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.sgn_sgn_complex B)))) (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.sgn_sgn_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.sgn_sgn_real B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B)))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer A))) (=> (= (@ tptp.sgn_sgn_Code_integer B) _let_1) (= (@ tptp.sgn_sgn_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B)) _let_1)))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (=> (= (@ tptp.sgn_sgn_real B) _let_1) (= (@ tptp.sgn_sgn_real (@ (@ tptp.plus_plus_real A) B)) _let_1)))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (=> (= (@ tptp.sgn_sgn_rat B) _let_1) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int A))) (=> (= (@ tptp.sgn_sgn_int B) _let_1) (= (@ tptp.sgn_sgn_int (@ (@ tptp.plus_plus_int A) B)) _let_1)))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ (@ tptp.minus_minus_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ _let_1 A))))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int A) B)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int A) N2) (@ (@ tptp.bit_se1146084159140164899it_int B) N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) N2) (and (@ (@ tptp.bit_se1148574629649215175it_nat A) N2) (@ (@ tptp.bit_se1148574629649215175it_nat B) N2)))) (forall ((X4 tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int X4))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((Y tptp.int) (Z tptp.int) (X4 tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.bit_se6526347334894502574or_int Y) Z)) X4) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.bit_se725231765392027082nd_int Y) X4)) (@ (@ tptp.bit_se725231765392027082nd_int Z) X4)))) (forall ((K tptp.int) (L tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L)) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A)) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int B))) (= (@ _let_1 A) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 A))) (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int A))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N2) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) N2) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int)) (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 ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2))) tptp.zero_zero_int))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))) (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 ((N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) tptp.zero_zero_int)) (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 ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (= (@ tptp.exp_real X5) Y)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X4))) (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X4)) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X4))) (forall ((X4 tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) tptp.zero_zero_real))) (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real B))) (let ((_let_2 (@ tptp.sgn_sgn_real A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.sgn_sgn_int B))) (let ((_let_2 (@ tptp.sgn_sgn_int A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_int)) (=> (not (= _let_1 tptp.zero_zero_int)) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))) (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.sgn_sgn_Code_integer B))) (let ((_let_2 (@ tptp.sgn_sgn_Code_integer A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))) (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.sgn_sgn_rat B))) (let ((_let_2 (@ tptp.sgn_sgn_rat A))) (=> (not (= _let_1 _let_2)) (=> (not (= _let_2 tptp.zero_zero_rat)) (=> (not (= _let_1 tptp.zero_zero_rat)) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))) (= (@ tptp.sgn_sgn_real _let_24) _let_24) (= (@ tptp.sgn_sgn_int _let_255) _let_255) (= (@ tptp.sgn_sgn_complex _let_189) _let_189) (= (@ tptp.sgn_sgn_Code_integer _let_254) _let_254) (= (@ tptp.sgn_sgn_rat _let_253) _let_253) (forall ((Y tptp.int) (Z tptp.int) (X4 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 X4) 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) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) X4))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X4) Y))))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int (@ tptp.bit_ri7919022796975470100ot_int A)) B))) (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ tptp.times_3573771949741848930nteger K3) (@ tptp.sgn_sgn_Code_integer K3)))) (= tptp.abs_abs_rat (lambda ((K3 tptp.rat)) (@ (@ tptp.times_times_rat K3) (@ tptp.sgn_sgn_rat K3)))) (= tptp.abs_abs_real (lambda ((K3 tptp.real)) (@ (@ tptp.times_times_real K3) (@ tptp.sgn_sgn_real K3)))) (= tptp.abs_abs_int (lambda ((K3 tptp.int)) (@ (@ tptp.times_times_int K3) (@ tptp.sgn_sgn_int K3)))) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.sgn_sgn_Code_integer A)) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.sgn_sgn_rat A)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.abs_abs_complex A)) (@ tptp.sgn_sgn_complex A)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.sgn_sgn_real A)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.sgn_sgn_int A)) A)) (forall ((A tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer A)) (@ tptp.abs_abs_Code_integer A)) A)) (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat A)) (@ tptp.abs_abs_rat A)) A)) (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sgn_sgn_complex A)) (@ tptp.abs_abs_complex A)) A)) (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ tptp.abs_abs_real A)) A)) (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.abs_abs_int A)) A)) (forall ((X4 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.sgn_sgn_Code_integer X4)) (@ tptp.abs_abs_Code_integer X4)) X4)) (forall ((X4 tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.sgn_sgn_rat X4)) (@ tptp.abs_abs_rat X4)) X4)) (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) (@ tptp.abs_abs_real X4)) X4)) (forall ((X4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int X4)) (@ tptp.abs_abs_int X4)) X4)) (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (= (@ tptp.sgn_sgn_Code_integer B) (@ tptp.sgn_sgn_Code_integer A)) (= (@ 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 ((B tptp.real) (A tptp.real)) (=> (= (@ tptp.sgn_sgn_real B) (@ tptp.sgn_sgn_real A)) (= (@ 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 ((B tptp.rat) (A tptp.rat)) (=> (= (@ tptp.sgn_sgn_rat B) (@ tptp.sgn_sgn_rat A)) (= (@ 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 ((B tptp.int) (A tptp.int)) (=> (= (@ tptp.sgn_sgn_int B) (@ tptp.sgn_sgn_int A)) (= (@ 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 ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ (@ tptp.times_times_complex Y) X4)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ (@ tptp.times_times_real Y) X4)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X4) Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X4) Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X4)) (@ tptp.exp_real Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X4)) (@ tptp.exp_complex Y)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N2))) (forall ((N2 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N2)))) (forall ((N2 tptp.nat)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X4)))) (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))) (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))) (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4))) (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer (@ tptp.sgn_sgn_Code_integer A)))) (let ((_let_2 (= A tptp.zero_z3403309356797280102nteger))) (and (=> _let_2 (= _let_1 tptp.zero_z3403309356797280102nteger)) (=> (not _let_2) (= _let_1 tptp.one_one_Code_integer)))))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real (@ tptp.sgn_sgn_real A)))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat (@ tptp.sgn_sgn_rat A)))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int (@ tptp.sgn_sgn_int A)))) (let ((_let_2 (= A tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.zero_zero_int)) (=> (not _let_2) (= _let_1 tptp.one_one_int)))))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) K))) (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))) (forall ((Y tptp.int) (Z tptp.int) (X4 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 X4) Y)) Z)))) _let_252 _let_251 (= tptp.bit_ri7632146776885996613nteger (lambda ((A3 tptp.code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A3)) tptp.one_one_Code_integer))) (= tptp.bit_ri7919022796975470100ot_int (lambda ((A3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A3)) tptp.one_one_int))) (= tptp.uminus1351360451143612070nteger (lambda ((A3 tptp.code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ (@ tptp.minus_8373710615458151222nteger A3) tptp.one_one_Code_integer)))) (= tptp.uminus_uminus_int (lambda ((A3 tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int A3) tptp.one_one_int)))) (forall ((V tptp.int) (K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))) (= tptp.bit_ri7919022796975470100ot_int (lambda ((K3 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K3)) tptp.one_one_int))) (forall ((X4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X4)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))) tptp.one_one_real)) (forall ((X4 tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X4)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X4))) tptp.one_one_complex)) (forall ((X4 tptp.complex) (N2 tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X4) (@ tptp.semiri8010041392384452111omplex N2))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N2))) (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X4) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N2))) (forall ((N2 tptp.nat) (X4 tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) X4)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) N2))) (forall ((N2 tptp.nat) (X4 tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) X4)) (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) N2))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L) K) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L)) (@ tptp.sgn_sgn_int L))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))) (forall ((N2 tptp.num)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N2))) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger N2)))) (forall ((N2 tptp.num)) (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.ord_less_nat N2) (@ tptp.bit_se2002935070580805687sk_nat N2)))) (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.real)) (= (= (@ tptp.sgn_sgn_real A) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))) (forall ((A tptp.int)) (= (= (@ tptp.sgn_sgn_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))) (forall ((A tptp.code_integer)) (= (= (@ tptp.sgn_sgn_Code_integer A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))) (forall ((A tptp.rat)) (= (= (@ tptp.sgn_sgn_rat A) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))) _let_250 _let_249 _let_248 _let_247 (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ tptp.exp_real X4)))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (or (@ _let_1 K) (@ _let_1 L))))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X4)))) (= 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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) X4))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N2))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real (@ tptp.sgn_sgn_real X4)))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex (@ tptp.sgn_sgn_complex X4)))) (let ((_let_2 (= X4 tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N2) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N2))) (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7632146776885996613nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bitM N2))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N2))))) (forall ((N2 tptp.num)) (= (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bitM N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (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 ((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))))) (@ (@ tptp.ord_less_eq_real _let_236) _let_213) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N2)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X4) (@ tptp.semiri8010041392384452111omplex N2)))) N2) (@ tptp.exp_complex X4)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X4) (@ tptp.semiri5074537144036343181t_real N2)))) N2) (@ tptp.exp_real X4)))) (forall ((R3 tptp.int) (L tptp.int) (K tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R3) (@ tptp.sgn_sgn_int L)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R3)) (@ tptp.abs_abs_int L)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) L)) R3)) (@ (@ (@ tptp.eucl_rel_int K) L) (@ (@ tptp.product_Pair_int_int Q3) R3)))))) (= tptp.tanh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))) (let ((_let_2 (@ tptp.exp_real X))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))) _let_246 (forall ((A tptp.int) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_int) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2)))) (forall ((A tptp.nat) (N2 tptp.nat)) (= (= (@ (@ tptp.bit_se727722235901077358nd_nat A) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.zero_zero_nat) (not (@ (@ tptp.bit_se1148574629649215175it_nat A) N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real _let_220)) _let_32) (forall ((N2 tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((A tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int A)) N2) (and (not (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2) tptp.zero_zero_int)) (not (@ (@ tptp.bit_se1146084159140164899it_int A) N2))))) (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))) (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))) _let_245 (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 ((Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q2) A23)))))) (not (forall ((R2 tptp.int) (Q2 tptp.int)) (=> (= A33 (@ (@ tptp.product_Pair_int_int Q2) R2)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) A23)) R2)))))))))))) (forall ((L tptp.int) (K tptp.int)) (=> (not (= L tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L))) (= (@ (@ tptp.divide_divide_int K) L) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K)))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N2)) (= N2 tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) _let_244 _let_243 (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))) (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))) (= tptp.bit_se2002935070580805687sk_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (= tptp.bit_se2000444600071755411sk_int (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (= 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))))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X4)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X4))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) _let_1))) N2)) (@ tptp.exp_real X4)))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) _let_1))) N2)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X4))))))) (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))) (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N2) K) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X4))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.log _let_1) X4) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X4)))))) _let_242 (= tptp.divide_divide_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K3))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K3) (@ tptp.sgn_sgn_int L2))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L2) K3))))))))))) (= tptp.arctan (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 X4) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X4)))))) (= _let_141 (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_140) (@ tptp.arctan (@ _let_180 _let_227)))) (@ tptp.arctan (@ _let_180 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 _let_226)))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X4) Y))) (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real) (forall ((X4 tptp.real)) (= (= (@ tptp.sqrt X4) tptp.one_one_real) (= X4 tptp.one_one_real))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) 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 ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (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 ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) 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 ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))) (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 ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)) (= (@ tptp.sqrt _let_140) _let_32) (= _let_239 _let_230) (forall ((I2 tptp.int)) (= (= (@ tptp.nat2 I2) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I2) tptp.zero_zero_int))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))) (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 ((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) (X4 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 X4) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X4) Y)))))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) A))))) (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_real A) X4)))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))))) (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X4) (= (@ _let_2 (@ (@ tptp.log A) X4)) (@ _let_1 X4))))))) (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 ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X4)) (@ (@ tptp.ord_less_eq_real A) X4))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) A))))) (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))))) (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 ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)) (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))) (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 ((X4 tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X4))) (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))) (forall ((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 ((X4 tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4))) (forall ((X4 tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))) (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))) (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) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N2)) (@ tptp.bit_se2002935070580805687sk_nat N2))) _let_241 (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y)))) (forall ((X4 tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X4) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) K))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sqrt X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (@ _let_1 (@ tptp.sqrt X4))))) _let_240 (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X4) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y)))) (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))) (= (lambda ((P3 (-> tptp.nat Bool))) (forall ((X6 tptp.nat)) (@ P3 X6))) (lambda ((P4 (-> tptp.nat Bool))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ P4 (@ tptp.nat2 X)))))) (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)))))) (= tptp.one_one_nat _let_239) (not (@ _let_234 tptp.zero_zero_real)) (@ _let_229 tptp.pi) (@ _let_228 tptp.pi) _let_238 (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real X4) _let_1) _let_1)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X4)) (@ tptp.sqrt Y))))))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X4) X4)) (@ (@ tptp.times_times_real Y) Y))))) (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 ((X4 tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X4)) N2) (@ (@ tptp.ord_less_eq_int X4) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))) (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 ((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))) _let_237 _let_235 (@ (@ tptp.ord_less_real _let_174) _let_32) (= 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 ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X4) (@ (@ tptp.divide_divide_real (@ _let_1 X4)) (@ _let_1 B))))))) (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log B) _let_1)))))) (forall ((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 ((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 ((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 ((P (-> tptp.nat Bool)) (I2 tptp.int)) (= (@ P (@ tptp.nat2 I2)) (and (forall ((N tptp.nat)) (=> (= I2 (@ tptp.semiri1314217659103216013at_int N)) (@ P N))) (=> (@ (@ tptp.ord_less_int I2) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N2) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N2)) K)))) (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 ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))) (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 ((K tptp.int) (L tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))) (forall ((Y tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X4) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))) (forall ((Z tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N2)))) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X4) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X4)) (@ tptp.nat2 Y))))))) (@ _let_234 _let_140) (@ (@ tptp.ord_less_eq_real _let_32) tptp.pi) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))) (not (= _let_34 _let_32)) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (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) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))))) (forall ((K tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N2) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.nat2 K))))) (forall ((X4 tptp.real)) (=> (not (= X4 tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X4)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X4))))) (forall ((K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N2)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X4) (@ tptp.sqrt Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt Y)))) (= _let_233 _let_231) (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X4) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X4)) (@ _let_1 Y)))))))))) (forall ((A tptp.real) (N2 tptp.nat) (X4 tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N2)) X4) (=> (= X4 (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= A B))))) (forall ((A tptp.real) (X4 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 X4) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X4)) (@ _let_1 Y)))))))))) (forall ((B tptp.real) (N2 tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N2)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) M))))) (forall ((A tptp.real) (N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N2)) X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X4)) (@ tptp.semiri5074537144036343181t_real N2))))) (forall ((X4 tptp.real) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ _let_1 (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_1 X4)))))) (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))))))) (not (= _let_34 tptp.zero_zero_real)) (@ (@ tptp.ord_less_real _let_34) _let_32) (@ (@ tptp.ord_less_eq_real _let_34) _let_32) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X4)) Y)))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X4) 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 ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X4) (= Y tptp.zero_zero_real)))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X4 tptp.zero_zero_real)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((Y tptp.real) (X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= (@ tptp.semiri5074537144036343181t_real N2) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.log A) X4) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X4)))))))))) (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)))))) (@ _let_229 _let_34) (@ _let_228 _let_34) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_194)) tptp.pi) (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_141) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X4)) Y)))))) (forall ((X4 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 X4) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X4) Y))))))) (forall ((M tptp.nat) (B tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N2)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((X4 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 X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real Y))))) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X4 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 X4)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.sqrt X4)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X4)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N2) (= (@ tptp.sqrt (@ _let_3 N2)) (@ _let_3 (@ (@ tptp.divide_divide_nat N2) _let_2)))))))) (@ (@ tptp.ord_less_real _let_35) tptp.zero_zero_real) (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))) (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M6 tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))) (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X4)) N2) (@ (@ tptp.power_power_real X4) (@ (@ tptp.divide_divide_nat N2) _let_1))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X4) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))) (= tptp.bit_se727722235901077358nd_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (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))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((X4 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 X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))) (forall ((X4 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 X4)) _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 X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (= (@ tptp.arcosh_real X4) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X4) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))) (forall ((X4 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 X4) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X4) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N2)))))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_227) (@ tptp.arctan (@ _let_180 (@ tptp.numeral_numeral_real _let_226))))) (@ _let_98 (@ tptp.arctan (@ _let_223 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_20))))))))) _let_141) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)))) (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))) _let_225 (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))) (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N2)) tptp.one_one_int))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))) (= (@ tptp.cos_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.cos_real tptp.zero_zero_real) tptp.one_one_real) (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))) (= (@ tptp.archim2889992004027027881ng_rat tptp.one_one_rat) tptp.one_one_int) (= (@ tptp.archim7802044766580827645g_real tptp.one_one_real) tptp.one_one_int) (= (@ tptp.cos_real tptp.pi) _let_24) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.sin_complex X4))) (let ((_let_2 (@ tptp.cos_complex X4))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex _let_2) _let_2)) (@ (@ tptp.times_times_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (let ((_let_2 (@ tptp.cos_real X4))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real _let_2) _let_2)) (@ (@ tptp.times_times_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.numeral_numeral_real V)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.numeral_numeral_rat V)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat V)) X4))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real V)) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real tptp.one_one_real) X4))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))) (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.rat)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.one_one_int))) (forall ((X4 tptp.real)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) tptp.one_one_int))) (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (forall ((X4 tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))) A) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real A)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X4))) (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 ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))) (= (@ tptp.cos_real _let_34) tptp.zero_zero_real) (= (@ tptp.sin_real _let_194) tptp.zero_zero_real) (= (@ tptp.sin_real _let_34) tptp.one_one_real) (= (@ tptp.cos_real _let_194) tptp.one_one_real) (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X4))) (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X4))) (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.cos_real X4))) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2))) (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) tptp.one_one_real))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) tptp.one_one_complex))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1)) tptp.one_one_real))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1)) tptp.one_one_complex))) (forall ((N2 tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.zero_zero_real)) (forall ((N2 tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N2))) tptp.pi)) tptp.one_one_real)) (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X4)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))) (= (@ tptp.cos_real _let_224) tptp.zero_zero_real) (= (@ tptp.sin_real _let_224) _let_24) (forall ((X4 tptp.complex)) (=> (= (@ tptp.cos_complex X4) tptp.one_one_complex) (= (@ tptp.sin_complex X4) tptp.zero_zero_complex))) (forall ((X4 tptp.real)) (=> (= (@ tptp.cos_real X4) tptp.one_one_real) (= (@ tptp.sin_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.sin_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.sin_real Y))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y))))) (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.cos_real X4)) tptp.one_one_real))) (forall ((X4 tptp.complex)) (=> (= (@ tptp.sin_complex X4) tptp.zero_zero_complex) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cos_complex X4)) tptp.one_one_real))) (forall ((X4 tptp.real)) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X4)) tptp.one_one_real))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sin_complex X4))) (@ tptp.cos_complex X4))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sin_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sin_real X4))) (@ tptp.cos_real X4))))) (forall ((X4 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 X4)) (= (@ tptp.cos_real Y3) (@ tptp.cos_real X4))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real Y)) (@ tptp.archim7802044766580827645g_real X4)))) (forall ((Y tptp.rat) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X4) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat Y)) (@ tptp.archim2889992004027027881ng_rat X4)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) X4))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y)) (@ (@ tptp.ord_less_rat X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.one_one_real)) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) tptp.one_one_real)) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) (@ tptp.abs_abs_real X4))) (forall ((X4 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 X4)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y))))) tptp.one_one_real)) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_1))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_1) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_1))))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real R3) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real R3))))) (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat R3) (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim2889992004027027881ng_rat R3))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X4)) (@ tptp.sin_real X4)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ _let_1 (@ tptp.sin_real X4)))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim2889992004027027881ng_rat Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim7802044766580827645g_real Y)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X4))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X4))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X4) (@ tptp.cos_real Y)) (= X4 Y)))))))) (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)) (@ _let_1 X4))))))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X4))) tptp.one_one_real)) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X4))) tptp.one_one_real)) (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.sin_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.sin_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real W) Z))) (@ tptp.sin_real (@ (@ tptp.minus_minus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex W) Z))) (@ tptp.sin_complex (@ (@ tptp.minus_minus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.sin_real W)) (@ tptp.sin_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.sin_complex W)) (@ tptp.sin_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real Z) W)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.sin_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex Z) W)) _let_1)))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cos_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sin_complex X4)) _let_2)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sin_real X4)) _let_2)))))) (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_222 tptp.zero_zero_real)) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X4)))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.pi) (=> (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.pi) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X4)))))) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _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) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sin_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))) (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X4))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B))) (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B))) (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X4)))))) (@ (@ tptp.ord_less_real _let_222) 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))))) (@ (@ tptp.ord_less_eq_real _let_222) tptp.zero_zero_real) (forall ((Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X4)))))) (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 ((X4 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 X4) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _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)))) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3)))))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real 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)) (= X4 (@ tptp.cos_real T3)) (= Y (@ tptp.sin_real T3))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real 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)) (=> (= X4 (@ tptp.cos_real T3)) (not (= Y (@ tptp.sin_real T3))))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))) (= (@ tptp.sin_real _let_141) _let_221) (= (@ tptp.cos_real _let_141) _let_221) (forall ((W tptp.real) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.cos_real (@ (@ tptp.minus_minus_real W) Z))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real W) Z)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((W tptp.complex) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex W) Z))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex W) Z)))) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (forall ((W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_real (@ tptp.cos_real W)) (@ tptp.cos_real Z)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_1) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real W) Z)) _let_1)))) (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real W) Z)) _let_1)))))) (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex W)) (@ tptp.cos_complex Z)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_1) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex W) Z)) _let_1)))) (@ tptp.cos_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex W) Z)) _let_1)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X4)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X4))) tptp.one_one_real))))) (= (@ tptp.sin_real _let_215) _let_220) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X4)))))) (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X4) (@ tptp.sin_real Y)) (= X4 Y))))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X4))))))) (= (@ tptp.cos_real _let_216) _let_220) (= (@ tptp.sin_real _let_216) _let_219) (= (@ tptp.cos_real _let_215) _let_219) (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 ((X4 tptp.complex)) (let ((_let_1 (@ tptp.cos_complex X4))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_2)))) (= (@ tptp.cos_complex (@ _let_3 X4)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.cos_real X4))) (let ((_let_2 (@ tptp.bit1 tptp.one))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_2)))) (= (@ tptp.cos_real (@ _let_3 X4)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat _let_2)))) (@ _let_3 _let_1))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) tptp.zero_zero_real)))) (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X4) Y))))))))) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X4))))))) (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 ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X4)))))) (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (or (exists ((X tptp.nat)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X tptp.nat)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((X4 tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real X4) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X4 tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X4)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.sin_real X4) 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) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (= (@ tptp.cos_real X4) 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)) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))) (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.zero_zero_real) (or (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X4 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= X4 (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cos_real _let_4) tptp.zero_zero_real)) (= (@ tptp.tan_real _let_4) (@ (@ tptp.divide_divide_real (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)))) (let ((_let_4 (@ _let_3 X4))) (=> (not (= (@ tptp.cos_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cos_complex _let_4) tptp.zero_zero_complex)) (= (@ tptp.tan_complex _let_4) (@ (@ tptp.divide1717551699836669952omplex (@ _let_3 _let_2)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X4))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X4) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X4)) (@ tptp.numeral_numeral_nat _let_1))))))))) (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 ((X4 tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X4)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X4) (@ (@ tptp.ord_less_eq_real X4) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))) (forall ((A tptp.real)) (= (@ (@ tptp.powr_real tptp.one_one_real) A) tptp.one_one_real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.powr_real X4) tptp.zero_zero_real))) (let ((_let_2 (= X4 tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))) (forall ((X4 tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) A)) (not (= X4 tptp.zero_zero_real)))) (forall ((A tptp.real) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real) (= A tptp.zero_zero_real))) (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X4) tptp.one_one_real) (= X4 tptp.zero_zero_real)))) (forall ((X4 tptp.real)) (= (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) tptp.one_one_real) X4))) (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N2))))) (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))) (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X4) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X4)) X4)))))) (forall ((X4 tptp.real) (N2 tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N2)) tptp.pi))) (@ tptp.tan_real X4))) (forall ((T2 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T2)) (@ tptp.sin_real T2))) tptp.one_one_real)) (forall ((X4 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N2))))) (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X4))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X4)))) (forall ((A tptp.real) (X4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X4)) tptp.zero_zero_real))) (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X4) A)))))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X4) Y))) (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real A) B))))) (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))) (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))) (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X4) A)))))) (forall ((A tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A)))))) (forall ((A tptp.real) (X4 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 X4) (@ _let_1 Y)) (= X4 Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X4) Y)))))) (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X4) A)))))) (forall ((A tptp.real) (B tptp.real) (X4 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) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) B))))))) (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X4) A)) tptp.one_one_real)))))) (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X4) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((X4 tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X4) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X4) A)) (@ (@ tptp.powr_real Y) A))))))) (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))) (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))) (forall ((X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.times_times_real (@ _let_1 A)) (@ _let_1 B))))) (forall ((W tptp.real) (Z1 tptp.real) (Z22 tptp.real)) (let ((_let_1 (@ tptp.powr_real W))) (= (@ _let_1 (@ (@ tptp.minus_minus_real Z1) Z22)) (@ (@ tptp.divide_divide_real (@ _let_1 Z1)) (@ _let_1 Z22))))) _let_218 _let_217 (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X4) N2)))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X4))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X4)) Y) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real X4) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X4)) Y))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X4) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X4)))))) (forall ((X4 tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 A))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.times_times_real X4) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X4))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X4)) Y) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B) Y)))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X4)) Y))))) (forall ((B tptp.real) (X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X4) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X4)))))) (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X4) A)) A))))) (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X4)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X4))))) (= (@ tptp.tan_real _let_141) tptp.one_one_real) (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.plus_plus_real (@ _let_1 X4)) Y) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B) Y)))))))))) (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X4))))))))) (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X4)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X4))))))))) (= (@ tptp.tan_real _let_216) _let_214) (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 ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))) (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) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X4))))))) (forall ((Y tptp.real) (X4 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 X4) (=> (@ (@ tptp.ord_less_real X4) _let_2) (= (@ _let_1 X4) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X4))))))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X4) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) (@ 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_141)) _let_24) (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))) (forall ((B tptp.real) (X4 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 X4) (= (@ (@ tptp.minus_minus_real (@ _let_1 X4)) Y) (@ _let_1 (@ (@ tptp.times_times_real X4) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X4) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y)) (@ (@ tptp.divide_divide_real (@ tptp.sin_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.tan_complex X4)) (@ tptp.tan_complex Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X4)))) (forall ((X4 tptp.real) (N2 tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.powr_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat N2)))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X5) (@ (@ tptp.ord_less_real X5) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X5) Y))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X4)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X4)) tptp.zero_zero_real)))) (forall ((X4 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 X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))))))) (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X4))) tptp.one_one_real))) (= (@ tptp.tan_real _let_215) (@ _let_180 _let_214)) (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (=> (= (@ tptp.tan_real X4) Y) (= (@ tptp.arctan Y) X4)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_real X4) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X4)) X4))))) (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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.cos_real Y))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (=> (not (= _let_1 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.tan_real X4)) (@ tptp.tan_real Y))) (@ (@ tptp.divide_divide_real (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y))) (@ (@ tptp.times_times_real _let_2) _let_1)))))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.cos_complex Y))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (=> (not (= _let_1 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ tptp.tan_complex X4)) (@ tptp.tan_complex Y))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y))) (@ (@ tptp.times_times_complex _let_2) _let_1)))))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.minus_minus_real X4) Y))) (=> (not (= (@ tptp.cos_real X4) 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 ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.minus_minus_complex X4) Y))) (=> (not (= (@ tptp.cos_complex X4) 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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tan_real Y))) (let ((_let_2 (@ tptp.tan_real X4))) (let ((_let_3 (@ (@ tptp.plus_plus_real X4) Y))) (=> (not (= (@ tptp.cos_real X4) 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 ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tan_complex Y))) (let ((_let_2 (@ tptp.tan_complex X4))) (let ((_let_3 (@ (@ tptp.plus_plus_complex X4) Y))) (=> (not (= (@ tptp.cos_complex X4) 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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (exists ((Z2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z2) (@ (@ tptp.ord_less_real Z2) _let_1) (= (@ tptp.tan_real Z2) X4)))))) (= tptp.tan_real (lambda ((X tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide_divide_real (@ tptp.sin_real _let_1)) (@ (@ tptp.plus_plus_real (@ tptp.cos_real _let_1)) tptp.one_one_real))))) (= tptp.tan_complex (lambda ((X tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) X))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sin_complex _let_1)) (@ (@ tptp.plus_plus_complex (@ tptp.cos_complex _let_1)) tptp.one_one_complex))))) _let_211 (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X4)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))) (= tptp.arsinh_real (lambda ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) tptp.one_one_real)) (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X4 tptp.real)) (= (= (@ tptp.real_V1803761363581548252l_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))) (forall ((X4 tptp.real)) (= (= (@ tptp.real_V4546457046886955230omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_real))) (= (@ tptp.real_V1803761363581548252l_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.real_V4546457046886955230omplex tptp.one_one_real) tptp.one_one_complex) (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.numeral_numeral_real W)) (@ tptp.numera6690914467698888265omplex W))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y)))) (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real (@ tptp.real_V1803761363581548252l_real X4)) N2))) (forall ((X4 tptp.real) (N2 tptp.nat)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_complex (@ tptp.real_V4546457046886955230omplex X4)) N2))) (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real) _let_210 (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V1803761363581548252l_real _let_1) _let_1))) (forall ((W tptp.num)) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cos_real _let_207) _let_24) (= (@ tptp.cos_complex _let_192) _let_189) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))) (forall ((X4 tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) tptp.one_one_real)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))) (forall ((X4 tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) tptp.one_one_complex)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))) (forall ((X4 tptp.real) (B tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real B))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real X4)) _let_1)) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) _let_1))))) (forall ((X4 tptp.real) (B tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.numera6690914467698888265omplex B))) (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real X4) (@ tptp.numeral_numeral_real B))))) (= (@ tptp.arccos tptp.zero_zero_real) _let_34) (= (@ tptp.arcsin tptp.one_one_real) _let_34) (= (@ tptp.cos_real _let_208) tptp.zero_zero_real) (= (@ tptp.cos_complex _let_206) tptp.zero_zero_complex) (= (@ tptp.sin_real _let_208) tptp.one_one_real) (= (@ tptp.sin_complex _let_206) tptp.one_one_complex) (= (@ tptp.arcsin _let_24) _let_35) (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V1803761363581548252l_real (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real X4)) (@ tptp.real_V1803761363581548252l_real Y))))) (forall ((Y tptp.real) (X4 tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.divide_divide_real X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex X4)) (@ tptp.real_V4546457046886955230omplex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X4)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X4)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X4))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X4) (@ tptp.arccos Y)) (= X4 Y)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X4)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X4)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X4) (@ tptp.arcsin Y)) (= X4 Y))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1803761363581548252l_real _let_1)) tptp.one_one_real))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X4))) (@ (@ tptp.ord_less_real _let_1) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex _let_1)) tptp.one_one_complex))))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X4)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X4)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X4))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X4)) X4)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X4)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X4) Y))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))) (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1803761363581548252l_real B)) (@ tptp.real_V1803761363581548252l_real A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((B tptp.real) (A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.real_V4546457046886955230omplex B)) (@ tptp.real_V4546457046886955230omplex A)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))) (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))) (forall ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X4)) tptp.zero_zero_real))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (= (@ tptp.arccos (@ tptp.cos_real X4)) (@ tptp.uminus_uminus_real X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X4)) tptp.zero_zero_real))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X4)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X4))))) _let_205 _let_204 (= tptp.sin_real (lambda ((X tptp.real)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)))) (= tptp.sin_complex (lambda ((X tptp.complex)) (@ tptp.cos_complex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) X)))) (forall ((X4 tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.sin_real X4)) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real (@ tptp.real_V1803761363581548252l_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X4 tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.sin_complex X4)) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))) (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))) (forall ((Y tptp.real)) (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 ((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)) (=> (@ (@ 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 ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X4)) X4))))) (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 ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X4))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X4)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))) (forall ((X4 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)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X4))))))))) (forall ((B tptp.nat) (K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))))))) (forall ((N2 tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N2))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X4)) tptp.zero_zero_real)))) (forall ((B tptp.nat) (N2 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N2)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N2))))))) (forall ((X4 tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X4))) (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N))))) (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N))))) (forall ((X4 tptp.rat)) (= (= (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_rat N))))) (forall ((X4 tptp.real)) (= (= (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)) X4) (exists ((N tptp.int)) (= X4 (@ tptp.ring_1_of_int_real N))))) (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_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))) (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N2)) (= Z (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N2)) (= Z (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N2)) (= Z (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_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_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 ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.numeral_numeral_real V)) (@ tptp.numeral_numeral_int V))) (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.numeral_numeral_rat V)) (@ tptp.numeral_numeral_int V))) (= (@ tptp.archim6058952711729229775r_real tptp.one_one_real) tptp.one_one_int) (= (@ tptp.archim3151403230148437115or_rat tptp.one_one_rat) tptp.one_one_int) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N2))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N2))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N2))) (forall ((Z tptp.int) (N2 tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N2)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N2))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X4)) (= (@ (@ tptp.power_power_int B) W) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X4)) (= (@ (@ tptp.power_power_int B) W) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X4)) (= (@ (@ tptp.power_power_int B) W) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X4)) (= (@ (@ tptp.power_power_int B) W) X4))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X4) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X4) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X4) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X4) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X4 (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim2889992004027027881ng_rat X4)) Z))) (forall ((X4 tptp.real) (Z tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real X4)) Z))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_rat _let_1)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_real _let_1)))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) K))) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 _let_1)) (@ tptp.ring_1_of_int_int _let_1)))) (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.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)) (= (@ (@ 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 ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N2)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N2)))) (forall ((Z tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))) (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N2)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N2)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)) Z))) (forall ((N2 tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.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_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 ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4))) (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 ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.zero_zero_rat))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real V)) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat V)) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.zero_zero_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real V)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat V)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) tptp.one_one_real))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat))) (forall ((V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (forall ((V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) (@ tptp.numeral_numeral_real V))) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 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 X4)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((X4 tptp.real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.minus_minus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int))) (forall ((X4 tptp.rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.minus_minus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((B tptp.int) (W tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X4))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((X4 tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X4)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X4) (@ (@ tptp.power_power_int B) W)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_real Z)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) (@ tptp.ring_1_of_int_int Z)))) (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (forall ((X4 tptp.num) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int V)) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)) X4))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) tptp.one_one_real)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.numeral_numeral_int V)) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) tptp.one_one_rat)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ (@ tptp.ord_less_rat X4) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) X4))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X4)) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X4)) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((Y tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X4))) N2) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))) (forall ((X4 tptp.num) (N2 tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2) Y))) (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))) (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))) (forall ((N2 tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.zero_zero_real)) (forall ((N2 tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N2))) tptp.one_one_real)) (forall ((V tptp.num) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)) X4))) (forall ((V tptp.num) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)) X4))) (forall ((X4 tptp.real) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) tptp.one_one_real)))) (forall ((X4 tptp.rat) (V tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) tptp.one_one_rat)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((X4 tptp.num) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)) A))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (forall ((A tptp.int) (X4 tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X4))) N2)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X4))) N2)))) (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 ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z2)))) (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z2)))) (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z2)) X4))) (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z2)) X4))) (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z2)))) (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z2)))) (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) X4)))) (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) X4)))) (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) (@ tptp.ring_1_of_int_real Z))))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) (@ tptp.ring_1_of_int_rat Z))))) (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real K)) (@ tptp.ring_1_of_int_real L))) (@ (@ tptp.divide_divide_int K) L))) (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat K)) (@ tptp.ring_1_of_int_rat L))) (@ (@ tptp.divide_divide_int K) L))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real X4))) X4)) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat X4))) X4)) (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real Z)))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) X4))) (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) X4))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (=> (= X4 (@ tptp.ring_1_of_int_real _let_1)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_int _let_1) N2))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (=> (= X4 (@ tptp.ring_1_of_int_rat _let_1)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_int _let_1) N2))))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_real R3) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3))) tptp.one_one_real))) (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N2))))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real R3) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3))) tptp.one_one_real))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3)))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R3)))) (forall ((P (-> tptp.int Bool)) (T2 tptp.real)) (= (@ P (@ tptp.archim6058952711729229775r_real T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_eq_real _let_1) T2) (@ (@ tptp.ord_less_real T2) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))) (@ P I3)))))) (forall ((P (-> tptp.int Bool)) (T2 tptp.rat)) (= (@ P (@ tptp.archim3151403230148437115or_rat T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_eq_rat _let_1) T2) (@ (@ tptp.ord_less_rat T2) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))) (@ P I3)))))) (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim6058952711729229775r_real X4) A) (and (@ (@ tptp.ord_less_eq_real _let_1) X4) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))) (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim3151403230148437115or_rat X4) A) (and (@ (@ tptp.ord_less_eq_rat _let_1) X4) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))) (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) Z))))) (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_eq_rat _let_1) X4) (=> (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim3151403230148437115or_rat X4) Z))))) (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim6058952711729229775r_real X4)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))) (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim3151403230148437115or_rat X4)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))) (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) Z) (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) Z) (@ (@ tptp.ord_less_rat X4) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim6058952711729229775r_real X4))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real _let_1)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archim3151403230148437115or_rat X4))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))) (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_eq_real _let_1) X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X4) N2))))) (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 ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)) (@ (@ tptp.ord_less_rat X4) Y))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim7802044766580827645g_real X4))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim2889992004027027881ng_rat X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))) (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)) P2))) (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)) P2))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))) (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))) (forall ((K tptp.int)) (= (@ tptp.ring_1_of_int_int (@ tptp.bit_ri7919022796975470100ot_int K)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.ring_1_of_int_int K)))) (forall ((K tptp.int) (L tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se6526347334894502574or_int K) L)) (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N2))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real P2) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)))) (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat P2) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)))) (forall ((X4 tptp.real) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) A))) (forall ((X4 tptp.rat) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) A))) (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ tptp.ring_1_of_int_real Z)))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ tptp.ring_1_of_int_rat Z)))) (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) X4))) (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) X4))) (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4)))) (forall ((D tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N2) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real D))))) (forall ((R3 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real R3)))) R3))) (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R3) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat R3)))) R3))) (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) tptp.one_one_int) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) tptp.one_one_int) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)))) (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))) (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat A))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.nat2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.divide_divide_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N2))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N2)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) tptp.zero_zero_nat))) (forall ((X4 tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X4)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X4) (@ (@ tptp.ord_less_real X4) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))) (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 ((N2 tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X4)))) (forall ((N2 tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))) (forall ((N2 tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))) (forall ((N2 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X4)))) (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 ((N2 tptp.int) (X4 tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X4)))) (forall ((N2 tptp.int) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))) (forall ((N2 tptp.int) (X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))) (forall ((N2 tptp.int) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N2))) X4) (or (= N2 tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X4)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N2)))) (forall ((X4 tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X4)) A) (@ (@ tptp.ord_less_eq_nat X4) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))) (forall ((X4 tptp.real)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X5)) X4) (@ (@ tptp.ord_less_real X4) (@ 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)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))) (forall ((X4 tptp.rat)) (exists ((X5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X5)) X4) (@ (@ tptp.ord_less_rat X4) (@ 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)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y4) tptp.one_one_int)))) (= Y4 X5)))))) (forall ((X4 tptp.real)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z2)) X4) (@ (@ tptp.ord_less_real X4) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))) (forall ((X4 tptp.rat)) (exists ((Z2 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z2)) X4) (@ (@ tptp.ord_less_rat X4) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z2) tptp.one_one_int)))))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R3))) (@ (@ tptp.plus_plus_real R3) tptp.one_one_real))) (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R3))) (@ (@ tptp.plus_plus_rat R3) tptp.one_one_rat))) (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))) (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))) (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)))) (forall ((R3 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real R3))) tptp.one_one_real)) R3)) (forall ((R3 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat R3))) tptp.one_one_rat)) R3)) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim7802044766580827645g_real X4)) (@ tptp.archim6058952711729229775r_real X4))) tptp.one_one_int)) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.archim2889992004027027881ng_rat X4)) (@ tptp.archim3151403230148437115or_rat X4))) tptp.one_one_int)) (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ tptp.ring_1_of_int_rat X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X4))) (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ tptp.ring_1_of_int_real X4)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)) X4))) (forall ((N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N2)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X4)) (@ _let_1 X4)))) (= tptp.ord_less_eq_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M6)) tptp.one_one_real)))) (= tptp.ord_less_int (lambda ((N tptp.int) (M6 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M6)))) (forall ((K tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B)))) (forall ((X4 tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X4) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X4) D))) _let_1))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B))) (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B))) (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N2)) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X4)) N2)))) (forall ((P (-> tptp.int Bool)) (T2 tptp.real)) (= (@ P (@ tptp.archim7802044766580827645g_real T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real I3))) (=> (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) T2) (@ (@ tptp.ord_less_eq_real T2) _let_1)) (@ P I3)))))) (forall ((P (-> tptp.int Bool)) (T2 tptp.rat)) (= (@ P (@ tptp.archim2889992004027027881ng_rat T2)) (forall ((I3 tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat I3))) (=> (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) T2) (@ (@ tptp.ord_less_eq_rat T2) _let_1)) (@ P I3)))))) (forall ((X4 tptp.real) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real A))) (= (= (@ tptp.archim7802044766580827645g_real X4) A) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1))))) (forall ((X4 tptp.rat) (A tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_rat A))) (= (= (@ tptp.archim2889992004027027881ng_rat X4) A) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1))))) (forall ((Z tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real Z))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) _let_1) (= (@ tptp.archim7802044766580827645g_real X4) Z))))) (forall ((Z tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat Z))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) _let_1) (= (@ tptp.archim2889992004027027881ng_rat X4) Z))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real X4)))) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) X4) (@ (@ tptp.ord_less_eq_real X4) _let_1)))) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat X4)))) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)) X4) (@ (@ tptp.ord_less_eq_rat X4) _let_1)))) _let_203 _let_202 (forall ((X4 tptp.real) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim7802044766580827645g_real X4)) Z) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)))) (forall ((X4 tptp.rat) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.archim2889992004027027881ng_rat X4)) Z) (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)))) (forall ((Z tptp.int) (X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim2889992004027027881ng_rat X4)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat)) X4))) (forall ((Z tptp.int) (X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_int Z) (@ tptp.archim7802044766580827645g_real X4)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real)) X4))) (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4))))) (forall ((N2 tptp.int) (X4 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N2)) (@ tptp.ring_1_of_int_real X4))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N2) X4)))) tptp.one_one_real)) (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_eq_real P2) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) Q3)))) (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_eq_rat P2) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) Q3)))) (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)))) _let_201 _let_200 _let_199 _let_198 _let_197 (forall ((Q3 tptp.rat) (P2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Q3) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.divide_divide_rat P2) Q3)))) tptp.one_one_rat)) Q3)) P2))) (forall ((Q3 tptp.real) (P2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Q3) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real P2) Q3)))) tptp.one_one_real)) Q3)) P2))) (forall ((N2 tptp.int) (X4 tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N2))) (=> (@ (@ tptp.ord_less_real _let_1) X4) (=> (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim7802044766580827645g_real X4) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))) (forall ((N2 tptp.int) (X4 tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat N2))) (=> (@ (@ tptp.ord_less_rat _let_1) X4) (=> (@ (@ tptp.ord_less_eq_rat X4) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (= (@ tptp.archim2889992004027027881ng_rat X4) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int)))))) (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) tptp.one_one_real) (exists ((X tptp.int)) (= X4 (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))) (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 ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ (@ tptp.ord_less_real X4) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X4)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N2) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N2) _let_2))))) tptp.one_one_int))))))) (forall ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.cot_real X4))) (forall ((X4 tptp.real)) (= (= (@ tptp.cos_real X4) 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)) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X4 tptp.real)) (= (= (@ tptp.sin_real X4) 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) (= X4 (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))) (forall ((X4 tptp.real) (I2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ 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) X4) (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)))))))))))) (forall ((X4 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 X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X4) _let_1)) (= (@ tptp.archim8280529875227126926d_real X4) Y)))))) (forall ((X4 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 X4) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X4) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X4) Y)))))) (forall ((X4 tptp.rat) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) (@ tptp.ring_1_of_int_rat N2)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X4) N2))) (forall ((X4 tptp.real) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) (@ tptp.ring_1_of_int_real N2)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X4) N2))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) X4))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) X4))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4)))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4)))) (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N2)) (@ tptp.numeral_numeral_int N2))) (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int) (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int) (forall ((N2 tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (forall ((N2 tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X4) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X4)) (@ tptp.archim7778729529865785530nd_rat Y)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim8280529875227126926d_real X4))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim7778729529865785530nd_rat X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_int (@ tptp.archim8280529875227126926d_real X4)) (@ tptp.archim7802044766580827645g_real X4))) (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)))))) _let_196 _let_195 (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X4))) (@ (@ tptp.plus_plus_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X4))) (@ (@ tptp.plus_plus_rat X4) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))) (= tptp.archim8280529875227126926d_real (lambda ((X tptp.real)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.archim2898591450579166408c_real X))) (@ tptp.archim7802044766580827645g_real X)) (@ tptp.archim6058952711729229775r_real X)))) (= tptp.archim7778729529865785530nd_rat (lambda ((X tptp.rat)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ tptp.archimedean_frac_rat X))) (@ tptp.archim2889992004027027881ng_rat X)) (@ tptp.archim3151403230148437115or_rat X)))) (forall ((X4 tptp.real) (N2 tptp.int)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.powr_real X4) (@ tptp.ring_1_of_int_real N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N2))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N2)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N2)))))))))))) (= (@ tptp.cis _let_194) tptp.one_one_complex) (forall ((N2 tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N2))) (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)))))) (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 ((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.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)) (= (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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))) _let_188 _let_187 _let_186 (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 ((X4 tptp.rat)) (= (= (@ tptp.inverse_inverse_rat X4) tptp.one_one_rat) (= X4 tptp.one_one_rat))) (forall ((X4 tptp.real)) (= (= (@ tptp.inverse_inverse_real X4) tptp.one_one_real) (= X4 tptp.one_one_real))) (forall ((X4 tptp.complex)) (= (= (@ tptp.invers8013647133539491842omplex X4) tptp.one_one_complex) (= X4 tptp.one_one_complex))) (= (@ tptp.inverse_inverse_rat tptp.one_one_rat) tptp.one_one_rat) (= (@ tptp.inverse_inverse_real tptp.one_one_real) tptp.one_one_real) (= (@ tptp.invers8013647133539491842omplex tptp.one_one_complex) tptp.one_one_complex) (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)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ tptp.inverse_inverse_rat 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.abs_abs_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.abs_abs_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)) (let ((_let_1 (@ tptp.sgn_sgn_rat A))) (= (@ tptp.inverse_inverse_rat _let_1) _let_1))) (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sgn_sgn_real A))) (= (@ tptp.inverse_inverse_real _let_1) _let_1))) (forall ((A tptp.rat)) (= (@ tptp.sgn_sgn_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat (@ tptp.sgn_sgn_rat A)))) (forall ((A tptp.real)) (= (@ tptp.sgn_sgn_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real (@ tptp.sgn_sgn_real A)))) (forall ((A tptp.complex)) (= (@ tptp.sgn_sgn_complex (@ tptp.invers8013647133539491842omplex A)) (@ tptp.invers8013647133539491842omplex (@ tptp.sgn_sgn_complex 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)) (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)) (= (@ (@ 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)) (= (@ (@ 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)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ tptp.inverse_inverse_rat A)) (@ _let_1 A)))) (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)) (= (@ (@ 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)) (= (@ (@ 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) (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) (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 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 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 ((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 ((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)) (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real) (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)) (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)) (=> (@ (@ 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)) (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) (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)) (=> (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 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 (@ tptp.inverse_inverse_rat A)) 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 ((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)))) (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.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 ((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)))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex _let_192) _let_193))) tptp.one_one_complex) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_193) _let_192)) tptp.imaginary_unit)) tptp.one_one_complex) _let_191 (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) _let_50) _let_189) (= (@ tptp.cis _let_35) _let_176) (forall ((Y tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real Y))) (let ((_let_2 (@ tptp.times_times_real X4))) (=> (= (@ (@ tptp.times_times_real Y) X4) (@ _let_2 Y)) (= (@ (@ tptp.times_times_real _let_1) X4) (@ _let_2 _let_1)))))) (forall ((Y tptp.complex) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex Y))) (let ((_let_2 (@ tptp.times_times_complex X4))) (=> (= (@ (@ tptp.times_times_complex Y) X4) (@ _let_2 Y)) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ _let_2 _let_1)))))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real A)) N2) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real A) N2)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex A)) N2) (@ tptp.invers8013647133539491842omplex (@ (@ tptp.power_power_complex A) N2)))) (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))) _let_188 _let_187 _let_186 (forall ((A tptp.rat)) (=> (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))) (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) (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) (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)) (=> (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)) (= (@ 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)) (not (= (@ tptp.inverse_inverse_rat A) tptp.zero_zero_rat)))) (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 ((R3 tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real R3) (@ tptp.real_V7735802525324610683m_real X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.inverse_inverse_real X4))) (@ tptp.inverse_inverse_real R3))))) (forall ((R3 tptp.real) (X4 tptp.complex)) (=> (@ (@ tptp.ord_less_eq_real R3) (@ tptp.real_V1022390504157884413omplex X4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.invers8013647133539491842omplex X4))) (@ tptp.inverse_inverse_real R3))))) (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)) (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)) (=> (@ (@ 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)) (=> (@ (@ 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)) (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)) (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)) (=> (@ (@ 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)) (=> (@ (@ 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) (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) (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)) (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)) (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)) (=> (@ (@ 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)) (=> (@ (@ 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 (@ 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 (@ 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)) (=> (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) (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)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat (@ 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) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.one_one_rat) (= (@ tptp.inverse_inverse_rat A) B))) (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))) (= (@ tptp.inverse_inverse_real _let_185) _let_185) (= (@ tptp.invers8013647133539491842omplex _let_184) _let_184) _let_183 _let_182 (= 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_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)))) _let_181 (= tptp.inverse_inverse_real _let_180) (= tptp.invers8013647133539491842omplex (@ tptp.divide1717551699836669952omplex tptp.one_one_complex)) (forall ((X4 tptp.real) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ tptp.inverse_inverse_real X4))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))) (forall ((X4 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex X4))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))) (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X4) M))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X4)) N2))) (= (@ (@ tptp.times_times_real _let_1) _let_2) (@ (@ tptp.times_times_real _let_2) _let_1))))) (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X4) M))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X4)) N2))) (= (@ (@ tptp.times_times_complex _let_1) _let_2) (@ (@ tptp.times_times_complex _let_2) _let_1))))) (forall ((Xa tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real Xa)))) (= (@ (@ tptp.times_times_real _let_1) X4) (@ (@ tptp.times_times_real X4) _let_1)))) (forall ((Xa tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex (@ tptp.semiri8010041392384452111omplex Xa)))) (= (@ (@ tptp.times_times_complex _let_1) X4) (@ (@ tptp.times_times_complex X4) _let_1)))) (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 ((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))))) (= tptp.divide_divide_real (lambda ((X tptp.real) (Y5 tptp.real)) (@ (@ tptp.times_times_real X) (@ tptp.inverse_inverse_real Y5)))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4))) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.archim2898591450579166408c_real X4)) tptp.one_one_real)) (forall ((X4 tptp.rat)) (@ (@ tptp.ord_less_rat (@ tptp.archimedean_frac_rat X4)) tptp.one_one_rat)) (forall ((X4 tptp.real)) (= (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) tptp.one_one_real)) (@ tptp.archim2898591450579166408c_real X4))) (forall ((X4 tptp.rat)) (= (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) tptp.one_one_rat)) (@ tptp.archimedean_frac_rat X4))) (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 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 (@ 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 (@ 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 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 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 (@ 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 ((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 ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4)))) (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)) (=> (@ (@ 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 ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))) (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)) (=> (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) (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.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 (@ (@ 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 (@ (@ 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.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) (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)) (=> (not (= A tptp.zero_zero_rat)) (= (@ tptp.inverse_inverse_rat A) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))) (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.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) (N2 tptp.nat)) (let ((_let_1 (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real N2)))) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N2) K)))))) (forall ((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 ((X4 tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X4) Y) tptp.imaginary_unit) (and (= X4 tptp.zero_zero_real) (= Y tptp.one_one_real)))) (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.times_times_rat A) B))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.inverse_inverse_rat A)) (@ tptp.inverse_inverse_rat B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) _let_1) (@ (@ tptp.ord_less_eq_rat B) A)) (=> (@ (@ tptp.ord_less_eq_rat _let_1) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)))))) (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)))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real A) B))) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real A)) (@ tptp.inverse_inverse_real B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real B) A)) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) B)))))) (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat A))))) (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real A))))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat X4)) tptp.one_one_rat) (or (@ (@ tptp.ord_less_eq_rat X4) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real X4)) tptp.one_one_real) (or (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) X4)))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.inverse_inverse_rat X4)) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_eq_rat X4) tptp.one_one_rat)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.inverse_inverse_real X4)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))) (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.inverse_inverse_rat B))) (let ((_let_2 (@ tptp.inverse_inverse_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat _let_2) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat _let_2) (@ (@ tptp.minus_minus_rat A) B))) _let_1)))))))) (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.inverse_inverse_real B))) (let ((_let_2 (@ tptp.inverse_inverse_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real _let_2) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.minus_minus_real A) B))) _let_1)))))))) (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.invers8013647133539491842omplex B))) (let ((_let_2 (@ tptp.invers8013647133539491842omplex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex _let_2) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex _let_2) (@ (@ tptp.minus_minus_complex A) B))) _let_1)))))))) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) X4)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) X4)))) (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.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 ((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 ((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.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 ((A tptp.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex A) _let_3) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))) (forall ((A tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_real A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_real 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 _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.complex) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.gbinomial_complex A))) (let ((_let_3 (@ _let_2 K))) (= (@ (@ tptp.times_times_complex _let_3) A) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex K)) _let_3)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex _let_1)) (@ _let_2 _let_1)))))))) (forall ((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 ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ P E2))))) (forall ((P (-> tptp.real Bool)) (E2 tptp.real)) (=> (forall ((D3 tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E) (=> (@ P D3) (@ P E)))) (=> (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) E2) (@ P E2))))) (forall ((E2 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N)))) (and (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E2)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.sqrt X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.divide_divide_real _let_1) X4) (@ tptp.inverse_inverse_real _let_1))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X4))))) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X4) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_rat (@ tptp.inverse_inverse_rat (@ tptp.semiri681578069525770553at_rat N3))) X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ (@ tptp.ord_less_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))) X4))))) (forall ((X4 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (not (= X4 tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.power_power_rat (@ tptp.inverse_inverse_rat X4)) M))))))) (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (not (= X4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real X4)) M))))))) (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (not (= X4 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N2) M)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex X4)) M))))))) (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.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.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) (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) (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) (M tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.gbinomial_complex A))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (= (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex M)) K)) (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex A) (@ tptp.semiri8010041392384452111omplex K))) (@ (@ tptp.minus_minus_nat M) K))))))) (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 ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X4) (= (@ _let_1 (@ tptp.inverse_inverse_real X4)) (@ tptp.uminus_uminus_real (@ _let_1 X4))))))))) (forall ((X4 tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) X4) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))) (forall ((X4 tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) X4) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X4) (@ (@ tptp.ord_less_rat X4) tptp.one_one_rat)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y)))) (let ((_let_2 (@ tptp.archim2898591450579166408c_real (@ (@ tptp.plus_plus_real X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)))))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y)))) (let ((_let_2 (@ tptp.archimedean_frac_rat (@ (@ tptp.plus_plus_rat X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat _let_1) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_rat _let_1) tptp.one_one_rat)))))))) (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))))))) (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.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.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)))))) (= 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_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)))) (= 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)))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (= (@ (@ tptp.times_times_complex (@ _let_1 K)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) K)) (@ (@ tptp.times_times_complex (@ _let_1 N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.semiri8010041392384452111omplex K))) tptp.one_one_complex)) N2))))) (forall ((K tptp.nat) (N2 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 N2))) tptp.one_one_rat)) K)) (@ (@ tptp.times_times_rat (@ _let_1 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.semiri681578069525770553at_rat K))) tptp.one_one_rat)) N2))))) (forall ((K tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (= (@ (@ tptp.times_times_real (@ _let_1 K)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) K)) (@ (@ tptp.times_times_real (@ _let_1 N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real K))) tptp.one_one_real)) N2))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))) (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 ((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.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 ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X4)))) (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)))))) _let_179 _let_178 _let_177 (= 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_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_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 ((X4 tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X4)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X4)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y)))) (let ((_let_2 (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.archim2898591450579166408c_real X4)) (@ tptp.archim2898591450579166408c_real Y))) tptp.one_one_real))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y)))) (let ((_let_2 (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)))) (let ((_let_3 (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ tptp.archimedean_frac_rat X4)) (@ tptp.archimedean_frac_rat Y))) tptp.one_one_rat))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real X4) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.exp_real X4))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_real X4))) (=> (not (= _let_2 tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real _let_2)) _let_1)))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.cos_complex X4))) (=> (not (= _let_2 tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ tptp.tan_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.invers8013647133539491842omplex _let_2)) _let_1)))))) (= (@ tptp.arg _let_176) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_32)) (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ _let_175 tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex _let_174))) (= (@ tptp.arg tptp.imaginary_unit) _let_34) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_complex))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_real X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X4)) (@ _let_1 X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (or (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real X4)) (@ tptp.archim6058952711729229775r_real Y))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (or (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat)) (= (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.plus_plus_int (@ tptp.archim3151403230148437115or_rat X4)) (@ tptp.archim3151403230148437115or_rat Y))))) (forall ((X4 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.archim2898591450579166408c_real X4)) (not (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real)))) (forall ((X4 tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.archimedean_frac_rat X4)) (not (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat)))) (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)) (forall ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N2)) tptp.ring_1_Ints_real))) (forall ((A tptp.int) (N2 tptp.nat)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.power_power_int A) N2)) tptp.ring_1_Ints_int))) (forall ((A tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N2)) tptp.ring_1_Ints_complex))) (forall ((N2 tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex N2)) tptp.ring_1_Ints_complex)) (forall ((N2 tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real N2)) tptp.ring_1_Ints_real)) (forall ((N2 tptp.num)) (@ (@ tptp.member_int (@ tptp.numeral_numeral_int N2)) tptp.ring_1_Ints_int)) (@ _let_138 tptp.ring_1_Ints_complex) (@ (@ tptp.member_rat tptp.one_one_rat) tptp.ring_1_Ints_rat) (@ (@ tptp.member_int tptp.one_one_int) tptp.ring_1_Ints_int) (@ _let_139 tptp.ring_1_Ints_real) (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (=> (@ (@ tptp.member_complex B) tptp.ring_1_Ints_complex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.ring_1_Ints_complex)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real B) tptp.ring_1_Ints_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.ring_1_Ints_real)))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat B) tptp.ring_1_Ints_rat) (@ (@ tptp.member_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.ring_1_Ints_rat)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int B) tptp.ring_1_Ints_int) (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int A) B)) tptp.ring_1_Ints_int)))) (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (= (= (@ (@ tptp.plus_plus_complex A) A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))) (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))) (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int)))) (forall ((A tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.ring_1_Ints_complex) (not (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) A)) A) tptp.zero_zero_complex)))) (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (not (= (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (not (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_rat (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat A)) (@ tptp.ring_1_of_int_rat B))) tptp.ring_1_Ints_rat))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_int (@ (@ tptp.divide_divide_int (@ tptp.ring_1_of_int_int A)) (@ tptp.ring_1_of_int_int B))) tptp.ring_1_Ints_int))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real A)) (@ tptp.ring_1_of_int_real B))) tptp.ring_1_Ints_real))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex (@ tptp.ring_17405671764205052669omplex A)) (@ tptp.ring_17405671764205052669omplex B))) tptp.ring_1_Ints_complex))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (@ (@ tptp.member_Code_integer (@ (@ tptp.divide6298287555418463151nteger (@ tptp.ring_18347121197199848620nteger A)) (@ tptp.ring_18347121197199848620nteger B))) tptp.ring_11222124179247155820nteger))) (forall ((A tptp.real)) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) A)) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))) (forall ((A tptp.rat)) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat tptp.one_one_rat) A)) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))) (forall ((A tptp.int)) (=> (@ (@ tptp.member_int A) tptp.ring_1_Ints_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (not (= X4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X4))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (not (= X4 tptp.zero_zero_real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.abs_abs_real X4))))) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (not (= X4 tptp.zero_zero_rat)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X4))))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (not (= X4 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.abs_abs_int X4))))) (forall ((X4 tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X4)) tptp.one_one_Code_integer) (= X4 tptp.zero_z3403309356797280102nteger)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= X4 tptp.zero_zero_real)))) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X4)) tptp.one_one_rat) (= X4 tptp.zero_zero_rat)))) (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X4)) tptp.one_one_int) (= X4 tptp.zero_zero_int)))) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.member_Code_integer X4) tptp.ring_11222124179247155820nteger) (=> (@ (@ tptp.member_Code_integer Y) tptp.ring_11222124179247155820nteger) (= (= X4 Y) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X4) Y))) tptp.one_one_Code_integer))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real) (=> (@ (@ tptp.member_real Y) tptp.ring_1_Ints_real) (= (= X4 Y) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X4) Y))) tptp.one_one_real))))) (forall ((X4 tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat) (=> (@ (@ tptp.member_rat Y) tptp.ring_1_Ints_rat) (= (= X4 Y) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X4) Y))) tptp.one_one_rat))))) (forall ((X4 tptp.int) (Y tptp.int)) (=> (@ (@ tptp.member_int X4) tptp.ring_1_Ints_int) (=> (@ (@ tptp.member_int Y) tptp.ring_1_Ints_int) (= (= X4 Y) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X4) Y))) tptp.one_one_int))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X4)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X4))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.archim2898591450579166408c_real (@ tptp.uminus_uminus_real X4)))) (let ((_let_2 (@ (@ tptp.member_real X4) tptp.ring_1_Ints_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.archim2898591450579166408c_real X4)))))))) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.archimedean_frac_rat (@ tptp.uminus_uminus_rat X4)))) (let ((_let_2 (@ (@ tptp.member_rat X4) tptp.ring_1_Ints_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.archimedean_frac_rat X4)))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim6058952711729229775r_real A)) (@ tptp.archim6058952711729229775r_real B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim6058952711729229775r_real (@ (@ tptp.times_times_real A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_real (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_rat (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim3151403230148437115or_rat A)) (@ tptp.archim3151403230148437115or_rat B)))) (@ tptp.ring_1_of_int_int (@ tptp.archim3151403230148437115or_rat (@ (@ tptp.times_times_rat A) B))))))) (forall ((X4 tptp.real) (A tptp.real)) (= (= (@ tptp.archim2898591450579166408c_real X4) A) (and (@ (@ tptp.member_real (@ (@ tptp.minus_minus_real X4) A)) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real A) tptp.one_one_real)))) (forall ((X4 tptp.rat) (A tptp.rat)) (= (= (@ tptp.archimedean_frac_rat X4) A) (and (@ (@ tptp.member_rat (@ (@ tptp.minus_minus_rat X4) A)) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.member_real A) tptp.ring_1_Ints_real) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim7802044766580827645g_real (@ (@ tptp.times_times_real A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim7802044766580827645g_real A)) (@ tptp.archim7802044766580827645g_real B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat B))))))) (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.member_rat A) tptp.ring_1_Ints_rat) (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int (@ tptp.archim2889992004027027881ng_rat (@ (@ tptp.times_times_rat A) B)))) (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int (@ tptp.archim2889992004027027881ng_rat A)) (@ tptp.archim2889992004027027881ng_rat 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 ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.zero_zero_real))) (forall ((N2 tptp.real)) (=> (@ (@ tptp.member_real N2) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N2)) tptp.one_one_real))) (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)))))) _let_173 _let_172 (forall ((Z tptp.complex) (X4 tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X4)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.pi) (= (@ tptp.arg Z) X4))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X4) (@ tptp.inverse_inverse_real X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X4)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_2)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_2)))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ tptp.cosh_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_2)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_2)))))) (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 ((X4 tptp.real)) (= (= (@ tptp.cosh_real X4) tptp.zero_zero_real) (= (@ (@ tptp.power_power_real (@ tptp.exp_real X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus_uminus_real tptp.one_one_real)))) (forall ((X4 tptp.complex)) (= (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex X4)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ (@ tptp.bit_se7788150548672797655nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1))))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N2 tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se545348938243370406it_int N2) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))) (forall ((N2 tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se547839408752420682it_nat N2) A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) A)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.plus_plus_nat M) N2)) A))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat M) (@ (@ tptp.bit_se547839408752420682it_nat N2) A)) (@ (@ tptp.bit_se547839408752420682it_nat (@ (@ tptp.plus_plus_nat M) N2)) A))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int A) B)) (@ (@ tptp.bit_se6526347334894502574or_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.bit_se6528837805403552850or_nat A) B)) (@ (@ tptp.bit_se6528837805403552850or_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (L tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N2) tptp.zero_zero_int) L) (@ (@ tptp.bit_se545348938243370406it_int N2) L))) (= (@ tptp.cosh_complex tptp.zero_zero_complex) tptp.one_one_complex) (= (@ tptp.cosh_real tptp.zero_zero_real) tptp.one_one_real) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.suc N2)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger N2) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_int K)) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.numeral_numeral_nat L)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.pred_numeral L)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se7788150548672797655nteger N2) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_ri7632146776885996613nteger (@ tptp.bit_se2119862282449309892nteger N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int N2)))) (forall ((N2 tptp.nat) (A tptp.int)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.suc N2)) A) (@ (@ tptp.bit_se545348938243370406it_int N2) (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat) (A tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat (@ tptp.suc N2)) A) (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7788150548672797655nteger N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se547839408752420682it_nat N2) A)) (or (not (= N2 tptp.zero_zero_nat)) (@ _let_1 A))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K))) (@ (@ tptp.bit_se7788150548672797655nteger (@ tptp.pred_numeral L)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 K)))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ (@ tptp.bit_se545348938243370406it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.semiri1314217659103216013at_int N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ tptp.semiri1316708129612266289at_nat (@ _let_1 N2)) (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N2))))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se547839408752420682it_nat N2) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N2) K)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.bit_se7788150548672797655nteger N2))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int (@ _let_1 A))))) (forall ((N2 tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))))) (forall ((N2 tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X4))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ _let_1 X4)))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y)))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X4))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int M))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N2) A)) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat M))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) A)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ _let_1 A))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N2)) A))))) (forall ((M tptp.nat) (N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat M) N2)) A))))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))) (forall ((X4 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4))) (= tptp.bit_se2161824704523386999it_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ (@ tptp.bit_se547839408752420682it_nat M6) tptp.one_one_nat)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X4) Y)))))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X4))))) (forall ((M tptp.nat) (K tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N2) M))))) (forall ((M tptp.nat) (Q3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q3)) N2) (and (@ (@ tptp.ord_less_eq_nat M) N2) (@ (@ tptp.bit_se1148574629649215175it_nat Q3) (@ (@ tptp.minus_minus_nat N2) M))))) _let_171 (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ tptp.arcosh_real (@ tptp.cosh_real X4)) X4))) (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int A3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (= tptp.bit_se2161824704523386999it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.cosh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X4)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X4)) (@ tptp.sinh_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.cosh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.sinh_real Y))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ tptp.sinh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex Y))) (@ (@ tptp.times_times_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex Y))))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ tptp.sinh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real Y))) (@ (@ tptp.times_times_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real Y))))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.cosh_complex X4)) (@ tptp.sinh_complex X4)) (@ tptp.exp_complex X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.cosh_real X4)) (@ tptp.sinh_real X4)) (@ tptp.exp_real X4))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.sinh_complex X4)) (@ tptp.cosh_complex X4)) (@ tptp.exp_complex X4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.sinh_real X4)) (@ tptp.cosh_real X4)) (@ tptp.exp_real X4))) (= tptp.bit_se2159334234014336723it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (= tptp.tanh_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X)))) (= tptp.tanh_complex (lambda ((X tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.sinh_complex X)) (@ tptp.cosh_complex X)))) (forall ((N2 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se545348938243370406it_int N2))) (= (@ _let_2 (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int (@ _let_2 A)) _let_1))))) (forall ((N2 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.bit_se547839408752420682it_nat N2))) (= (@ _let_2 (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 A)) _let_1))))) (= tptp.bit_se1146084159140164899it_int (lambda ((A3 tptp.int) (N tptp.nat)) (not (= (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)) tptp.zero_zero_int)))) (= tptp.bit_se1148574629649215175it_nat (lambda ((A3 tptp.nat) (N tptp.nat)) (not (= (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ (@ tptp.bit_se547839408752420682it_nat N) tptp.one_one_nat)) tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int M) (@ tptp.bit_se2000444600071755411sk_int N2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.plus_plus_nat N2) M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.bit_se2000444600071755411sk_int M))))) (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))) (= tptp.bit_se4203085406695923979it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K3) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int))))) _let_170 _let_169 (= tptp.bit_se545348938243370406it_int (lambda ((N tptp.nat) (A3 tptp.int)) (@ (@ tptp.times_times_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))) (= tptp.bit_se547839408752420682it_nat (lambda ((N tptp.nat) (A3 tptp.nat)) (@ (@ tptp.times_times_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (forall ((N2 tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.bit_se7788150548672797655nteger N2) B5))))))) (forall ((N2 tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.bit_se545348938243370406it_int N2) B5))))))) (forall ((N2 tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.bit_se547839408752420682it_nat N2) B5))))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_complex (@ _let_1 X4)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.sinh_complex X4))) (@ tptp.cosh_complex X4))))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ tptp.sinh_real (@ _let_1 X4)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.sinh_real X4))) (@ tptp.cosh_real X4))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N2) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))) (forall ((X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.tanh_real Y))) (let ((_let_2 (@ tptp.tanh_real X4))) (=> (not (= (@ tptp.cosh_real X4) tptp.zero_zero_real)) (=> (not (= (@ tptp.cosh_real Y) tptp.zero_zero_real)) (= (@ tptp.tanh_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.tanh_complex Y))) (let ((_let_2 (@ tptp.tanh_complex X4))) (=> (not (= (@ tptp.cosh_complex X4) tptp.zero_zero_complex)) (=> (not (= (@ tptp.cosh_complex Y) tptp.zero_zero_complex)) (= (@ tptp.tanh_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ (@ tptp.times_times_complex _let_2) _let_1))))))))) _let_168 _let_167 (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real)))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex)))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) tptp.one_one_complex)))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) tptp.one_one_real)))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ tptp.cosh_complex X4)) _let_1)) (@ (@ tptp.power_power_complex (@ tptp.sinh_complex X4)) _let_1)) tptp.one_one_complex))) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.cosh_real X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.sinh_real X4)) _let_1)) tptp.one_one_real))) (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se9216721137139052372nteger (@ (@ (@ tptp.groups3417619833198082522nteger tptp.zero_n356916108424825756nteger) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))) (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ (@ tptp.groups9119017779487936845_o_nat tptp.zero_n2687167440665602831ol_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))) (forall ((Bs tptp.list_o) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Bs)) N2) (and (@ (@ tptp.ord_less_nat N2) (@ tptp.size_size_list_o Bs)) (@ (@ tptp.nth_o Bs) N2)))) _let_166 (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa Mi3) (= Xa Ma3)))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (= Y (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3))))))))))))))) (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)))) (= (lambda ((H2 tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)) (= (lambda ((H2 tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)) (= (lambda ((H2 tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)) (= (lambda ((H2 tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)) (= (lambda ((H2 tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)) _let_165 _let_164 _let_163 (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))) _let_162 (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X tptp.real)) (@ (@ tptp.member_real X) A6))) (lambda ((X tptp.real)) (@ (@ tptp.member_real X) B6))))) (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) A6))) (lambda ((X tptp.nat)) (@ (@ tptp.member_nat X) B6))))) (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) A6))) (lambda ((X tptp.complex)) (@ (@ tptp.member_complex X) B6))))) (= tptp.ord_le3146513528884898305at_nat (lambda ((A6 tptp.set_Pr1261947904930325089at_nat) (B6 tptp.set_Pr1261947904930325089at_nat)) (@ (@ tptp.ord_le704812498762024988_nat_o (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) A6))) (lambda ((X tptp.product_prod_nat_nat)) (@ (@ tptp.member8440522571783428010at_nat X) B6))))) (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X tptp.int)) (@ (@ tptp.member_int X) A6))) (lambda ((X tptp.int)) (@ (@ tptp.member_int X) B6))))) (forall ((A2 tptp.set_Pr1261947904930325089at_nat) (P (-> tptp.product_prod_nat_nat Bool))) (@ (@ tptp.ord_le3146513528884898305at_nat (@ tptp.collec3392354462482085612at_nat (lambda ((X tptp.product_prod_nat_nat)) (and (@ (@ tptp.member8440522571783428010at_nat X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X tptp.complex)) (and (@ (@ tptp.member_complex X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X tptp.real)) (and (@ (@ tptp.member_real X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_list_nat) (P (-> tptp.list_nat Bool))) (@ (@ tptp.ord_le6045566169113846134st_nat (@ tptp.collect_list_nat (lambda ((X tptp.list_nat)) (and (@ (@ tptp.member_list_nat X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X tptp.nat)) (and (@ (@ tptp.member_nat X) A2) (@ P X))))) A2)) (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.member_int X) A2) (@ P X))))) A2)) (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 ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))) (= (lambda ((X tptp.rat)) X) (@ tptp.times_times_rat tptp.one_one_rat)) (= (lambda ((X tptp.complex)) X) (@ tptp.times_times_complex tptp.one_one_complex)) (= (lambda ((X tptp.real)) X) (@ tptp.times_times_real tptp.one_one_real)) (= (lambda ((X tptp.nat)) X) (@ tptp.times_times_nat tptp.one_one_nat)) (= (lambda ((X tptp.int)) X) (@ tptp.times_times_int tptp.one_one_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)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N2))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat N2))) (= (@ tptp.numera1916890842035813515d_enat (@ tptp.bit1 N2)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) _let_1)) tptp.one_on7984719198319812577d_enat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N2))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N2))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))) (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))) (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))) (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))) (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))) _let_161 _let_160 (= 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))))) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X4)) (@ tptp.real_V1022390504157884413omplex X4))) (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real) _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 (forall ((Z6 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z6))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z6)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z6) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.real_V1022390504157884413omplex X4))) (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))) _let_152 _let_151 (= tptp.bit_ri631733984087533419it_int (lambda ((N tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int _let_1) A3))) (@ (@ (@ tptp.if_int (@ (@ tptp.bit_se1146084159140164899it_int _let_2) N)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.bit_se545348938243370406it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)))) _let_2))))) _let_150 _let_149 _let_148 _let_147 _let_146 (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)))))) (= 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 ((L2 tptp.nat) (__flatten_var_0 tptp.rat)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A3) (@ tptp.semiri681578069525770553at_rat L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_rat)) (@ tptp.semiri773545260158071498ct_rat K3))))) (= 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 ((L2 tptp.nat) (__flatten_var_0 tptp.complex)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A3) (@ tptp.semiri8010041392384452111omplex L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_complex)) (@ tptp.semiri5044797733671781792omplex 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 ((L2 tptp.nat) (__flatten_var_0 tptp.real)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A3) (@ tptp.semiri5074537144036343181t_real L2))) __flatten_var_0))) tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat)) tptp.one_one_real)) (@ tptp.semiri2265585572941072030t_real K3))))) (forall ((Uy tptp.option4927543243414619207at_nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (S tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uy) _let_1) TreeList2) S)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))) (forall ((X8 (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.topolo6517432010174082258omplex X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M2)) (@ X8 N6)))) E2))))))))) (forall ((X8 (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.topolo4055970368930404560y_real X8) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.nat)) (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) M2) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M9) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M2)) (@ X8 N6)))) E2))))))))) (forall ((X8 (-> tptp.nat tptp.complex))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ X8 M5)) (@ X8 N3)))) E)))))))) (@ tptp.topolo6517432010174082258omplex X8))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((M10 tptp.nat)) (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) M5) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M10) N3) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X8 M5)) (@ X8 N3)))) E)))))))) (@ tptp.topolo4055970368930404560y_real X8))) _let_145 (= tptp.topolo4055970368930404560y_real (lambda ((X3 (-> tptp.nat tptp.real))) (forall ((E3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E3) (exists ((M8 tptp.nat)) (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M6) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ X3 M6)) (@ X3 N)))) E3)))))))))) (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd2)) X4) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4))))))) (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X4 tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X4) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc2)) X4) (or (= X4 Mi) (= X4 Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X4) _let_2))) _let_4)))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) Y) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (not (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= X4 (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2)))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((S3 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3))) (and (=> _let_3 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa Mi3) (= Xa Ma3))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) (@ tptp.suc V2)) TreeList3) Vc))) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_1))) _let_3)))))))) (not (forall ((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 Xa) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd tptp.vEBT_VEBT)) (= X4 (@ (@ (@ (@ 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 Xa) _let_1))) _let_3)))))))))))) (= tptp.ring_1_of_int_real (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_real (= K3 tptp.zero_zero_int)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_real (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_real (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_real _let_3) tptp.one_one_real))))))))) (= tptp.ring_1_of_int_int (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_int _let_1) (@ tptp.ring_1_of_int_int (@ (@ tptp.divide_divide_int K3) _let_1))))) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int (@ tptp.ring_1_of_int_int (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int K3) _let_1) tptp.zero_zero_int)) _let_2) (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)))))))) (= tptp.ring_17405671764205052669omplex (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_complex (= K3 tptp.zero_zero_int)) tptp.zero_zero_complex) (@ (@ (@ tptp.if_complex (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1482373934393186551omplex (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_complex (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_complex _let_3) tptp.one_one_complex))))))))) (= tptp.ring_18347121197199848620nteger (lambda ((K3 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K3) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K3 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K3) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K3)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K3) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))) (= 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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))))) _let_144 (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.ln_ln_real X4) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ tptp.suc N))))))))) (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ F tptp.zero_zero_nat))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ F tptp.zero_zero_nat))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_real (@ tptp.re X4)) N2)))) (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 ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X4) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.im X4))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X4)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X4)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X4)))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.re X4))) (=> (= (@ tptp.im X4) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X4) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))) (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real) (forall ((X4 tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.real_V1022390504157884413omplex X4))) (forall ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X4) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X4))) (@ tptp.abs_abs_real (@ tptp.im Y)))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X4) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X4))) (@ tptp.abs_abs_real (@ tptp.re Y)))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X4))))) (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 ((X4 tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X4) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X4))) (@ tptp.im X4))))) (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X4) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))) (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)))) _let_143 (forall ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X4))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X4)) _let_1))))))) (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 ((X4 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 X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))) (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 ((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 ((X4 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X4))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X4)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))) (forall ((X4 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 X4) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X4)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X4)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))) (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))))) _let_142 (= tptp.divide1717551699836669952omplex (lambda ((X tptp.complex) (Y5 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y5))) (let ((_let_3 (@ tptp.re Y5))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))) (= _let_141 (@ 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 ((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)))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (= (@ tptp.arctan X4) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))))))) (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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ tptp.summable_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1)))))))) (forall ((X4 tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X4) Y) (=> (=> (= X4 tptp.zero_zero_nat) _let_1) (=> (=> (= X4 (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X4 _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 ((R3 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R3))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.nat Bool)) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X4)) I2))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.int Bool)) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X4)) I2))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (=> (@ P X4) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) I2))))) (forall ((M tptp.nat) (X4 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X4) (@ (@ tptp.replicate_VEBT_VEBT N2) Y)) (and (= M N2) (=> (not (= M tptp.zero_zero_nat)) (= X4 Y))))) (forall ((N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) N2)) (forall ((N2 tptp.nat) (X4 Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N2) X4)) N2)) (forall ((N2 tptp.nat) (X4 tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N2) X4)) N2)) (forall ((N2 tptp.nat) (X4 tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N2) X4)) N2)) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ tptp.summable_real F))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X tptp.int)) (=> (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (or (@ P A) (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) A))) (@ P X))) (and (@ P A) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X4) (@ tptp.set_real2 (@ (@ tptp.replicate_real N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X4) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.product_prod_nat_nat) (N2 tptp.nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ tptp.member8440522571783428010at_nat X4) (@ tptp.set_Pr5648618587558075414at_nat (@ (@ tptp.replic4235873036481779905at_nat N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X4) (@ tptp.set_int2 (@ (@ tptp.replicate_int N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.nat) (N2 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X4) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((X4 tptp.vEBT_VEBT) (N2 tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N2) Y))) (and (= X4 Y) (not (= N2 tptp.zero_zero_nat))))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N2) X4)) I2) X4))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N2) X4)) I2) X4))) (forall ((I2 tptp.nat) (N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I2) N2) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N2) X4)) I2) X4))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (or (= C tptp.zero_zero_real) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (or (= C tptp.zero_zero_complex) (@ tptp.summable_complex F)))) (forall ((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 ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_complex F)))) (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ G N3)))) (@ tptp.summable_real F)))) (forall ((G (-> tptp.nat tptp.real)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real G) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3)))) (@ tptp.summable_complex F)))) (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 ((A tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.power_power_real A) N2)) tptp.real_V470468836141973256s_real))) (forall ((A tptp.complex) (N2 tptp.nat)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.power_power_complex A) N2)) tptp.real_V2521375963428798218omplex))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex)))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (@ (@ tptp.member_real (@ (@ tptp.plus_plus_real A) B)) tptp.real_V470468836141973256s_real)))) (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (@ (@ tptp.member_complex (@ (@ tptp.plus_plus_complex A) B)) tptp.real_V2521375963428798218omplex)))) (@ _let_139 tptp.real_V470468836141973256s_real) (@ _let_138 tptp.real_V2521375963428798218omplex) (forall ((W tptp.num)) (@ (@ tptp.member_complex (@ tptp.numera6690914467698888265omplex W)) tptp.real_V2521375963428798218omplex)) (forall ((W tptp.num)) (@ (@ tptp.member_real (@ tptp.numeral_numeral_real W)) tptp.real_V470468836141973256s_real)) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (@ tptp.summable_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N))))))) (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ tptp.summable_real F))) (@ tptp.summable_real _let_137) (@ tptp.summable_int _let_136) (@ tptp.summable_complex _let_135) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (@ tptp.summable_real G) (= (@ (@ tptp.plus_plus_real (@ tptp.suminf_real F)) (@ tptp.suminf_real G)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat))) (=> (@ tptp.summable_nat F) (=> (@ tptp.summable_nat G) (= (@ (@ tptp.plus_plus_nat (@ tptp.suminf_nat F)) (@ tptp.suminf_nat G)) (@ tptp.suminf_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.summable_int F) (=> (@ tptp.summable_int G) (= (@ (@ tptp.plus_plus_int (@ tptp.suminf_int F)) (@ tptp.suminf_int G)) (@ tptp.suminf_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))))))) (forall ((F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real (@ tptp.suminf_real F)) C)))) (forall ((F (-> tptp.nat tptp.complex)) (C tptp.complex)) (=> (@ tptp.summable_complex F) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.suminf_complex F)) C)))) (forall ((G (-> tptp.nat tptp.complex)) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_complex G) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.member_complex (@ G N3)) tptp.real_V2521375963428798218omplex)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ G N3)))) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F N3))) (@ tptp.real_V1022390504157884413omplex (@ G N3))))) (@ tptp.summable_real F)))))) (forall ((G (-> tptp.nat tptp.complex)) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_complex G) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.member_complex (@ G N3)) tptp.real_V2521375963428798218omplex)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ G N3)))) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ tptp.real_V1022390504157884413omplex (@ G N3))))) (@ tptp.summable_complex F)))))) (forall ((F (-> tptp.nat tptp.real)) (X4 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))))) (forall ((F (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (=> (forall ((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 ((N tptp.nat)) (= (@ F N) 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 ((N tptp.nat)) (= (@ F N) 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 ((N tptp.nat)) (= (@ F N) 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 ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))) (forall ((F (-> tptp.nat tptp.complex))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))))) (forall ((F (-> tptp.nat tptp.real))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N))))) (forall ((F (-> tptp.nat tptp.int))) (@ tptp.summable_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ F N)) (@ (@ tptp.power_power_int tptp.zero_zero_int) N))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))))) (forall ((Xs tptp.list_real) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N2) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.member_real Y3) (@ tptp.set_real2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_real N2) X4))))) (forall ((Xs tptp.list_complex) (N2 tptp.nat) (X4 tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N2) (=> (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) (@ tptp.set_complex2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_complex N2) X4))))) (forall ((Xs tptp.list_P6011104703257516679at_nat) (N2 tptp.nat) (X4 tptp.product_prod_nat_nat)) (=> (= (@ tptp.size_s5460976970255530739at_nat Xs) N2) (=> (forall ((Y3 tptp.product_prod_nat_nat)) (=> (@ (@ tptp.member8440522571783428010at_nat Y3) (@ tptp.set_Pr5648618587558075414at_nat Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replic4235873036481779905at_nat N2) X4))))) (forall ((Xs tptp.list_VEBT_VEBT) (N2 tptp.nat) (X4 tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N2) (=> (forall ((Y3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y3) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N2) X4))))) (forall ((Xs tptp.list_o) (N2 tptp.nat) (X4 Bool)) (=> (= (@ tptp.size_size_list_o Xs) N2) (=> (forall ((Y3 Bool)) (=> (@ (@ tptp.member_o Y3) (@ tptp.set_o2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_o N2) X4))))) (forall ((Xs tptp.list_nat) (N2 tptp.nat) (X4 tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N2) (=> (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) (@ tptp.set_nat2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_nat N2) X4))))) (forall ((Xs tptp.list_int) (N2 tptp.nat) (X4 tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N2) (=> (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) (@ tptp.set_int2 Xs)) (= Y3 X4))) (= Xs (@ (@ tptp.replicate_int N2) X4))))) (forall ((Xs tptp.list_VEBT_VEBT) (X4 tptp.vEBT_VEBT)) (=> (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X4) Xs))) (forall ((Xs tptp.list_o) (X4 Bool)) (=> (forall ((X5 Bool)) (=> (@ (@ tptp.member_o X5) (@ tptp.set_o2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X4) Xs))) (forall ((Xs tptp.list_nat) (X4 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) (@ tptp.set_nat2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X4) Xs))) (forall ((Xs tptp.list_int) (X4 tptp.int)) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) (@ tptp.set_int2 Xs)) (= X5 X4))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X4) Xs))) (forall ((F (-> tptp.nat tptp.complex)) (M tptp.nat) (Z tptp.complex)) (= (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_complex Z) N)))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (Z tptp.real)) (= (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.power_power_real Z) N)))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))))) (forall ((F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.member_real A) tptp.real_V470468836141973256s_real) (=> (@ (@ tptp.member_real B) tptp.real_V470468836141973256s_real) (=> (not (= B tptp.zero_zero_real)) (@ (@ tptp.member_real (@ (@ tptp.divide_divide_real A) B)) tptp.real_V470468836141973256s_real))))) (forall ((A tptp.complex) (B tptp.complex)) (=> (@ (@ tptp.member_complex A) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex B) tptp.real_V2521375963428798218omplex) (=> (not (= B tptp.zero_zero_complex)) (@ (@ tptp.member_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.real_V2521375963428798218omplex))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.abs_abs_real (@ F N))))))) (forall ((F (-> tptp.nat tptp.real)) (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 ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) tptp.one_one_real) (@ tptp.summable_real (@ tptp.power_power_real X4)))) (forall ((X4 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) tptp.one_one_real) (@ tptp.summable_complex (@ tptp.power_power_complex X4)))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F N))))))) (forall ((F (-> tptp.nat tptp.complex))) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex F))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F N))))))) (forall ((F (-> tptp.nat tptp.real)) (X4 tptp.real) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) (@ tptp.real_V7735802525324610683m_real X4)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))))) (forall ((F (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex X4) N)))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.real_V1022390504157884413omplex X4)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))))) (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.invers8013647133539491842omplex (@ tptp.semiri5044797733671781792omplex N))) (@ (@ tptp.power_power_complex X4) N))))) (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.plus_plus_complex (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.plus_plus_real (@ F tptp.zero_zero_nat)) (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z))))) (forall ((F (-> tptp.nat tptp.complex)) (Z tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N)))) (= (@ (@ tptp.times_times_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N))))) Z) (@ (@ tptp.minus_minus_complex (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ F N)) (@ (@ tptp.power_power_complex Z) N))))) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N)))) (= (@ (@ tptp.times_times_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N))))) Z) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real Z) N))))) (@ F tptp.zero_zero_nat))))) (forall ((R3 tptp.real) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (=> (@ tptp.summable_real F) (exists ((N8 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ tptp.suminf_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N6)))))) R3))))))) (forall ((R3 tptp.real) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R3) (=> (@ tptp.summable_complex F) (exists ((N8 tptp.nat)) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N6) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ tptp.suminf_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N6)))))) R3))))))) (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 ((R3 tptp.real) (R0 tptp.real) (A (-> tptp.nat tptp.complex)) (M7 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R3) (=> (@ (@ tptp.ord_less_real R3) 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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex (@ A N))) (@ (@ tptp.power_power_real R3) N)))))))) (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V7735802525324610683m_real (@ F N3)))))) (@ tptp.summable_real F)))) (forall ((C tptp.real) (N4 tptp.nat) (F (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real C) tptp.one_one_real) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N4) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F (@ tptp.suc N3)))) (@ (@ tptp.times_times_real C) (@ tptp.real_V1022390504157884413omplex (@ F N3)))))) (@ tptp.summable_complex F)))) (forall ((R3 tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R3) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R3) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R3)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.sin_real X4))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (= Y (or (= Xa Mi3) (= Xa Ma3))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))) (not (forall ((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 Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (or (= Xa Mi3) (= Xa Ma3)))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))) (not (forall ((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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))))) (forall ((Z tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Z)) tptp.one_one_real) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((Z tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N))) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (forall ((A (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (= (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) X4) (= (@ A tptp.zero_zero_nat) X4))) (forall ((A (-> tptp.nat tptp.real)) (X4 tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) X4) (= (@ A tptp.zero_zero_nat) X4))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (S tptp.real) (T2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_real F) S) (=> (@ (@ tptp.sums_real G) T2) (@ (@ tptp.ord_less_eq_real S) T2))))) (forall ((F (-> tptp.nat tptp.nat)) (G (-> tptp.nat tptp.nat)) (S tptp.nat) (T2 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_nat F) S) (=> (@ (@ tptp.sums_nat G) T2) (@ (@ tptp.ord_less_eq_nat S) T2))))) (forall ((F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int)) (S tptp.int) (T2 tptp.int)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ G N3))) (=> (@ (@ tptp.sums_int F) S) (=> (@ (@ tptp.sums_int G) T2) (@ (@ tptp.ord_less_eq_int S) T2))))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.sums_real F) A) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) C))) (@ (@ tptp.divide_divide_real A) C)))) (forall ((F (-> tptp.nat tptp.complex)) (A tptp.complex) (C tptp.complex)) (=> (@ (@ tptp.sums_complex F) A) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) C))) (@ (@ tptp.divide1717551699836669952omplex A) C)))) (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (G (-> tptp.nat tptp.real)) (B tptp.real)) (=> (@ (@ tptp.sums_real F) A) (=> (@ (@ tptp.sums_real G) B) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_real A) B))))) (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (G (-> tptp.nat tptp.nat)) (B tptp.nat)) (=> (@ (@ tptp.sums_nat F) A) (=> (@ (@ tptp.sums_nat G) B) (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_nat (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_nat A) B))))) (forall ((F (-> tptp.nat tptp.int)) (A tptp.int) (G (-> tptp.nat tptp.int)) (B tptp.int)) (=> (@ (@ tptp.sums_int F) A) (=> (@ (@ tptp.sums_int G) B) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_int (@ F N)) (@ G N)))) (@ (@ tptp.plus_plus_int A) B))))) (forall ((C tptp.real) (F (-> tptp.nat tptp.real)) (A tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_real)) (@ (@ tptp.sums_real F) (@ (@ tptp.divide_divide_real A) C))))) (forall ((C tptp.complex) (F (-> tptp.nat tptp.complex)) (A tptp.complex)) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex C) (@ F N)))) A) (=> (not (= C tptp.zero_zero_complex)) (@ (@ tptp.sums_complex F) (@ (@ tptp.divide1717551699836669952omplex A) C))))) (forall ((F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (=> (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) 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 ((N tptp.nat)) (@ F (@ tptp.suc N)))) S) (@ (@ tptp.sums_real F) S)))) (forall ((F (-> tptp.nat tptp.real)) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real L) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.nat)) (L tptp.nat)) (=> (@ (@ tptp.sums_nat (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_nat F) (@ (@ tptp.plus_plus_nat L) (@ F tptp.zero_zero_nat))))) (forall ((F (-> tptp.nat tptp.int)) (L tptp.int)) (=> (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ F (@ tptp.suc N)))) L) (@ (@ tptp.sums_int F) (@ (@ tptp.plus_plus_int L) (@ F tptp.zero_zero_nat))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.complex)) (S tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_complex))) (= (@ (@ tptp.sums_complex (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_complex F) S)))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (S tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N2) (= (@ F I4) tptp.zero_zero_real))) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) S)))) (forall ((M tptp.nat) (Z tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= N M)) tptp.one_one_complex) tptp.zero_zero_complex)) (@ (@ tptp.power_power_complex Z) N)))) (@ (@ tptp.power_power_complex Z) M))) (forall ((M tptp.nat) (Z tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= N M)) tptp.one_one_real) tptp.zero_zero_real)) (@ (@ tptp.power_power_real Z) N)))) (@ (@ tptp.power_power_real Z) M))) (forall ((M tptp.nat) (Z tptp.int)) (@ (@ tptp.sums_int (lambda ((N tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= N M)) tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.power_power_int Z) N)))) (@ (@ tptp.power_power_int Z) M))) (forall ((A (-> tptp.nat tptp.complex))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ A N)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N)))) (@ A tptp.zero_zero_nat))) (forall ((A (-> tptp.nat tptp.real))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ A N)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N)))) (@ A tptp.zero_zero_nat))) (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real C)) tptp.one_one_real) (@ (@ tptp.sums_real (@ tptp.power_power_real C)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) C))))) (forall ((C tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex C)) tptp.one_one_real) (@ (@ tptp.sums_complex (@ tptp.power_power_complex C)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) C))))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N)))) tptp.one_one_real) (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) X4))) (forall ((G (-> tptp.nat tptp.real)) (X4 tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X4) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N)) (@ F (@ (@ tptp.divide_divide_nat N) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X4) Y))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.cos_real X4))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Mi3 tptp.nat) (Ma3 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 Mi3) Ma3))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (or (= Xa Mi3) (= Xa Ma3))))))) (=> (forall ((Mi3 tptp.nat) (Ma3 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) _let_1) TreeList3) Vc))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (or (= Xa Mi3) (= Xa Ma3) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))) (not (forall ((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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4)))))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X4 _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa tptp.one_one_nat))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 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 Xa) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (=> (= X4 _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa)) (not (and (=> _let_4 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_2))) _let_4))))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa tptp.one_one_nat))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= X4 _let_1) (=> (= 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) Xa))))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Uu2) tptp.zero_zero_nat) Uv2) Uw2))) (=> (= X4 _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node Uy2) _let_1) TreeList3) S3))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X4 _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa))))))))))))))))) (forall ((C (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N)))) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ C N))) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N))))))) (forall ((C (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N)))) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ C N))) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N))))))) _let_134 _let_133 _let_132 (forall ((C (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (forall ((X5 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N)))))) (forall ((C (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (forall ((X5 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N)))))) (forall ((X4 tptp.real) (K5 tptp.real) (C (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X4)) K5) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X5)) K5) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ C N)) (@ (@ tptp.power_power_real X5) N)))))) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.diffs_real C) N)) (@ (@ tptp.power_power_real X4) N))))))) (forall ((X4 tptp.complex) (K5 tptp.real) (C (-> tptp.nat tptp.complex))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X4)) K5) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X5)) K5) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ C N)) (@ (@ tptp.power_power_complex X5) N)))))) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.diffs_complex C) N)) (@ (@ tptp.power_power_complex X4) N))))))) _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 (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))) (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 ((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 ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.real_V1485227260804924795R_real X4) Y)) N2) (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)))) (forall ((X4 tptp.real) (Y tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.real_V2046097035970521341omplex X4) Y)) N2) (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_complex Y) N2)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ tptp.uminus_uminus_real X4))) (forall ((X4 tptp.complex)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (@ tptp.uminus1482373934393186551omplex X4))) (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.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 ((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 ((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 ((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 ((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 ((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 ((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.real) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X4)) (@ _let_1 Y))))) (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real A) B)) X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) X4)))) (forall ((X4 tptp.real) (Y tptp.real) (Xa tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.plus_plus_real X4) Y)) Xa) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real X4) Xa)) (@ (@ tptp.real_V1485227260804924795R_real Y) Xa)))) _let_123 _let_122 (forall ((A tptp.real) (B tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) X4))))) (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) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real B) A)) E2)) D)))) (forall ((A tptp.real) (E2 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) E2)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real B) E2)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.minus_minus_real A) B)) E2)) C)) D))) (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)) (= (@ (@ 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)) (=> (@ (@ 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 ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))) (forall ((A tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))) (forall ((A tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.real_V1485227260804924795R_real A) X4)))))) (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) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 X4))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) tptp.zero_zero_real)))) (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) (B tptp.real) (X4 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 X4) Y) (=> (@ _let_1 B) (=> (@ _let_1 X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) (@ (@ tptp.real_V1485227260804924795R_real B) Y)))))))) (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real A) X4)) X4)))) (forall ((X4 tptp.real)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) X4) (@ (@ tptp.plus_plus_real X4) X4))) (forall ((M tptp.real) (X4 tptp.real) (C tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X4)) C) Y) (= X4 (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C))))))) (forall ((M tptp.real) (Y tptp.real) (X4 tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real M)))) (=> (not (= M tptp.zero_zero_real)) (= (= Y (@ (@ tptp.plus_plus_real (@ (@ tptp.real_V1485227260804924795R_real M) X4)) C)) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ _let_1 C)) X4))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) B)))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))) (forall ((X4 tptp.complex)) (@ tptp.summable_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.sin_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.sin_complex X4))) _let_121 _let_120 (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.cos_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.cos_complex X4))) (= tptp.cos_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X) N)))))) (= tptp.cos_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X) N)))))) (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real X4) N)))))) (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex X4) N)))))) (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real X4) N)))))) (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex X4) N)))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.real_V1485227260804924795R_real C) A))))) (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real C)) B))) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V1485227260804924795R_real C) A)) (@ tptp.uminus_uminus_real B))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))) (@ tptp.exp_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N)))) (@ tptp.exp_complex X4))) (= tptp.exp_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))) (= tptp.exp_complex (lambda ((X tptp.complex)) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))))) (forall ((X4 tptp.real)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N)))))) (forall ((X4 tptp.complex)) (@ tptp.summable_real (lambda ((N tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N)))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ tptp.uminus_uminus_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) N))))) (@ tptp.sin_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.sin_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) N))))) (@ tptp.sin_complex X4))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X4)) N)))) (@ tptp.cos_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.cos_coeff N)) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X4)) N)))) (@ tptp.cos_complex X4))) (= tptp.cosh_real (lambda ((X tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))) (= tptp.cosh_complex (lambda ((X tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))) (= tptp.sinh_real (lambda ((X tptp.real)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X)))))) (= tptp.sinh_complex (lambda ((X tptp.complex)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.minus_minus_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X)))))) (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))))) (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1)))))))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))) tptp.zero_zero_real))) (@ tptp.cosh_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))) tptp.zero_zero_complex))) (@ tptp.cosh_complex X4))) (forall ((X4 tptp.real)) (@ (@ tptp.sums_real (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_real) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X4) N))))) (@ tptp.sinh_real X4))) (forall ((X4 tptp.complex)) (@ (@ tptp.sums_complex (lambda ((N tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_complex) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X4) N))))) (@ tptp.sinh_complex X4))) (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 ((X3 (-> tptp.nat tptp.real))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X3 (@ tptp.suc N))) (@ X3 N)))))) (= tptp.topolo3100542954746470799et_int (lambda ((X3 (-> tptp.nat tptp.set_int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ X3 (@ tptp.suc N))) (@ X3 N)))))) (= tptp.topolo4267028734544971653eq_rat (lambda ((X3 (-> tptp.nat tptp.rat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ X3 (@ tptp.suc N))) (@ X3 N)))))) (= tptp.topolo1459490580787246023eq_num (lambda ((X3 (-> tptp.nat tptp.num))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ X3 (@ tptp.suc N))) (@ X3 N)))))) (= tptp.topolo4902158794631467389eq_nat (lambda ((X3 (-> tptp.nat tptp.nat))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ X3 (@ tptp.suc N))) (@ X3 N)))))) (= tptp.topolo4899668324122417113eq_int (lambda ((X3 (-> tptp.nat tptp.int))) (or (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X3 N)) (@ X3 (@ tptp.suc N)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ X3 (@ tptp.suc N))) (@ X3 N)))))) _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.sin_complex X4)) (@ tptp.sin_complex Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (not (@ _let_2 N)))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5)))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.sin_real X4)) (@ tptp.sin_real Y)))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_atMost_nat X4) (@ tptp.set_ord_atMost_nat Y)) (= X4 Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_atMost_int X4) (@ tptp.set_ord_atMost_int Y)) (= X4 Y))) (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 ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ tptp.set_or58775011639299419et_int X4)) (@ tptp.set_or58775011639299419et_int Y)) (@ (@ tptp.ord_less_eq_set_int X4) Y))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_atMost_rat X4)) (@ tptp.set_ord_atMost_rat Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_atMost_num X4)) (@ tptp.set_ord_atMost_num Y)) (@ (@ tptp.ord_less_eq_num X4) Y))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_atMost_nat X4)) (@ tptp.set_ord_atMost_nat Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int X4)) (@ tptp.set_ord_atMost_int Y)) (@ (@ tptp.ord_less_eq_int X4) Y))) (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (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 ((S2 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S2))) (@ (@ tptp.groups8097168146408367636l_real G) S2)))) (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X5 tptp.int)) (=> (@ (@ tptp.member_int X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S2))) (@ (@ tptp.groups8778361861064173332t_real G) S2)))) (forall ((S2 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) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups6381953495645901045omplex F) S2))) (@ (@ tptp.groups4567486121110086003t_real G) S2)))) (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))) (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) S2) (@ (@ 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) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))) (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X5 tptp.complex)) (=> (@ (@ tptp.member_complex X5) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X5))) (@ G X5)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S2))) (@ (@ tptp.groups5808333547571424918x_real G) S2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial K3) M))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc N2)) (@ tptp.suc M)))) (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 ((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 ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ 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 N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_atMost_nat N2))))) (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)) (N2 tptp.nat) (D (-> tptp.nat tptp.complex))) (= (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ D I3)) (@ (@ tptp.power_power_complex X) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))) (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (D (-> tptp.nat tptp.real))) (= (forall ((X tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ D I3)) (@ (@ tptp.power_power_real X) I3)))) _let_1)))) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) (@ D I3)))))) (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)))) _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 (forall ((R3 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R3) K3)) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R3) N2))) N2))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N2) M)) tptp.one_one_nat)) M))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N2) J3)) N2))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) tptp.zero_zero_complex))))) (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)) (forall ((I3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I3) N2) (= (@ C I3) tptp.zero_zero_real))))) (forall ((C (-> tptp.nat tptp.complex)) (N2 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 N2)) tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_complex)))) (forall ((C (-> tptp.nat tptp.real)) (N2 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 N2)) tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat K) N2) (= (@ C K) tptp.zero_zero_real)))) (forall ((A tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex A) (@ tptp.semiri8010041392384452111omplex N2))) tptp.one_one_complex)) N2))) (forall ((A tptp.rat) (N2 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 N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat A) (@ tptp.semiri681578069525770553at_rat N2))) tptp.one_one_rat)) N2))) (forall ((A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real K3))) K3))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real A) (@ tptp.semiri5074537144036343181t_real N2))) tptp.one_one_real)) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N2) K3)) (@ (@ tptp.minus_minus_nat M) K3)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N2)) M)))) (forall ((M tptp.nat) (N2 tptp.nat) (R3 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K3)) (@ (@ tptp.binomial N2) (@ (@ tptp.minus_minus_nat R3) K3))))) (@ tptp.set_ord_atMost_nat R3)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N2)) R3))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ (@ tptp.times_times_rat (@ _let_2 X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ (@ tptp.times_times_complex (@ _let_2 X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ (@ tptp.times_times_int (@ _let_2 X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ (@ tptp.times_times_real (@ _let_2 X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_atMost_nat N2))) (@ _let_2 (@ _let_1 (@ tptp.suc N2))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N2)) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((G (-> tptp.nat tptp.rat)) (N2 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))) N2)))) (@ (@ 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 N2)))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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 N2)))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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 N2)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N2)))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.rat)) (N2 tptp.nat) (B (-> tptp.nat tptp.rat)) (X4 tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_rat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) 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 X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B J3)) (@ (@ tptp.power_power_rat X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.complex)) (N2 tptp.nat) (B (-> tptp.nat tptp.complex)) (X4 tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_complex))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_complex))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B J3)) (@ (@ tptp.power_power_complex X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.int)) (N2 tptp.nat) (B (-> tptp.nat tptp.int)) (X4 tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_int))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_int))) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_int (@ B J3)) (@ (@ tptp.power_power_int X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.real)) (N2 tptp.nat) (B (-> tptp.nat tptp.real)) (X4 tptp.real)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_real))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_real))) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ B J3)) (@ (@ tptp.power_power_real X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))) (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.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_rat A) K3))) (@ (@ tptp.power_power_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_complex A) K3))) (@ (@ tptp.power_power_complex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_int A) K3))) (@ (@ tptp.power_power_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.nat) (B tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_nat A) K3))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.power_power_real A) K3))) (@ (@ tptp.power_power_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N2 tptp.nat) (B (-> tptp.nat tptp.nat)) (X4 tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I3)) (@ (@ tptp.power_power_nat X4) I3)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X4) J3)))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ 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 X4) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N2))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N2) K3)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) N2))) (forall ((A tptp.rat) (B tptp.rat) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4028243227959126397er_rat (@ (@ tptp.plus_plus_rat A) B)) N2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat A) K3))) (@ (@ tptp.comm_s4028243227959126397er_rat B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.complex) (B tptp.complex) (N2 tptp.nat)) (= (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex A) B)) N2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s2602460028002588243omplex A) K3))) (@ (@ tptp.comm_s2602460028002588243omplex B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.int) (B tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.comm_s4660882817536571857er_int (@ (@ tptp.plus_plus_int A) B)) N2) (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s4660882817536571857er_int A) K3))) (@ (@ tptp.comm_s4660882817536571857er_int B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((A tptp.real) (B tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real A) B)) N2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) K3))) (@ (@ tptp.comm_s7457072308508201937r_real A) K3))) (@ (@ tptp.comm_s7457072308508201937r_real B) (@ (@ tptp.minus_minus_nat N2) K3))))) (@ tptp.set_ord_atMost_nat N2)))) (forall ((X4 tptp.complex) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I5))))) (forall ((X4 tptp.int) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I5))))) (forall ((X4 tptp.real) (M tptp.nat) (I5 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.plus_plus_nat M) I3)))) I5) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I5))))) (forall ((P2 tptp.nat) (K tptp.nat) (G (-> tptp.nat tptp.complex)) (H (-> 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) (@ H (@ (@ 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)) (@ H 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)) (H (-> 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) (@ H (@ (@ 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)) (@ H 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)) (H (-> 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) (@ H (@ (@ 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)) (@ H 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)) (H (-> 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) (@ H (@ (@ 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)) (@ H 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)) (H (-> 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) (@ H (@ (@ 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)) (@ H J3)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat P2) (@ tptp.suc tptp.zero_zero_nat)))))))) (forall ((M tptp.nat) (A tptp.complex) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.rat) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X4 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 X4) 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 X4)) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((X4 tptp.complex) (Y tptp.complex) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X4) Y) (@ (@ tptp.times_times_complex Y) X4)) (= (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) N2)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I3))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I3))) (@ (@ tptp.power_power_complex X4) I3))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((X4 tptp.real) (Y tptp.real) (N2 tptp.nat)) (=> (= (@ (@ tptp.times_times_real X4) Y) (@ (@ tptp.times_times_real Y) X4)) (= (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) I3))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real I3))) (@ (@ tptp.power_power_real X4) I3))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real Y) _let_1)))))) (@ tptp.set_ord_atMost_nat N2))))) (forall ((N2 tptp.nat) (Z tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_int Z) N2) A) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ (@ tptp.if_int (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int A)) (@ (@ (@ tptp.if_int (= I3 N2)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.power_power_int Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int)))) (forall ((N2 tptp.nat) (Z tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_complex Z) N2) A) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ (@ tptp.if_complex (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1482373934393186551omplex A)) (@ (@ (@ tptp.if_complex (= I3 N2)) tptp.one_one_complex) tptp.zero_zero_complex))) (@ (@ tptp.power_power_complex Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex)))) (forall ((N2 tptp.nat) (Z tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_8256067586552552935nteger Z) N2) A) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ (@ tptp.if_Code_integer (= I3 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ (@ tptp.if_Code_integer (= I3 N2)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))) (@ (@ tptp.power_8256067586552552935nteger Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger)))) (forall ((N2 tptp.nat) (Z tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_rat Z) N2) 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 N2)) tptp.one_one_rat) tptp.zero_zero_rat))) (@ (@ tptp.power_power_rat Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat)))) (forall ((N2 tptp.nat) (Z tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (= (@ (@ tptp.power_power_real Z) N2) A) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= I3 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_real A)) (@ (@ (@ tptp.if_real (= I3 N2)) tptp.one_one_real) tptp.zero_zero_real))) (@ (@ tptp.power_power_real Z) I3)))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real)))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_atMost_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 (@ tptp.suc N2)))) (@ _let_1 X4)))))))))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (not (= N2 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) 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.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.rat) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.complex) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (forall ((M tptp.nat) (A tptp.real) (X4 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 X4) 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 X4) K3))) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X4) Y)) (@ (@ tptp.minus_minus_nat M) K3))))) _let_1)))) (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 ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_nat I3) (@ (@ tptp.binomial N2) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_nat N2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_complex))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) I3)) (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.binomial N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_z3403309356797280102nteger))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_rat))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))))) (@ tptp.set_ord_atMost_nat N2)) tptp.zero_zero_real))) (forall ((E2 tptp.real) (C (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.real)) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z3))) (=> (@ (@ tptp.ord_less_eq_real M9) _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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))) (forall ((E2 tptp.real) (C (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((M9 tptp.real)) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z3))) (=> (@ (@ tptp.ord_less_eq_real M9) _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 Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)))) (@ (@ tptp.times_times_real E2) (@ (@ tptp.power_power_real _let_1) (@ tptp.suc N2)))))))))) (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.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_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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3))) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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 N2) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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 N2) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ 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 N2) I3))) tptp.zero_zero_rat))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_rat _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_complex))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_complex _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_int (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_int))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_int _let_1) N2))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I3)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial N2) I3))) tptp.zero_zero_real))) (@ tptp.set_ord_atMost_nat N2))) (@ (@ tptp.power_power_real _let_1) N2))))) (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.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.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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N2)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N2))))))) (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_complex (and (@ _let_2 P5) (@ _let_2 N))) (@ (@ tptp.times_times_complex (@ (@ tptp.real_V2046097035970521341omplex (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_complex (@ tptp.cos_complex X4)) (@ tptp.cos_complex Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ (@ tptp.if_real (and (@ _let_2 P5) (@ _let_2 N))) (@ (@ tptp.times_times_real (@ (@ tptp.real_V1485227260804924795R_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.divide_divide_nat P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real))))) (@ tptp.set_ord_atMost_nat P5)))) (@ (@ tptp.times_times_real (@ tptp.cos_real X4)) (@ tptp.cos_real Y)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (@ (@ tptp.sums_complex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_complex (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ 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 P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_complex X4) N))) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_complex)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_complex (@ (@ tptp.plus_plus_complex X4) Y)))) (forall ((X4 tptp.real) (Y tptp.real)) (@ (@ tptp.sums_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) P5)) (@ (@ 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 P5) _let_1))) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.binomial P5) N))))) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real X4) N))) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat P5) N)))) tptp.zero_zero_real)))) (@ tptp.set_ord_atMost_nat P5)))) (@ tptp.cos_real (@ (@ tptp.plus_plus_real X4) Y)))) (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))) (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.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ tptp.abs_abs_real (@ F I3)))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I3 tptp.int)) (@ tptp.abs_abs_int (@ F I3)))) A2))) (forall ((I5 tptp.set_real) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_nat) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_complex) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_int) (X4 (-> 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) I5) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X4 I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X4) I5) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_real) (X4 (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_complex) (X4 (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_int) (X4 (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X4 I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X4) I5) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_real) (X4 (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_nat) (X4 (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I5) (@ (@ 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)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((I5 tptp.set_complex) (X4 (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X4 I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X4) I5) tptp.one_one_rat) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I5) (@ (@ 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.groups5058264527183730370ex_rat (lambda ((I3 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I3)) (@ X4 I3)))) I5)) B))) Delta))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real X4) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X4) (@ tptp.set_ord_lessThan_nat Y)) (= X4 Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X4) (@ tptp.set_ord_lessThan_int Y)) (= X4 Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X4) (@ tptp.set_or5984915006950818249n_real Y)) (= X4 Y))) (= tptp.semiri1316708129612266289at_nat (lambda ((N tptp.nat)) N)) (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))) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X4)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X4) Y))) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X4)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X4) Y))) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X4)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X4) Y))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X4)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X4) Y))) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X4)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X4) Y))) (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M6)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) tptp.one_one_real)) (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N2))) (=> (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 ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))) (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N2 tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N2))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))) (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (=> (forall ((X5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X5)) (@ P X5))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X)) (@ Q X)))) _let_1))))) _let_106 _let_105 _let_104 _let_103 _let_102 (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 ((X tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_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 ((X tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_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 ((X tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_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 ((X tptp.product_prod_nat_nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) 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 ((X tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X)) (@ G X)))) 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) (N2 tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N2)) (exists ((X5 tptp.nat)) (and (@ (@ tptp.member_nat X5) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X5)))))) (forall ((M tptp.rat) (N2 tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N2)) (@ (@ tptp.ord_less_rat M) N2))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N2)) (@ (@ tptp.ord_less_num M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N2)) (@ (@ tptp.ord_less_int M) N2))) (forall ((M tptp.real) (N2 tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N2)) (@ (@ tptp.ord_less_real M) N2))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat 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 ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))) (forall ((F (-> tptp.nat tptp.int)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_int (@ tptp.suminf_int F)) X4)))) (forall ((F (-> tptp.nat tptp.nat)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suminf_nat F)) X4)))) (forall ((F (-> tptp.nat tptp.real)) (X4 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))) X4)) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real F)) X4)))) (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ 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 N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F (@ tptp.suc N))))) (@ 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 ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F (@ tptp.suc N))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N))) (@ F N)))) (@ 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 ((N tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N))) (@ F N)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))) (forall ((F (-> tptp.nat tptp.int)) (X4 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))) X4)) (@ tptp.summable_int F)))) (forall ((F (-> tptp.nat tptp.nat)) (X4 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))) X4)) (@ tptp.summable_nat F)))) (forall ((F (-> tptp.nat tptp.real)) (X4 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))) X4)) (@ tptp.summable_real F)))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) S) (@ (@ tptp.sums_real F) (@ (@ tptp.plus_plus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (S tptp.real)) (= (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.sums_real F) S))) (forall ((F (-> tptp.nat tptp.real)) (S tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.sums_real F) S) (@ (@ tptp.sums_real (lambda ((I3 tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat I3) N2)))) (@ (@ tptp.minus_minus_real S) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) tptp.zero_zero_complex))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N2)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) tptp.one_one_int)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_rat (@ _let_2 X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_complex (@ _let_2 X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_int (@ _let_2 X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_2 (@ _let_1 N2)) (@ (@ tptp.times_times_real (@ _let_2 X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (not (= X4 tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N2)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X4) tptp.one_one_rat)))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (not (= X4 tptp.one_one_complex)) (= (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N2)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X4) tptp.one_one_complex)))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (not (= X4 tptp.one_one_real)) (= (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N2)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X4) tptp.one_one_real)))))) (forall ((G (-> tptp.nat tptp.rat)) (N2 tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ 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 N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ tptp.set_ord_lessThan_nat 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 ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K))))) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (= (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ F (@ (@ tptp.plus_plus_nat N) K)))) (@ (@ tptp.minus_minus_real (@ tptp.suminf_real F)) (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K)))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N2) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) X)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) tptp.zero_zero_complex))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F M5)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F M5)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F M5)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ tptp.set_ord_lessThan_nat N2)))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N2))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N2))) (@ _let_1 X4)))))))))) (forall ((Z tptp.rat) (H tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P5)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z tptp.complex) (H tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P5)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z tptp.int) (H tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P5)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((Z tptp.real) (H tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) (@ (@ tptp.minus_minus_nat M) P5))) (@ _let_1 P5))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P5))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P5)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))) (forall ((X4 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X4) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X4) P5)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X4) _let_1)) (@ (@ tptp.power_power_complex Y) _let_1)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X4) P5)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X4) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X4) P5)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X4) P5)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))) (forall ((X4 tptp.rat) (N2 tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.power_power_rat Y) N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X4) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_rat X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X4 tptp.complex) (N2 tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.power_power_complex Y) N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X4) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_complex X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.power_power_int Y) N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X4) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_int X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.power_power_real Y) N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X4) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3)))) (@ (@ tptp.power_power_real X4) I3)))) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((C (-> tptp.nat tptp.rat)) (A tptp.rat) (N2 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 N2)) tptp.zero_zero_rat) (not (forall ((B5 (-> tptp.nat tptp.rat))) (not (forall ((Z3 tptp.rat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z3) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C (-> tptp.nat tptp.complex)) (A tptp.complex) (N2 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 N2)) tptp.zero_zero_complex) (not (forall ((B5 (-> tptp.nat tptp.complex))) (not (forall ((Z3 tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C (-> tptp.nat tptp.int)) (A tptp.int) (N2 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 N2)) tptp.zero_zero_int) (not (forall ((B5 (-> tptp.nat tptp.int))) (not (forall ((Z3 tptp.int)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C (-> tptp.nat tptp.real)) (A tptp.real) (N2 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 N2)) tptp.zero_zero_real) (not (forall ((B5 (-> tptp.nat tptp.real))) (not (forall ((Z3 tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))))))))) (forall ((C (-> tptp.nat tptp.rat)) (N2 tptp.nat) (A tptp.rat)) (exists ((B5 (-> tptp.nat tptp.rat))) (forall ((Z3 tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I3)) (@ (@ tptp.power_power_rat Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat Z3) A)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ B5 I3)) (@ (@ tptp.power_power_rat Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ 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.complex)) (N2 tptp.nat) (A tptp.complex)) (exists ((B5 (-> tptp.nat tptp.complex))) (forall ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex Z3) A)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ B5 I3)) (@ (@ tptp.power_power_complex Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ 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.int)) (N2 tptp.nat) (A tptp.int)) (exists ((B5 (-> tptp.nat tptp.int))) (forall ((Z3 tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ C I3)) (@ (@ tptp.power_power_int Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z3) A)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ B5 I3)) (@ (@ tptp.power_power_int Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ 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)) (N2 tptp.nat) (A tptp.real)) (exists ((B5 (-> tptp.nat tptp.real))) (forall ((Z3 tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real Z3) I3)))) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real Z3) A)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ B5 I3)) (@ (@ tptp.power_power_real Z3) I3)))) (@ tptp.set_ord_lessThan_nat N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real A) I3)))) _let_1))))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ 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 N2) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N2)) K5))))) (forall ((N2 tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N2) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) K5))))) (forall ((F (-> tptp.nat tptp.int)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_int F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F I2)) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_int F))))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_nat F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_nat F))))))) (forall ((F (-> tptp.nat tptp.real)) (N2 tptp.nat) (I2 tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M5) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F M5)))) (=> (@ (@ tptp.ord_less_eq_nat N2) I2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I2)) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat N2))) (@ tptp.suminf_real F))))))) (forall ((X4 tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X4) N2)) (@ (@ tptp.times_times_rat (@ _let_1 X4)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_rat X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X4) N2)) (@ (@ tptp.times_times_complex (@ _let_1 X4)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_complex X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X4) N2)) (@ (@ tptp.times_times_int (@ _let_1 X4)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_int X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X4) N2)) (@ (@ tptp.times_times_real (@ _let_1 X4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc I3))))) (@ tptp.set_ord_lessThan_nat N2)))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.complex tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_complex)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_complex))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_real))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.rat tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_rat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_rat))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.nat tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_nat)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_nat))))) (forall ((X4 tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.int tptp.real))) (=> (= X4 tptp.zero_zero_real) (=> (not (= N2 tptp.zero_zero_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_int)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ Diff tptp.zero_zero_nat) tptp.zero_zero_int))))) (forall ((H tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (exists ((B7 tptp.real)) (= (@ F H) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M6)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real B7) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H) N2)) (@ tptp.semiri2265585572941072030t_real N2)))))))) (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N2))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((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))) N2))) (@ (@ 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 ((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_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_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_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_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_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_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_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_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_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 ((G (-> tptp.nat tptp.nat)) (H (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H) A2)))) (forall ((G (-> tptp.nat tptp.real)) (H (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H) A2)))) (forall ((G (-> tptp.complex tptp.complex)) (H (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H) A2)))) (forall ((G (-> tptp.int tptp.int)) (H (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int (@ G X)) (@ H X)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H) A2)))) (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R3 tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R3) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N)) R3))) A2))) (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R3 tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R3) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N)) R3))) A2))) (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) 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 X4) 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 X4) J3)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N2) J3))))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((K tptp.nat)) (= tptp.exp_complex (lambda ((X tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((N tptp.nat)) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_complex X) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_complex (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V2046097035970521341omplex (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_complex X) _let_1))))))))) (forall ((K tptp.nat)) (= tptp.exp_real (lambda ((X tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((N tptp.nat)) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.real_V1485227260804924795R_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X4)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X4)) N2)))) (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 ((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_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_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_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_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_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_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_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_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 ((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_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_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_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_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_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_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_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_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_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_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_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 ((X4 tptp.real) (N2 tptp.nat)) (=> (not (= X4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (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 X4)) (= (@ tptp.exp_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X4) M6)) (@ tptp.semiri2265585572941072030t_real M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))) (forall ((H tptp.rat) (Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H 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) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H)) Q5)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.complex) (Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P5 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H)) Q5)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((H tptp.real) (Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H 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) H)) N2)) (@ _let_2 N2))) H)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H)) Q5)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) P5))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X4) (= (@ tptp.sin_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))) (forall ((X4 tptp.real) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_real T3) X4) (= (@ tptp.cos_real X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M6)) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ 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 N2))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K3 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K3))) (@ tptp.semiri5074537144036343181t_real N2))))) (@ tptp.set_ord_lessThan_nat N2)) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))))) (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) 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 N2) 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 N2)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X4)))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X4)))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (let ((_let_3 (= X4 tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N2) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)))))))))))) (forall ((R3 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 R3) K3)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat R3) (@ 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 R3) _let_1))))) (forall ((R3 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.gbinomial_complex R3) K3)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex R3) (@ 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 R3) _let_1))))) (forall ((R3 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 R3) K3)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real R3) (@ 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 R3) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((I2 tptp.set_int) (L tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I2) (@ (@ tptp.set_or370866239135849197et_int L) U)) (and (@ (@ tptp.ord_less_eq_set_int L) I2) (@ (@ tptp.ord_less_eq_set_int I2) U)))) (forall ((I2 tptp.rat) (L tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I2) (@ (@ tptp.set_or633870826150836451st_rat L) U)) (and (@ (@ tptp.ord_less_eq_rat L) I2) (@ (@ tptp.ord_less_eq_rat I2) U)))) (forall ((I2 tptp.num) (L tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I2) (@ (@ tptp.set_or7049704709247886629st_num L) U)) (and (@ (@ tptp.ord_less_eq_num L) I2) (@ (@ tptp.ord_less_eq_num I2) U)))) (forall ((I2 tptp.nat) (L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I2) (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (and (@ (@ tptp.ord_less_eq_nat L) I2) (@ (@ tptp.ord_less_eq_nat I2) U)))) (forall ((I2 tptp.int) (L tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I2) (@ (@ tptp.set_or1266510415728281911st_int L) U)) (and (@ (@ tptp.ord_less_eq_int L) I2) (@ (@ tptp.ord_less_eq_int I2) U)))) (forall ((I2 tptp.real) (L tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I2) (@ (@ tptp.set_or1222579329274155063t_real L) U)) (and (@ (@ tptp.ord_less_eq_real L) I2) (@ (@ tptp.ord_less_eq_real I2) U)))) (forall ((L tptp.set_int) (H tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L) H) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L) H)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))) (forall ((L tptp.rat) (H tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L) H) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_rat L) H)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))) (forall ((L tptp.num) (H tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L) H) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_num L) H)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))) (forall ((L tptp.nat) (H tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L) H) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_nat L) H)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))) (forall ((L tptp.int) (H tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L) H) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_int L) H)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))) (forall ((L tptp.real) (H tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L) H) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L L3) (= H H3)) (and (not (@ (@ tptp.ord_less_eq_real L) H)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))) (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 ((L tptp.set_int) (H tptp.set_int) (H3 tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int L) H)) (@ tptp.set_or58775011639299419et_int H3)) (or (not (@ (@ tptp.ord_less_eq_set_int L) H)) (@ (@ tptp.ord_less_eq_set_int H) H3)))) (forall ((L tptp.rat) (H tptp.rat) (H3 tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat L) H)) (@ tptp.set_ord_atMost_rat H3)) (or (not (@ (@ tptp.ord_less_eq_rat L) H)) (@ (@ tptp.ord_less_eq_rat H) H3)))) (forall ((L tptp.num) (H tptp.num) (H3 tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num L) H)) (@ tptp.set_ord_atMost_num H3)) (or (not (@ (@ tptp.ord_less_eq_num L) H)) (@ (@ tptp.ord_less_eq_num H) H3)))) (forall ((L tptp.nat) (H tptp.nat) (H3 tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat L) H)) (@ tptp.set_ord_atMost_nat H3)) (or (not (@ (@ tptp.ord_less_eq_nat L) H)) (@ (@ tptp.ord_less_eq_nat H) H3)))) (forall ((L tptp.int) (H tptp.int) (H3 tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int L) H)) (@ tptp.set_ord_atMost_int H3)) (or (not (@ (@ tptp.ord_less_eq_int L) H)) (@ (@ tptp.ord_less_eq_int H) H3)))) (forall ((L tptp.real) (H tptp.real) (H3 tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real L) H)) (@ tptp.set_ord_atMost_real H3)) (or (not (@ (@ tptp.ord_less_eq_real L) H)) (@ (@ tptp.ord_less_eq_real H) H3)))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((H3 tptp.int) (L tptp.int) (H tptp.int)) (not (= (@ tptp.set_ord_atMost_int H3) (@ (@ tptp.set_or1266510415728281911st_int L) H)))) (forall ((H3 tptp.real) (L tptp.real) (H tptp.real)) (not (= (@ tptp.set_ord_atMost_real H3) (@ (@ tptp.set_or1222579329274155063t_real L) H)))) (forall ((H tptp.int) (L3 tptp.int) (H3 tptp.int)) (not (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_atMost_int H)) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)))) (forall ((H tptp.real) (L3 tptp.real) (H3 tptp.real)) (not (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_ord_atMost_real H)) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ P X))))) (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N2) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I3) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (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 ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N2) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N2)) I3)))) _let_1)))) (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)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ 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 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N2))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N2))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ G (@ tptp.suc I3)))) _let_1)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ 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) N2)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I3))) (@ F I3)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ G (@ tptp.suc K3)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((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 ((A (-> tptp.nat tptp.nat tptp.nat)) (N2 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 N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))) (forall ((A (-> tptp.nat tptp.nat tptp.real)) (N2 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 N2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ A I3) J3))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc J3)) N2)))) (@ tptp.set_ord_lessThan_nat N2)))) (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 ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.rat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.int)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.nat)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (G (-> tptp.nat tptp.real)) (P2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N2))) (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 N2))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))) (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (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) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat M) N2))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real F))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.plus_plus_real (@ _let_2 (@ tptp.set_ord_atMost_nat M))) (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) _let_1))))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (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 N2) 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) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.plus_plus_nat K3) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ 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)) N2)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K3)) (@ F (@ (@ tptp.minus_minus_nat K3) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F M))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X4))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real _let_1))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ _let_2 (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_2 (@ tptp.set_ord_atMost_nat (@ (@ tptp.minus_minus_nat N2) M))))))))) (forall ((F (-> tptp.nat tptp.complex)) (E2 tptp.real)) (=> (@ tptp.summable_complex F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N6)))) E2)))))))))) (forall ((F (-> tptp.nat tptp.real)) (E2 tptp.real)) (=> (@ tptp.summable_real F) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (not (forall ((N8 tptp.nat)) (not (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) M2) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) (@ (@ tptp.set_or1269000886237332187st_nat M2) N6)))) E2)))))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X4)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X4)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X4)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((M tptp.nat) (N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real X4))) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X4)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N2))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N2))))))) (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N2 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 N2)))) (@ (@ 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) N2))))) (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2))))) (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2))))) (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N2)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((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) N2))))) (forall ((C (-> tptp.nat tptp.complex)) (N2 tptp.nat) (K tptp.complex)) (= (forall ((X tptp.complex)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I3)) (@ (@ tptp.power_power_complex X) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_complex)))))) (forall ((C (-> tptp.nat tptp.real)) (N2 tptp.nat) (K tptp.real)) (= (forall ((X tptp.real)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ C I3)) (@ (@ tptp.power_power_real X) I3)))) (@ tptp.set_ord_atMost_nat N2)) K)) (and (= (@ C tptp.zero_zero_nat) K) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2)) (= (@ C X) tptp.zero_zero_real)))))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_complex (@ tptp.semiri8010041392384452111omplex J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_complex (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N2 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) N2)) (@ (@ tptp.gbinomial_rat (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) tptp.one_one_rat)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((K tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.gbinomial_real (@ tptp.semiri5074537144036343181t_real J3)) K))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.gbinomial_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.rat) (D tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (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) N2))) (@ (@ 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.extended_enat) (D tptp.extended_enat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (let ((_let_2 (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups7108830773950497114d_enat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p3455044024723400733d_enat A) (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.semiri4216267220026989637d_enat I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat)) (@ (@ tptp.plus_p3455044024723400733d_enat (@ _let_2 A)) (@ (@ tptp.times_7803423173614009249d_enat _let_1) D))))))) (forall ((A tptp.complex) (D tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))) (forall ((A tptp.real) (D tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((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) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I3) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N2) D)))) _let_1)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((A tptp.code_integer) (D tptp.code_integer) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.semiri4939895301339042750nteger I3)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) tptp.one_one_Code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) A)) (@ (@ tptp.times_3573771949741848930nteger _let_2) D)))) _let_1))))) (forall ((A tptp.int) (D tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((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) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))) (forall ((A tptp.nat) (D tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N2))) (= (@ (@ tptp.groups7501900531339628137nteger tptp.semiri4939895301339042750nteger) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N2))) (= (@ (@ 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)) N2))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri4216267220026989637d_enat N2))) (= (@ (@ tptp.times_7803423173614009249d_enat (@ tptp.numera1916890842035813515d_enat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups7108830773950497114d_enat tptp.semiri4216267220026989637d_enat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_7803423173614009249d_enat _let_1) (@ (@ tptp.plus_p3455044024723400733d_enat _let_1) tptp.one_on7984719198319812577d_enat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N2))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N2))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N2))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N2))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (forall ((X4 tptp.rat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X4))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N2)) 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 N2))))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.complex) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X4))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N2)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X4)))))))))) (forall ((X4 tptp.real) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X4))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N2))))) (let ((_let_4 (= X4 tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N2))))) (@ _let_1 X4)))))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.rat)) (X4 tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I3)) (@ (@ tptp.power_power_rat X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_rat X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.complex)) (X4 tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_complex (@ A I3)) (@ (@ tptp.power_power_complex X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_complex X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.int)) (X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_int (@ A I3)) (@ (@ tptp.power_power_int X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_int X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((N2 tptp.nat) (A (-> tptp.nat tptp.real)) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.set_ord_atMost_nat N2))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N2) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I3 tptp.nat)) (@ (@ tptp.times_times_real (@ A I3)) (@ (@ tptp.power_power_real X4) 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 X4) 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)) N2))) (@ (@ tptp.power_power_real X4) J3)))) (@ tptp.set_ord_lessThan_nat N2))))))) (forall ((Z tptp.rat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ 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)) N2)) tptp.one_one_nat))))))) (forall ((Z tptp.complex) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.comm_s2602460028002588243omplex Z) _let_2)) (@ (@ tptp.comm_s2602460028002588243omplex (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex _let_1)))) _let_2)) (@ (@ tptp.groups6464643781859351333omplex (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.semiri8010041392384452111omplex K3)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((Z tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.suc N2))) (= (@ (@ tptp.times_times_real (@ (@ tptp.comm_s7457072308508201937r_real Z) _let_2)) (@ (@ tptp.comm_s7457072308508201937r_real (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1)))) _let_2)) (@ (@ tptp.groups129246275422532515t_real (lambda ((K3 tptp.nat)) (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real K3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) tptp.one_one_nat))))))) (forall ((X4 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 X4) Y) (=> (@ _let_2 X4) (=> (=> (= X4 tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X4 _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X4 _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ 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) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ 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) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))) _let_101 (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups708209901874060359at_nat (lambda ((Uu3 tptp.nat)) tptp.one_one_nat)) A2) tptp.one_one_nat)) (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 ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N2))) (@ G N2))))) (forall ((G (-> tptp.nat tptp.complex)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups6464643781859351333omplex G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_complex (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.real)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups129246275422532515t_real G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_real (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups708209901874060359at_nat G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_nat (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((G (-> tptp.nat tptp.int)) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.groups705719431365010083at_int G))) (= (@ _let_2 (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.times_times_int (@ _let_2 (@ tptp.set_ord_atMost_nat N2))) (@ G _let_1)))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N2))) (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 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6464643781859351333omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_complex (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups129246275422532515t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_real (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups708209901874060359at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_nat (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((N2 tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N2))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups705719431365010083at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.one_one_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.times_times_int (@ _let_3 (@ _let_2 N2))) (@ G _let_1))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N2)))) (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 ((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 ((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.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.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.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.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.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.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.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.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 ((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 ((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 ((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 ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.groups708209901874060359at_nat F) A2)) N2) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) (@ (@ tptp.power_power_nat (@ F X)) N2))) A2))) (forall ((F (-> tptp.nat tptp.int)) (A2 tptp.set_nat) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups705719431365010083at_int F) A2)) N2) (@ (@ tptp.groups705719431365010083at_int (lambda ((X tptp.nat)) (@ (@ tptp.power_power_int (@ F X)) N2))) A2))) (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (N2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) N2) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) (@ (@ tptp.power_power_int (@ F X)) N2))) 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.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_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (forall ((I4 tptp.int)) (let ((_let_1 (@ F I4))) (=> (@ (@ tptp.member_int I4) A2) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_eq_int _let_1) (@ G I4)))))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1705073143266064639nt_int F) A2)) (@ (@ tptp.groups1705073143266064639nt_int G) A2)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X4) (@ tptp.the_real (lambda ((X tptp.real)) false))))) (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 ((X3 tptp.int)) (@ P X3)) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X))))))) (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B3) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (= X2 T2) (= (@ (@ tptp.minus_minus_int X2) D4) T2))))))) (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B3) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (not (= X2 T2)) (not (= (@ (@ tptp.minus_minus_int X2) D4) T2)))))))) (forall ((D4 tptp.int) (B3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X2) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X2) D4)) T2)))))) (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.minus_minus_int X2) D4))))))))) (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (= X2 T2) (= (@ (@ tptp.plus_plus_int X2) D4) T2))))))) (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (not (= X2 T2)) (not (= (@ (@ tptp.plus_plus_int X2) D4) T2)))))))) (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T2) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_int X2) T2) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X2) D4)) T2))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.plus_plus_int X2) D4)))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N2)) M)))))) (forall ((D4 tptp.int) (B3 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X2) D4)) T2)))))) (forall ((D4 tptp.int) (T2 tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T2) tptp.one_one_int)) B3) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X2 (@ (@ tptp.plus_plus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.minus_minus_int X2) D4))))))))) (forall ((D4 tptp.int) (T2 tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T2) tptp.one_one_int)) A2) (forall ((X2 tptp.int)) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ (@ tptp.ord_less_eq_int X2) T2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X2) D4)) T2))))))) (forall ((D4 tptp.int) (A2 tptp.set_int) (T2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T2))) (=> (forall ((Xa2 tptp.int)) (=> (@ (@ tptp.member_int Xa2) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X2 (@ (@ tptp.minus_minus_int Xb2) Xa2))))))) (=> (@ _let_1 X2) (@ _let_1 (@ (@ tptp.plus_plus_int X2) D4)))))))) (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int Z3) X5) (= (@ P X5) (@ P6 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) A2) (not (= X5 (@ (@ tptp.minus_minus_int Xb3) Xa3))))))) (=> (@ P X5) (@ P (@ (@ tptp.plus_plus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X3 tptp.int)) (@ P X3)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) A2) (@ P (@ (@ tptp.minus_minus_int Y5) X))))))))))))) (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z3 tptp.int)) (forall ((X5 tptp.int)) (=> (@ (@ tptp.ord_less_int X5) Z3) (= (@ P X5) (@ P6 X5))))) (=> (forall ((X5 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb3 tptp.int)) (=> (@ (@ tptp.member_int Xb3) B3) (not (= X5 (@ (@ tptp.plus_plus_int Xb3) Xa3))))))) (=> (@ P X5) (@ P (@ (@ tptp.minus_minus_int X5) D4))))) (=> (forall ((X5 tptp.int) (K2 tptp.int)) (= (@ P6 X5) (@ P6 (@ (@ tptp.minus_minus_int X5) (@ (@ tptp.times_times_int K2) D4))))) (= (exists ((X3 tptp.int)) (@ P X3)) (or (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X))) (exists ((X tptp.int)) (and (@ (@ tptp.member_int X) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y5 tptp.int)) (and (@ (@ tptp.member_int Y5) B3) (@ P (@ (@ tptp.plus_plus_int Y5) X))))))))))))) (= tptp.arccos (lambda ((Y5 tptp.real)) (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.cos_real X) Y5)))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N2)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat)) M))))) _let_100 _let_99 (= _let_34 (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real))))) (= tptp.pi (@ _let_98 (@ tptp.the_real (lambda ((X tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X) tptp.zero_zero_real)))))) (forall ((M tptp.int) (N2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N2) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int M) N2)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N2) (@ (@ tptp.plus_plus_int N2) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))) _let_97 (= tptp.divmod_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M6) N))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M6)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ tptp.suc Q5)) __flatten_var_0))) (@ (@ tptp.divmod_nat (@ (@ tptp.minus_minus_nat M6) N)) N))))) (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 ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int J))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) J))) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I2) _let_1)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X tptp.int)) X)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I2)) (@ tptp.semiri1314217659103216013at_int _let_1)))))) (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)) (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)) (= (@ (@ 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_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)) (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 ((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 ((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)))))))) (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)))) _let_96 (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)))))) _let_95 (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) (N2 tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (exists ((X tptp.nat)) (and (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M6) N2) (@ P M6))) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ P X))))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L) U))) (= tptp.set_ord_lessThan_nat _let_22) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2)) (@ tptp.semiri1408675320244567234ct_nat N2))) (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)) (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 ((N2 tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J2))))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N2) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N2) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((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 ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L) U))) _let_93 _let_92 (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A12)))) _let_91 (= tptp.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K3)) (not (@ _let_2 L2))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1)))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L)) (and (@ _let_1 K) (@ _let_1 L))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L) tptp.zero_zero_int)))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))) (= tptp.unique3479559517661332726nteger (lambda ((M6 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M6))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))) (forall ((K tptp.int) (L tptp.int) (N2 tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L)) N2) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N2) (@ (@ tptp.bit_se1146084159140164899it_int L) N2)))) (= 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_90 tptp.zero_z3403309356797280102nteger) (forall ((X4 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X4) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)))))) (forall ((L tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L)))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X4) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)) (@ (@ tptp.plus_plus_int X4) Y))) (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))) (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))) _let_89 (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_88) _let_87) _let_86 (= tptp.bit_concat_bit (lambda ((N tptp.nat) (K3 tptp.int) (L2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N) K3)) (@ (@ tptp.bit_se545348938243370406it_int N) L2)))) (= tptp.bit_se7879613467334960850it_int (lambda ((N tptp.nat) (K3 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K3) (@ (@ tptp.bit_se545348938243370406it_int N) tptp.one_one_int)))) (= tptp.one_one_nat tptp.one_one_nat) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N2) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N2))) (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 ((N2 tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K3 tptp.nat)) K3)) (@ _let_1 N2))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2))))) (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) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))) (forall ((X4 tptp.int) (N2 tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X4) (=> (@ (@ tptp.ord_less_int X4) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X4) Y)) _let_1)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))))))) (= 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 ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N2)))))) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))) (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 ((X4 tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X4))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X4)))) (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 ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N2)))))) (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa) X4)))) (= tptp.abs_abs_Code_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K3)) K3))) (not (@ _let_85 tptp.zero_z3403309356797280102nteger)) (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ (@ tptp.ord_less_int Xa) X4))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one) (forall ((Xa tptp.int) (X4 tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa)) (@ tptp.code_integer_of_int X4)) (@ (@ tptp.ord_less_eq_int Xa) X4))) _let_84 (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) tptp.one) (@ tptp.bit0 tptp.one))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) tptp.one) tptp.one)) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) _let_83 (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N2)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N2) M)))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bit1 M5)))))) (=> (=> _let_3 (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X4 (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (=> (=> (exists ((N3 tptp.num)) (= X4 (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit0 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))) (not (forall ((N3 tptp.num)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (=> (= Xa (@ tptp.bit1 M5)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M5)))))))))))))))))))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N2) M))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N2))))) _let_82 (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.plus_plus_nat N2) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M6)) (not (@ _let_2 N))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1)))))))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 N3)) (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit1 M5))) (=> (= Xa _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.bit_se1409905431419307370or_int (lambda ((K3 tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K3 _let_2) (= L2 _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K3 tptp.zero_zero_int)) L2) (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K3) _let_1)) (@ (@ tptp.modulo_modulo_int L2) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q3) tptp.zero_z5237406670263579293d_enat) Q3)) (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q3) Q3)) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat N2) tptp.zero_zero_nat) N2)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N2) N2)) (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 ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) (@ tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N2)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q3)) (@ (@ tptp.plus_plus_nat N2) Q3)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N2) Q3)) (@ (@ tptp.ord_max_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N2)) Q3) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N2) M)) M) (@ (@ tptp.ord_max_nat N2) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M3) N2)))) M)))) (forall ((N2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N2))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N2) M3)))) M)))) (= tptp.bit_se1412395901928357646or_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M6 tptp.zero_zero_nat)) N) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) M6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M6) _let_1)) (@ (@ tptp.modulo_modulo_nat N) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M6) _let_1)) (@ (@ tptp.divide_divide_nat N) _let_1))))))))) _let_81 _let_80 _let_79 (= 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))))) (forall ((R3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R3) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T3) (not (= R3 (@ (@ tptp.plus_plus_rat S3) T3)))))))))) (= tptp.ord_less_eq_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y5) (= X Y5)))) (= 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))) _let_78 (= tptp.code_bit_cut_integer (lambda ((K3 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K3 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K3)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S4))) (= S4 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))) (forall ((Q3 tptp.int) (P2 tptp.int)) (=> (@ (@ tptp.ord_less_int Q3) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P2)) (@ tptp.uminus_uminus_int Q3)))))) _let_77 (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X4))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa) _let_1))))))))) (forall ((R3 tptp.product_prod_int_int) (P2 tptp.int) (Q3 tptp.int)) (=> (= (@ tptp.normalize R3) (@ (@ tptp.product_Pair_int_int P2) Q3)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q3))) (= 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 ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ tptp.suc X4))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa) X4))) (=> (= (@ (@ tptp.nat_prod_decode_aux X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa) (@ (@ tptp.minus_minus_nat X4) Xa)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa) _let_2))))) (not _let_1))))))))) (= tptp.code_divmod_integer (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K3) L2))) (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 L2)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K3)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L2) S4)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 K3)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K3) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S4 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S4 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L2)) S4)))))) _let_1))))))))))) (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 ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U))) (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L) 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 ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.divide_divide_nat M) N2))) _let_76 (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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N)) U)))))) (forall ((P (-> tptp.nat Bool)) (I2 tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (and (@ P K3) (@ (@ tptp.ord_less_nat K3) I2)))))) (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (forall ((X5 tptp.nat)) (=> (@ (@ tptp.member_nat X5) N4) (@ (@ tptp.ord_less_nat X5) N2))) (@ tptp.finite_finite_nat N4))) (= tptp.finite_finite_nat (lambda ((N9 tptp.set_nat)) (exists ((M6 tptp.nat)) (forall ((X tptp.nat)) (=> (@ (@ tptp.member_nat X) N9) (@ (@ tptp.ord_less_nat X) M6)))))) (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D5) M)))))) (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))) (forall ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ tptp.finite_finite_nat N4))) (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 ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) K))))) (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) K))))) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L) U))) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L) 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_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 ((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 ((N2 tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))))) (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))) (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_atMost_nat K3))))) (= tptp.finite_finite_nat (lambda ((S5 tptp.set_nat)) (exists ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S5) (@ tptp.set_ord_lessThan_nat K3))))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat S2) (@ tptp.set_ord_lessThan_nat K2))))) (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M6 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_eq_int M6) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))) (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M6 tptp.int)) (exists ((N tptp.int)) (and (@ (@ tptp.ord_less_int M6) (@ tptp.abs_abs_int N)) (@ (@ tptp.member_int N) S2)))))) (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M5) (exists ((N6 tptp.nat)) (and (@ (@ tptp.ord_less_nat M5) N6) (@ (@ tptp.member_nat N6) S2))))) (not (@ tptp.finite_finite_nat S2)))) (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_nat M6) N) (@ (@ tptp.member_nat N) S2)))))) (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M6 tptp.nat)) (exists ((N tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M6) N) (@ (@ tptp.member_nat N) S2)))))) (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N2) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N2)))))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C))))))) (forall ((X4 tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X4) X4)) (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ _let_1 X4) (@ _let_1 Y)) (= X4 Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X4) tptp.zero_zero_real) (= X4 tptp.zero_zero_real)))) (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X4) Y))))) (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X4) Y))))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) tptp.one_one_real) tptp.one_one_real))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (= (@ (@ tptp.root N2) X4) tptp.one_one_real) (= X4 tptp.one_one_real)))) (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real)))) (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X4) tptp.zero_zero_real)))) (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_real X4) tptp.one_one_real)))) (forall ((N2 tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.root N2) Y)) (@ _let_1 Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4)))) (forall ((X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N2) X4))))) (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real X4) Y) (@ (@ tptp.ord_less_real (@ _let_1 X4)) (@ _let_1 Y)))))) (forall ((N2 tptp.nat) (X4 tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real X4) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X4)) (@ _let_1 Y)))))) (forall ((N2 tptp.nat) (X4 tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ (@ tptp.power_power_real X4) K)) (@ (@ tptp.power_power_real (@ _let_1 X4)) K))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ _let_1 (@ tptp.abs_abs_real X4)) (@ tptp.abs_abs_real (@ _let_1 X4)))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N2) X4)) (@ tptp.sgn_sgn_real X4)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.root N2) X4)))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X4)) (@ (@ tptp.root N2) X4)))))) _let_75 (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.abs_abs_real (@ (@ tptp.root N2) (@ (@ tptp.power_power_real Y) N2))) (@ tptp.abs_abs_real Y)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N2) X4))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_nat N2) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N2) X4)) (@ (@ tptp.root N4) X4))))))) (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X4)) (@ (@ tptp.root N2) X4)))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4)))) (forall ((N2 tptp.nat) (Y tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N2) X4) (= (@ (@ tptp.root N2) X4) Y))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X4) N2)) X4)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.root N2) (@ (@ tptp.power_power_real X4) N2)) X4))) (forall ((N2 tptp.nat) (Y tptp.real) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (= (@ (@ tptp.power_power_real Y) N2) X4) (= (@ (@ tptp.root N2) X4) Y)))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N2) X4)) N2) X4))) (forall ((N2 tptp.nat) (N4 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_eq_nat N2) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N2) X4)) (@ (@ tptp.root N4) X4))))))) (forall ((N2 tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.root N2) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N2))) Y))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ (@ tptp.root N2) X4))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N2)) X4)))) (forall ((N2 tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N2) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N2)))))) (forall ((N2 tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N2) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((N2 tptp.nat) (B tptp.real) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N2) B)) X4) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.log B) X4)))))) (forall ((P (-> tptp.real Bool)) (N2 tptp.nat) (X4 tptp.real)) (= (@ P (@ (@ tptp.root N2) X4)) (and (=> (= N2 tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (forall ((Y5 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)) X4) (@ P Y5))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= (@ (@ tptp.root N2) X4) (@ (@ tptp.powr_real X4) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2))))))) (forall ((A2 tptp.set_nat) (N2 tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N2) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N2) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ tptp.nat_set_encode A2)))))) (forall ((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 ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)) (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_nat I3) N2)))) N2)) (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))) (forall ((N2 tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I3) N2)))) (@ tptp.suc N2))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L))) (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N2)) (@ (@ tptp.modulo_modulo_nat M) N2))) (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L)) tptp.one_one_int)))) (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_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 ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N2))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat N2) (@ _let_1 N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N2) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N2))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N2))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N2)) (@ (@ tptp.set_or1269000886237332187st_nat M) N2)))) (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 ((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 ((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 ((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 ((N4 tptp.set_nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N2))) (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) S2))) (forall ((C tptp.complex) (N2 tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) C)))) N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z5 tptp.complex)) (= (@ (@ tptp.power_power_complex Z5) N2) tptp.one_one_complex)))) N2))) (forall ((N2 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N2) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) Z)) (@ (@ tptp.insert_nat N2) _let_1))))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L)) (@ (@ tptp.modulo364778990260209775nteger K) L))) (forall ((K tptp.code_integer) (L tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L)))) (forall ((M tptp.int) (N2 tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N2))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N2))))))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2)))))) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N2))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2)))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (= (@ (@ 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) N2))))))) _let_74 (forall ((X4 tptp.int) (Xa 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 X4)) (not (@ _let_2 Xa)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X4) _let_4) (@ (@ tptp.member_int Xa) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) 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 X4) _let_1)) (@ (@ tptp.divide_divide_int Xa) _let_1)))))))))))))) (= tptp.bit_se725231765392027082nd_int (lambda ((K3 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 K3)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K3) _let_4) (@ (@ tptp.member_int L2) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K3) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))) (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) 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 X4) Xa))))))))))))) (= 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 ((Y tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X4) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X4) 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 X4) Y)))))))))) (= tptp.bezw (lambda ((X tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y5) (@ (@ tptp.modulo_modulo_nat X) Y5)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y5 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y5)))))))))) (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (@ (@ tptp.bezw Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X4) Xa) 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 X4) Xa)))))))) (not _let_1)))))))))) (forall ((K tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))))) (forall ((X4 tptp.int) (Xa tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X4)) (not (@ _let_3 Xa)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X4) _let_5) (@ (@ tptp.member_int Xa) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X4) Xa) 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 X4) _let_2)) (@ (@ tptp.divide_divide_int Xa) _let_2))))))) (not _let_1)))))))))))) _let_73 (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))) (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ _let_51 tptp.bot_bot_set_nat)) _let_71 _let_70 (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)) (forall ((N2 tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N2) tptp.bot_bot_set_nat) (= N2 tptp.zero_zero_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N2)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N2))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N2) (@ _let_1 N2)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N2) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))) (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 ((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)))) _let_69 (forall ((M tptp.int) (N2 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N2)) (or (not (= M tptp.zero_zero_int)) (not (= N2 tptp.zero_zero_int))))) (= tptp.gcd_gcd_int (lambda ((X tptp.int) (Y5 tptp.int)) (@ (@ tptp.gcd_gcd_int Y5) (@ (@ tptp.modulo_modulo_int X) Y5)))) (forall ((X4 tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X4) Y))) (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 ((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 ((X4 tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X4))) (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 X4)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X4) 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 X4))) (=> (=> _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) (X4 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X4) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X4) Y))))) (= tptp.gcd_gcd_int (lambda ((K3 tptp.int) (L2 tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L2 tptp.zero_zero_int)) K3) (@ (@ tptp.gcd_gcd_int L2) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K3)) (@ tptp.abs_abs_int L2))))))) (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) (N2 tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N2)) (or (not (= M tptp.zero_zero_nat)) (not (= N2 tptp.zero_zero_nat))))) (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y5) (@ (@ tptp.modulo_modulo_nat X) Y5)))) (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 ((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 ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N2)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N2) M)) N2) (@ (@ tptp.gcd_gcd_nat M) N2)))) (forall ((Y tptp.nat) (X4 tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X4) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X4) Y))))) (= tptp.gcd_gcd_nat (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y5 tptp.zero_zero_nat)) X) (@ (@ tptp.gcd_gcd_nat Y5) (@ (@ tptp.modulo_modulo_nat X) Y5))))) (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y) (and (=> _let_1 (= Y X4)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa)))))))) (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) (L2 tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L2 tptp.zero_z3403309356797280102nteger)) K3) (@ (@ tptp.gcd_gcd_Code_integer L2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K3)) (@ tptp.abs_abs_Code_integer L2))))))) (forall ((N2 tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) K2) (@ P K2))) (=> (forall ((K2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K2) N2) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat K2) I) (@ P I))) (@ P K2)))) (@ P M)))) (forall ((X4 tptp.nat) (Xa tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X4) Xa)))) (let ((_let_2 (= Xa tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X4)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa) (@ (@ tptp.modulo_modulo_nat X4) Xa))))) (not _let_1)))))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R2 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R2) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N6) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R2 N6)) S2))))))) (forall ((N2 tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) (@ _let_1 K)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N2) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N2) _let_1) _let_1))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))) (forall ((L tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N2) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N2) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N2)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N2) M)) K)))) _let_68 (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N2 tptp.zero_zero_nat)))) (forall ((N2 tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N2) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N2) K)))) _let_67 (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L) tptp.one_one_int))))) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L) U))) (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L) U))) (forall ((N2 tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)) K)))) (forall ((K tptp.int) (N2 tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))))) (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L)))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or5834768355832116004an_nat L) U))) (forall ((X4 tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X4)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))) (forall ((N2 tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N2)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N2) tptp.one)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.compow_nat_nat N2) tptp.suc) (@ tptp.plus_plus_nat N2))) (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 ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y5) X))) (lambda ((X tptp.nat) (Y5 tptp.nat)) (@ (@ tptp.ord_less_nat Y5) X))) (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 ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer 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 ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L2)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))) (forall ((X4 tptp.code_integer) (Xa tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X4) Xa)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X4)) (@ tptp.code_int_of_integer Xa)))) _let_66 (= tptp.ord_le6747313008572928689nteger (lambda ((X tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa4)))) _let_65 (= tptp.ord_le3102999989581377725nteger (lambda ((K3 tptp.code_integer) (L2 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K3)) (@ tptp.code_int_of_integer L2)))) (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.times_times_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 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 Y5))) (let ((_let_2 (@ tptp.times_times_nat X))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa) X4)))) (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))) (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa) X4))) (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat U2) Y5)))) __flatten_var_0))) Xa) X4))) (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) U2)) (@ (@ tptp.plus_plus_nat Y5) V4)))) __flatten_var_0))) Xa) X4)))) (forall ((Xa tptp.product_prod_nat_nat) (X4 tptp.product_prod_nat_nat)) (= (@ (@ tptp.minus_minus_int (@ tptp.abs_Integ Xa)) (@ tptp.abs_Integ X4)) (@ tptp.abs_Integ (@ (@ (@ tptp.produc27273713700761075at_nat (lambda ((X tptp.nat) (Y5 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X) V4)) (@ (@ tptp.plus_plus_nat Y5) U2)))) __flatten_var_0))) Xa) X4)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N2)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N2)))) (=> (not _let_2) (= _let_1 tptp.one)))))) _let_64 (forall ((Q3 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q3)) Q3)) (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N2)) N2))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N2) tptp.one_one_nat) (= (@ tptp.num_of_nat N2) tptp.one))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N2) N2)) (@ tptp.bit0 (@ tptp.num_of_nat N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N2) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N2)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N2))))))) (= tptp.ord_less_eq_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 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 Y5) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))) (= tptp.ord_less_int (lambda ((X tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y5 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 Y5) V4)) (@ (@ tptp.plus_plus_nat U2) Z5)))) __flatten_var_0))) (@ tptp.rep_Integ X)) (@ tptp.rep_Integ Xa4)))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Xa tptp.one_one_nat)) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (not (= Xa tptp.one_one_nat))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (not (and (= Deg2 Xa) (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 Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X4 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (= Y (not (= Xa tptp.one_one_nat)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (=> (= X4 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3)) (= Y (not (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))))) (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima2)))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_valid X4) Xa) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (= Y (= Xa tptp.one_one_nat)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa))))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary3))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_2)))) (=> (= X4 _let_1) (=> (= Y (and (= Deg2 Xa) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid X4) Xa) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (not (= Xa tptp.one_one_nat)))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 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) Summary3))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (not (and (= Deg2 Xa) (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 Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima)))))))))))))) (forall ((X4 tptp.vEBT_VEBT) (Xa tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_valid X4) Xa)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat X4) Xa)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X4 _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa)) (= Xa tptp.one_one_nat))))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary3 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) Summary3))) (=> (= X4 _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa)) (and (= Deg2 Xa) (forall ((X5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X5) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X5) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary3) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X3))) (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi2 Ma2))) (and (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (@ (@ tptp.ord_less_nat Ma2) (@ (@ 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 ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I3)) X3)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I3))))) (=> _let_2 (forall ((X tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X) X3)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma2) (forall ((X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X) (and (@ (@ tptp.ord_less_nat Mi2) X) (@ (@ tptp.ord_less_eq_nat X) Ma2)))))))))))))) Mima))))))))))))) _let_63 (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q5 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 Q5)))))) (@ (@ tptp.bit_take_bit_num _let_1) N2))))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((R3 tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N2) M)))) (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N2)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M)))) (forall ((R3 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R3)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R3)) M))))) (forall ((N2 tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N2)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N2))))) _let_62 (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N) M)))) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N2) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num tptp.one))) N2))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num tptp.one))) (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 ((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 ((N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N2)) tptp.none_num)) (forall ((N2 tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N2) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))) N2))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))) (forall ((M tptp.num) (N2 tptp.num) (Q3 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) (@ tptp.some_num Q3)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ tptp.numeral_numeral_int Q3)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_and_not_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N2) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) tptp.zero_zero_int))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N2)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N2) M)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N2))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N2)))) _let_61 (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I2))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (let ((_let_2 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y) (=> (=> _let_2 (=> (= Xa tptp.one) _let_1)) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit0 N3))) (not (= Y (@ tptp.some_num tptp.one))))) (=> (=> _let_2 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit1 N3))) _let_1)) (=> (forall ((M5 tptp.num)) (let ((_let_1 (@ tptp.bit0 M5))) (=> (= X4 _let_1) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num _let_1))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M5) N3))))))))))))))))))))) (= tptp.bit_take_bit_num (lambda ((N tptp.nat) (M6 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P5 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num O) P5)))) (lambda ((P5 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P5))))) X))) A3))) (@ (@ tptp.product_Pair_nat_num N) M6)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_and_not_num M) N2)))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_and_not_num_rel))) (=> (= (@ (@ tptp.bit_and_not_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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 ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (not (= Y (@ tptp.some_num tptp.one))))) (let ((_let_2 (= Xa tptp.one))) (let ((_let_3 (=> _let_2 _let_1))) (let ((_let_4 (not (= Y tptp.none_num)))) (let ((_let_5 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y) (=> (=> _let_5 _let_3) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit0 N3))) _let_4)) (=> (=> _let_5 (=> (exists ((N3 tptp.num)) (= Xa (@ tptp.bit1 N3))) _let_1)) (=> (=> (exists ((M5 tptp.num)) (= X4 (@ tptp.bit0 M5))) (=> _let_2 _let_4)) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (=> (=> (exists ((M5 tptp.num)) (= X4 (@ tptp.bit1 M5))) _let_3) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M5) N3)))))))) (not (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)))))))))))))))))))))))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y) (=> (=> _let_1 (=> (= Xa tptp.one) (not (= Y tptp.none_num)))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit1 N3))))))) (=> (=> _let_1 (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ tptp.some_num (@ tptp.bit0 N3))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit1 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit0 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (=> (= Xa tptp.one) (not (= Y (@ tptp.some_num (@ tptp.bit0 M5))))))) (=> (forall ((M5 tptp.num)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (=> (= Xa (@ tptp.bit1 N3)) (not (= Y (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M5) N3)))))))))))))))))))) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) tptp.one) (@ tptp.some_num tptp.one)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) tptp.one) tptp.none_num) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num tptp.one))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num tptp.one))) (forall ((M tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) tptp.one) tptp.none_num)) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num tptp.one) (@ tptp.bit0 N2)) tptp.none_num)) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un2480387367778600638or_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ (@ tptp.map_option_num_num tptp.bit0) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))) (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 ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit1 N2)) (@ tptp.some_num (@ tptp.bit0 N2)))) (forall ((N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num tptp.one) (@ tptp.bit0 N2)) (@ tptp.some_num (@ tptp.bit1 N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un7362597486090784418nd_num (@ tptp.bit1 M)) (@ tptp.bit1 N2)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N10 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N10)))) (@ (@ tptp.bit_un7362597486090784418nd_num M) N2)))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit1 M)) (@ tptp.bit0 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))) (forall ((M tptp.num) (N2 tptp.num)) (= (@ (@ tptp.bit_un2480387367778600638or_num (@ tptp.bit0 M)) (@ tptp.bit1 N2)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_un2480387367778600638or_num M) N2))))) (forall ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un4731106466462545111um_rel))) (=> (= (@ (@ tptp.bit_un7362597486090784418nd_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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 ((X4 tptp.num) (Xa tptp.num) (Y tptp.option_num)) (let ((_let_1 (= X4 tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_un2901131394128224187um_rel))) (=> (= (@ (@ tptp.bit_un2480387367778600638or_num X4) Xa) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X4) Xa)) (=> (=> _let_1 (=> (= Xa 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))) (=> (= Xa _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))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit0 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))) (=> (= X4 _let_1) (=> (= Xa 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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= Xa _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)) (=> (= X4 (@ tptp.bit1 M5)) (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= Xa _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))))))))))))))))))))))) _let_60 _let_59 _let_58 _let_57 (forall ((N2 tptp.nat) (J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N2) (@ (@ tptp.minus_minus_nat J) I2)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J))) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat I2) N2))))) (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X4)))) (forall ((L tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U))) (forall ((L tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L) U)) (@ (@ tptp.minus_minus_nat U) L))) (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N2)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N2))))) (= (@ tptp.sqr tptp.one) tptp.one) (forall ((L tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L)) U) (@ (@ tptp.set_or6659071591806873216st_nat L) U))) _let_56 (forall ((X4 tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X4))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))) (forall ((N2 tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N2)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N2)) N2))))) (= (@ tptp.code_integer_of_num _let_19) _let_55) (forall ((L tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L) U))) (forall ((L tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L)))) (forall ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L) U))) (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer) (forall ((N2 tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N2))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))) _let_54 (forall ((C tptp.nat) (Y tptp.nat) (X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X4) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X4) 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 X4) 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) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M7) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M7) N4))) (forall ((X4 tptp.real)) (= (@ (@ tptp.member_real (@ tptp.abs_abs_real X4)) tptp.field_5140801741446780682s_real) (@ (@ tptp.member_real X4) tptp.field_5140801741446780682s_real))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or1269000886237332187st_nat I2) J)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc I2)) (@ tptp.suc J)))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat I2) J)) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc I2)) (@ tptp.suc J)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X4) X5) (@ (@ tptp.ord_less_real X5) Y))))) (forall ((X4 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_real X5) X4)))) (forall ((X4 tptp.real)) (exists ((X5 tptp.real)) (and (@ (@ tptp.member_real X5) tptp.field_5140801741446780682s_real) (@ (@ tptp.ord_less_eq_real X4) X5)))) (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N2))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N2)))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))) (forall ((N2 tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N2)))))) (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N2))))) (forall ((N2 tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N2)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N2))))) (= 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))))))) _let_53 _let_52 (= tptp.finite_finite_int (lambda ((S5 tptp.set_int)) (exists ((K3 tptp.int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.image_int_int tptp.abs_abs_int) S5)) (@ 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 ((L tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X tptp.int)) (@ (@ tptp.plus_plus_int X) L))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L))) (@ (@ tptp.set_or4662586982721622107an_int L) U))) (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)))))) (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)))))) (= (@ 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) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.image_nat_nat (lambda ((M6 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M6) N2))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N2)))) (= tptp.top_top_set_nat (@ _let_51 _let_26)) (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat) (= (@ tptp.finite_card_o tptp.top_top_set_o) _let_50) _let_49 (= (@ tptp.finite_card_char tptp.top_top_set_char) _let_21) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.semiri5074537144036343181t_real N2))) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))))) (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) (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) (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_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_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) (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) (X4 tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X4) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (= (@ F X4) (@ F Y)))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (= (@ F X4) (@ F Y3)))) (= L tptp.zero_zero_real))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.minus_minus_real X4) H4))))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X4) H4))) (@ F X4)))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X4) H4))) (@ F X4)))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F (@ (@ tptp.plus_plus_real X4) H4))))))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X4)))))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) S2)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X4)) (@ F _let_1)))))))))))) (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)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F Y3)) (@ F X4)))) (= L tptp.zero_zero_real))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (X4 tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 X4) Y3))) D) (@ (@ tptp.ord_less_eq_real (@ F X4)) (@ F Y3)))) (= L tptp.zero_zero_real))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X4)) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ G X)) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ G X4)) (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)))) M)) _let_1)))) (forall ((N2 tptp.nat) (X4 tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real X) N2))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X4) S))) (forall ((Z tptp.real) (R3 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z5 tptp.real)) (@ (@ tptp.powr_real Z5) R3))) (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R3) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))) (forall ((X4 tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X4))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) R3))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R3) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R3) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))) (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real)) (R3 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (let ((_let_2 (@ G X4))) (let ((_let_3 (@ F X4))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R3) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ (@ tptp.powr_real (@ G X)) (@ F X)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R3) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X4))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (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 ((X tptp.real)) (@ (@ F X) 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 ((X tptp.real)) (@ tptp.suminf_real (@ F X)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))) (forall ((X4 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (forall ((X4 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X4)))) (=> (not (= X4 tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))) (forall ((X4 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 X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A2))) (forall ((X4 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X4) A2)))) (forall ((X4 tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) 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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X5) N)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R)) R)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X tptp.real)) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ F N)) (@ (@ tptp.power_power_real X) (@ tptp.suc N))))))) (@ tptp.suminf_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))) (@ (@ tptp.power_power_real X0) N))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X4) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 tptp.real) (N2 tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real)))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X4 tptp.real) (N2 tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (exists ((T3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))) (forall ((N2 tptp.nat) (X4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (=> (not (= X4 tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))) (forall ((H tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real H) 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 H) T3) (@ (@ tptp.ord_less_real T3) tptp.zero_zero_real) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2))))))))))) (forall ((H tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2)))))))))) (forall ((H tptp.real) (N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ 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) H) (= (@ F H) (@ (@ 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 H) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real H) N2))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X4 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 X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2)))))))))))) (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N2 tptp.nat) (X4 tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T3)) (@ tptp.abs_abs_real X4))) (@ (@ (@ 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 X4)) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real X4) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real X4) N2))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N2)))))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N2)))))))))))) (forall ((N2 tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M5 tptp.nat) (T3 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M5) N2) (@ (@ 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 X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (=> (not (= X4 C)) (exists ((T3 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real T3))) (let ((_let_2 (@ tptp.ord_less_real X4))) (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 X4))) (= (@ F X4) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M6 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M6) C)) (@ tptp.semiri2265585572941072030t_real M6))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) M6)))) (@ tptp.set_ord_lessThan_nat N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N2) T3)) (@ tptp.semiri2265585572941072030t_real N2))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X4) C)) N2))))))))))))))))))) (forall ((N2 tptp.nat) (H 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) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T3) (@ (@ tptp.ord_less_eq_real T3) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M5)) (@ (@ Diff (@ tptp.suc M5)) T3)) (@ (@ tptp.topolo2177554685111907308n_real T3) tptp.top_top_set_real)))) (=> (= N2 (@ tptp.suc K)) (forall ((M2 tptp.nat) (T4 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N2) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T4) (@ (@ tptp.ord_less_eq_real T4) H)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real U2) P5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real 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 ((P5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P5)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P5))) (@ (@ tptp.power_power_real T4) P5)))) (@ 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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X9 tptp.real)) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X9) _let_1)))))))) (@ tptp.suminf_real (lambda ((K3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) K3)) (@ (@ tptp.power_power_real X4) (@ (@ tptp.times_times_nat K3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))) (forall ((N2 tptp.nat) (X4 tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N2))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.power_power_real (@ _let_1 X4)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (not (= X4 tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X4) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X4) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)))))))))))) _let_48 (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_23) (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) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat _let_1) J))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.suc I2))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I2) J)) (@ (@ tptp.cons_nat _let_1) (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat _let_1) J))))))) (= 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))))) (forall ((X4 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X4) Xa)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))) (forall ((I2 tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I2) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I2))) (forall ((I2 tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I2) J)) (@ (@ tptp.ord_less_int J) I2))) (forall ((J tptp.int) (I2 tptp.int)) (=> (@ (@ tptp.ord_less_int J) I2) (= (@ (@ tptp.upto I2) J) 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) (J tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int I2) (@ tptp.semiri1314217659103216013at_int K)))) (=> (@ (@ tptp.ord_less_eq_int _let_1) J) (= (@ (@ tptp.nth_int (@ (@ tptp.upto I2) J)) K) _let_1)))) (forall ((I2 tptp.int) (J tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.upto I2) J)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int J) I2)) tptp.one_one_int)))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N2)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))) _let_47 _let_46 _let_45 (= tptp.upto (lambda ((I3 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I3) J3) tptp.nil_int))) _let_44 (forall ((I2 tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I2) J))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.set_or4665077453230672383an_nat I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.sup_sup_set_nat (@ _let_2 J)) (@ (@ tptp.set_or4665077453230672383an_nat J) _let_1))))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 J)) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K))))))) (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.upto J) K))))))) _let_43 _let_42 (= 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 ((X4 tptp.int) (Xa tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X4) Xa))) (=> (= (@ (@ tptp.upto X4) Xa) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X4) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X4) tptp.one_one_int)) Xa)))) (=> (not _let_1) (= Y tptp.nil_int)))))) (forall ((I2 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ (@ tptp.upto I2) J) (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (= (@ _let_1 J) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) tptp.nil_int)))))) _let_41 (forall ((I2 tptp.int) (J tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.upto I2))) (=> (@ (@ tptp.ord_less_eq_int I2) J) (=> (@ (@ tptp.ord_less_eq_int J) K) (= (@ _let_1 K) (@ (@ tptp.append_int (@ _let_1 (@ (@ tptp.minus_minus_int J) tptp.one_one_int))) (@ (@ tptp.cons_int J) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int J) tptp.one_one_int)) K)))))))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int I2) J))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I2) J)) (and (=> _let_2 (= _let_1 (@ (@ tptp.cons_int I2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I2) tptp.one_one_int)) J)))) (=> (not _let_2) (= _let_1 tptp.nil_int))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X2))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L tptp.zero_zero_real)) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (not (= (@ F X2) tptp.zero_zero_real))))))))) (forall ((F (-> tptp.real tptp.real)) (L tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L) tptp.zero_zero_real) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X2 tptp.real)) (=> (and (not (= X2 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X2))) R2)) (@ (@ tptp.ord_less_real (@ F X2)) tptp.zero_zero_real)))))))) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X)) (@ tptp.sin_real X)))) _let_31) (@ _let_39 tptp.top_top_set_real)) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real (@ A tptp.zero_zero_nat)) tptp.zero_zero_real) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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)))))))))) (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ A tptp.zero_zero_nat)) (forall ((N6 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N6))) (@ (@ tptp.member_real (@ tptp.suminf_real (lambda ((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))))))))))) (@ (@ (@ 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 (@ tptp.times_times_nat 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 (lambda ((X tptp.nat)) (@ (@ tptp.times_times_nat X) 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 ((N tptp.nat)) (@ (@ tptp.root N) (@ tptp.semiri5074537144036343181t_real N)))) _let_40) 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 ((N tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N)) (@ G N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N6)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N6))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))) (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R2 tptp.real)) (exists ((N7 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N7) N3) (@ (@ tptp.ord_less_real R2) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N)))) _let_31) tptp.at_top_nat) (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.root N) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))) _let_31) tptp.at_top_nat) (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)) (forall ((F (-> tptp.nat tptp.real)) (L tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L)) (=> (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N6 tptp.nat)) (@ (@ tptp.ord_less_eq_real L) (@ (@ tptp.plus_plus_real (@ F N6)) E))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L)) tptp.at_top_nat))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X4)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))) (forall ((X4 tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X4) N)))) (@ 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 ((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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X4) N)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.plus_plus_real R3) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))))))) (@ tptp.topolo2815343760600316023s_real R3)) tptp.at_top_nat)) (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) (@ tptp.semiri5074537144036343181t_real N)))) N))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_nat)) (forall ((R3 tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (@ (@ tptp.times_times_real R3) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)))))))) (@ tptp.topolo2815343760600316023s_real R3)) 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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N))))))) (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 ((N tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ A N)))))))) (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 ((N 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))) N))))) (@ 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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X4)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X4) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))) (forall ((A (-> tptp.nat tptp.real)) (N2 tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((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))) N2)))) (@ 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))) (=> (@ (@ (@ 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 ((N 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))) N))))) (@ 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))) (=> (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 ((N6 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))) N6)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N))))) _let_1) tptp.at_top_nat) (forall ((N6 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))) N6)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N 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))) N)) 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 ((N 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))) N)) 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))) (=> (@ (@ (@ 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 ((N 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))) N)) 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)) (N2 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))) N2)) tptp.one_one_nat)))))))) (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 ((N tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) 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 ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N9 tptp.nat)) (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N9) N) (@ P N)))))) (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)) (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 ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real B) A)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5984915006950818249n_real A))))) (@ (@ _let_38 _let_40) tptp.at_top_real) (@ (@ _let_29 tptp.at_top_real) (@ _let_30 (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))) (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) K)) (@ tptp.exp_real X)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)) (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X4) Y5))) Y5))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) tptp.at_top_real)) (@ (@ _let_36 tptp.at_top_real) (@ _let_39 (@ tptp.set_or5984915006950818249n_real _let_34))) (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_37 (@ tptp.topolo2815343760600316023s_real _let_34)) tptp.at_top_real) (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_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 ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X4) (=> (@ (@ tptp.ord_less_eq_real X4) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X4)) tptp.at_top_nat)))) (forall ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_top_real) F5))))) (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real) (@ (@ _let_38 (@ tptp.topolo2815343760600316023s_real _let_24)) tptp.at_bot_real) (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 ((N2 tptp.nat) (F (-> tptp.real tptp.real)) (F5 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F5) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X tptp.real)) (@ (@ tptp.power_power_real (@ F X)) N2))) tptp.at_bot_real) F5))))) (@ (@ _let_37 (@ tptp.topolo2815343760600316023s_real _let_35)) tptp.at_bot_real) (forall ((X4 tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X4) Y5))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y5)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X4))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (@ (@ _let_36 tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_35) (@ tptp.set_or5849166863359141190n_real _let_35))) (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.eventually_real (lambda ((X tptp.real)) (@ (@ tptp.member_real X) (@ (@ tptp.set_or1633881224788618240n_real A) B)))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))))) (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) _let_31) (@ _let_30 (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))) (@ (@ _let_29 tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_24) (@ tptp.set_or5849166863359141190n_real _let_24))) _let_28 (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))) (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.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_26) (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))))) (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_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) (M9 tptp.real)) (and (forall ((X2 tptp.real)) (let ((_let_1 (@ F X2))) (=> (and (@ (@ tptp.ord_less_eq_real A) X2) (@ (@ tptp.ord_less_eq_real X2) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y4 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y4) (@ (@ tptp.ord_less_eq_real Y4) M9)) (exists ((X5 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X5) (@ (@ tptp.ord_less_eq_real X5) B) (= (@ F X5) Y4)))))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi6264000038957366511cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_nat M) N2))) (forall ((A tptp.real) (X4 tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) 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 X4)) tptp.top_top_set_real)) G)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X4) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcosh_real))) (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X4 tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X4)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X4) (=> (@ (@ tptp.ord_less_real X4) B) (=> (forall ((Y3 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y3) (=> (@ (@ tptp.ord_less_real Y3) B) (= (@ F (@ G Y3)) Y3)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arccos)))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.arcsin)))) (forall ((B tptp.real) (X4 tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X4) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.member_real X5) (@ (@ tptp.set_or1633881224788618240n_real B) X4)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X4)))))) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X4) (=> (@ (@ tptp.ord_less_real X4) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X4) tptp.top_top_set_real)) tptp.artanh_real)))) (forall ((D tptp.real) (X4 tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (= (@ G (@ F Z2)) Z2))) (=> (forall ((Z2 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z2) X4))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X4)) tptp.top_top_set_real)) G))))) (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.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 ((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 ((X tptp.real)) (@ tptp.arcosh_real (@ F X)))))))) (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_25 tptp.arccos) (@ _let_25 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 ((X tptp.real)) (@ tptp.artanh_real (@ F X)))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ 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) (= (@ F4 Z2) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F4 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (exists ((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.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ 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_real A) X5) (=> (@ (@ tptp.ord_less_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.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))) (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)) (X4 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) X4) (=> (@ (@ tptp.ord_less_eq_real X4) B) (= (@ F X4) (@ F A)))))))) (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X5) (=> (@ (@ tptp.ord_less_real X5) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))))) (exists ((Z2 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z2) (@ (@ tptp.ord_less_real Z2) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z2) tptp.top_top_set_real))))))))) (@ tptp.order_mono_nat_nat tptp.suc) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N2)))) (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 ((X tptp.nat)) (@ F (@ G X)))) tptp.at_top_nat) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat)))))) (forall ((F (-> tptp.nat tptp.nat)) (N2 tptp.nat)) (=> (@ tptp.order_5726023648592871131at_nat F) (@ (@ tptp.ord_less_eq_nat N2) (@ F N2)))) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (@ (@ tptp.inj_on_real_real (lambda ((Y5 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y5)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y5)) N2)))) 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 ((F (-> tptp.real tptp.real)) (F4 (-> tptp.real tptp.real))) (=> (forall ((X5 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F4 X5)) (@ (@ tptp.topolo2177554685111907308n_real X5) tptp.top_top_set_real))) (=> (forall ((X5 tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F4 X5))) (@ tptp.order_7092887310737990675l_real F)))) (forall ((N4 tptp.set_nat) (K tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.member_nat N3) N4) (@ (@ tptp.ord_less_eq_nat K) N3))) (@ (@ tptp.inj_on_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) K))) N4))) (forall ((N4 tptp.set_nat)) (@ (@ tptp.inj_on_nat_nat tptp.suc) N4)) (@ (@ tptp.inj_on_nat_char tptp.unique3096191561947761185of_nat) _let_23) (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 ((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)))))) (= _let_18 _let_18) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.member8440522571783428010at_nat (@ (@ tptp.product_Pair_nat_nat M) N2)) (@ tptp.transi2905341329935302413cl_nat tptp.pred_nat)) (@ (@ tptp.ord_less_eq_nat M) N2))) _let_17 _let_16 (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 ((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)) (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 ((P (-> tptp.rat Bool)) (Q3 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q3))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))) (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)))) (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.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))) (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 ((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)))) (= tptp.ord_less_rat (lambda ((X tptp.rat) (Y5 tptp.rat)) (@ tptp.positive (@ (@ tptp.minus_minus_rat Y5) X)))) _let_14 (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc M)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat M) N2)))) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat N2) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat tptp.zero_zero_nat) N2) tptp.zero_zero_nat)) (forall ((N2 tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) (@ tptp.pred_numeral K))))) (forall ((K tptp.num) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N2)) (@ tptp.suc (@ (@ tptp.ord_min_nat (@ tptp.pred_numeral K)) N2)))) _let_13 (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_min_nat M) N2)) Q3) (@ (@ tptp.ord_min_nat (@ (@ tptp.times_times_nat M) Q3)) (@ (@ tptp.times_times_nat N2) Q3)))) (forall ((M tptp.nat) (N2 tptp.nat) (Q3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_min_nat N2) Q3)) (@ (@ tptp.ord_min_nat (@ _let_1 N2)) (@ _let_1 Q3))))) (forall ((M tptp.nat) (I2 tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ (@ tptp.minus_minus_nat M) I2)) (@ (@ tptp.minus_minus_nat N2) I2)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.ord_min_nat M) N2)) I2))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L tptp.int) (R3 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit M) (@ (@ (@ tptp.bit_concat_bit N2) K) L)) R3) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.minus_minus_nat M) N2)) L) R3)))) (forall ((M tptp.nat) (N2 tptp.nat) (K tptp.int) (L tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int M) (@ (@ (@ tptp.bit_concat_bit N2) K) L)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.ord_min_nat M) N2)) K) (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat M) N2)) L)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_min_nat (@ tptp.suc N2)) M) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat N2) M3)))) M))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.ord_min_nat M) (@ tptp.suc N2)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((M3 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_min_nat M3) N2)))) M))) (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat Q3) tptp.zero_z5237406670263579293d_enat) tptp.zero_z5237406670263579293d_enat)) (forall ((Q3 tptp.extended_enat)) (= (@ (@ tptp.ord_mi8085742599997312461d_enat tptp.zero_z5237406670263579293d_enat) Q3) tptp.zero_z5237406670263579293d_enat)) _let_12 (= 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 ((L2 tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L2))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K3) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))) (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))) (= tptp.divide_divide_nat (lambda ((M6 tptp.nat) (N tptp.nat)) (@ (@ (@ tptp.if_nat (= N tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K3) N)) M6))))))) (forall ((N2 tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N2) (= (@ (@ tptp.gcd_gcd_nat M) N2) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D5))) (and (@ _let_1 M) (@ _let_1 N2))))))))) (forall ((M tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ tptp.remdups_nat _let_1) _let_1))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.tl_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) N2))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ tptp.hd_nat (@ (@ tptp.upt I2) J)) I2))) (forall ((M tptp.nat) (I2 tptp.nat) (J tptp.nat)) (= (@ (@ tptp.drop_nat M) (@ (@ tptp.upt I2) J)) (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) M)) J))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I2) J)) (@ (@ tptp.minus_minus_nat J) I2))) (forall ((I2 tptp.nat) (M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) M))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) N2) (= (@ (@ tptp.take_nat M) (@ _let_2 N2)) (@ _let_2 _let_1)))))) (forall ((J tptp.nat) (I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I2) (= (@ (@ tptp.upt I2) J) tptp.nil_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N2)) (@ (@ tptp.upt M) N2))) (forall ((I2 tptp.nat) (J tptp.nat)) (= (= (@ (@ tptp.upt I2) J) tptp.nil_nat) (or (= J tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat J) I2)))) (forall ((I2 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat I2) K))) (=> (@ (@ tptp.ord_less_nat _let_1) J) (= (@ (@ tptp.nth_nat (@ (@ tptp.upt I2) J)) K) _let_1)))) _let_11 _let_10 _let_9 _let_8 (= tptp.set_ord_lessThan_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N)))) (forall ((M tptp.nat) (N2 tptp.nat) (Ns tptp.list_nat) (Q3 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N2) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q3)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q3))))) (forall ((I2 tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I2) J))) (forall ((I2 tptp.nat)) (= (@ (@ tptp.upt I2) tptp.zero_zero_nat) tptp.nil_nat)) (= tptp.set_ord_atMost_nat (lambda ((N tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N))))) (forall ((I2 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) J) (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat I2) (@ (@ tptp.upt (@ tptp.suc I2)) J))))) (forall ((I2 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat J) K))) (let ((_let_2 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_2 _let_1) (@ (@ tptp.append_nat (@ _let_2 J)) (@ (@ tptp.upt J) _let_1))))))) (forall ((I2 tptp.nat) (J tptp.nat) (X4 tptp.nat) (Xs tptp.list_nat)) (= (= (@ (@ tptp.upt I2) J) (@ (@ tptp.cons_nat X4) Xs)) (and (@ (@ tptp.ord_less_nat I2) J) (= I2 X4) (= (@ (@ tptp.upt (@ (@ tptp.plus_plus_nat I2) tptp.one_one_nat)) J) 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) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (let ((_let_2 (@ _let_1 (@ tptp.suc J)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat I2) J))) (and (=> _let_3 (= _let_2 (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))) (=> (not _let_3) (= _let_2 tptp.nil_nat))))))) (forall ((I2 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.upt I2))) (=> (@ (@ tptp.ord_less_eq_nat I2) J) (= (@ _let_1 (@ tptp.suc J)) (@ (@ tptp.append_nat (@ _let_1 J)) (@ (@ tptp.cons_nat J) tptp.nil_nat)))))) (forall ((M tptp.nat) (N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N2) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X tptp.nat)) X)) (@ (@ tptp.set_or4665077453230672383an_nat M) N2))))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N2)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2)))) (forall ((N2 tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I3 tptp.nat)) (@ (@ tptp.plus_plus_nat I3) N2))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N2) (@ (@ tptp.plus_plus_nat M) N2)))) (forall ((M tptp.nat) (N2 tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N tptp.nat)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N2))) (@ (@ tptp.upt M) N2))) _let_7 (forall ((M tptp.nat) (N4 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.plus_plus_nat (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) (= (@ tptp.groups4561878855575611511st_nat L2) N4)))))) (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ (@ tptp.plus_plus_nat (@ tptp.groups4561878855575611511st_nat L2)) tptp.one_one_nat) N4))))))))) (forall ((M tptp.nat) (N4 tptp.nat)) (= (@ tptp.finite_card_list_nat (@ tptp.collect_list_nat (lambda ((L2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat L2) M) (= (@ tptp.groups4561878855575611511st_nat L2) N4))))) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N4) M)) tptp.one_one_nat)) N4))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_eq_nat) (@ (@ tptp.upt M) N2))) (forall ((M tptp.nat) (N2 tptp.nat)) (@ (@ tptp.sorted_wrt_nat tptp.ord_less_nat) (@ (@ tptp.upt M) N2))) (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 ((I2 tptp.int) (J tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_int) (@ (@ tptp.upto I2) J))) (forall ((M tptp.int) (N2 tptp.int)) (@ (@ tptp.sorted_wrt_int tptp.ord_less_eq_int) (@ (@ tptp.upto M) N2))) (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 ((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)))) _let_6 (forall ((X4 tptp.list_nat) (Y tptp.nat)) (=> (= (@ tptp.nat_list_encode X4) Y) (=> (=> (= X4 tptp.nil_nat) (not (= Y tptp.zero_zero_nat))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (=> (= X4 (@ (@ tptp.cons_nat X5) Xs2)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2)))))))))))) (forall ((X4 tptp.nat) (Xs tptp.list_nat)) (= (@ tptp.nat_list_encode (@ (@ tptp.cons_nat X4) Xs)) (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X4) (@ tptp.nat_list_encode Xs)))))) (forall ((X4 tptp.list_nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.accp_list_nat tptp.nat_list_encode_rel))) (=> (= (@ tptp.nat_list_encode X4) Y) (=> (@ _let_1 X4) (=> (=> (= X4 tptp.nil_nat) (=> (= Y tptp.zero_zero_nat) (not (@ _let_1 tptp.nil_nat)))) (not (forall ((X5 tptp.nat) (Xs2 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X5) Xs2))) (=> (= X4 _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X5) (@ tptp.nat_list_encode Xs2))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))) (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))) (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))) (forall ((M tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N2))) (= (@ (@ tptp.linord738340561235409698at_nat (lambda ((X tptp.nat)) X)) _let_1) _let_1))) (forall ((I2 tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.upto I2) J))) (= (@ (@ tptp.linord1735203802627413978nt_int (lambda ((X tptp.int)) X)) _let_1) _let_1))) _let_5 (= tptp.positive (@ (@ (@ tptp.map_fu898904425404107465nt_o_o tptp.rep_Rat) tptp.id_o) (lambda ((X tptp.product_prod_int_int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int X)) (@ tptp.product_snd_int_int X)))))) (forall ((R3 tptp.real) (A tptp.real)) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.rcis R3) A)) (@ (@ tptp.rcis (@ (@ tptp.divide_divide_real tptp.one_one_real) R3)) (@ tptp.uminus_uminus_real A)))) _let_4 (forall ((R3 tptp.real) (A tptp.real) (N2 tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.rcis R3) A)) N2) (@ (@ tptp.rcis (@ (@ tptp.power_power_real R3) N2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) A)))) (forall ((X4 tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Y) (exists ((Q2 tptp.rat)) (let ((_let_1 (@ tptp.field_7254667332652039916t_real Q2))) (and (@ (@ tptp.ord_less_real X4) _let_1) (@ (@ tptp.ord_less_real _let_1) Y)))))) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X4) Y) Y)) (forall ((X4 tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X4) Y) X4)) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X4) Y) Y)) (forall ((X4 tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X4) Y) X4)) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X4) Y) Y)) (forall ((X4 tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X4) Y) X4)) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X4) Y) Y)) (forall ((X4 tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X4) Y) X4)) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X4) Y) Y)) (forall ((X4 tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X4) Y) X4)) (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X3 tptp.real)) (@ P X3)))) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X4) Y) Y)) (forall ((X4 tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X4) Y) X4)) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X4) Y) Y)) (forall ((X4 tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X4) Y) X4)) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int false) X4) Y) Y)) (forall ((X4 tptp.set_int) (Y tptp.set_int)) (= (@ (@ (@ tptp.if_set_int true) X4) Y) X4)) (forall ((X4 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int false) X4) Y) Y)) (forall ((X4 tptp.list_int) (Y tptp.list_int)) (= (@ (@ (@ tptp.if_list_int true) X4) Y) X4)) (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat false) X4) Y) Y)) (forall ((X4 tptp.list_nat) (Y tptp.list_nat)) (= (@ (@ (@ tptp.if_list_nat true) X4) Y) X4)) (forall ((X4 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int false) X4) Y) Y)) (forall ((X4 (-> tptp.int tptp.int)) (Y (-> tptp.int tptp.int))) (= (@ (@ (@ tptp.if_int_int true) X4) Y) X4)) (forall ((X4 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num false) X4) Y) Y)) (forall ((X4 tptp.option_num) (Y tptp.option_num)) (= (@ (@ (@ tptp.if_option_num true) X4) Y) X4)) (forall ((X4 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int false) X4) Y) Y)) (forall ((X4 tptp.product_prod_int_int) (Y tptp.product_prod_int_int)) (= (@ (@ (@ tptp.if_Pro3027730157355071871nt_int true) X4) Y) X4)) (forall ((X4 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat false) X4) Y) Y)) (forall ((X4 tptp.product_prod_nat_nat) (Y tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.if_Pro6206227464963214023at_nat true) X4) Y) X4)) (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int false) X4) Y) Y)) (forall ((X4 (-> tptp.nat tptp.int tptp.int)) (Y (-> tptp.nat tptp.int tptp.int))) (= (@ (@ (@ tptp.if_nat_int_int true) X4) Y) X4)) (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat false) X4) Y) Y)) (forall ((X4 (-> tptp.nat tptp.nat tptp.nat)) (Y (-> tptp.nat tptp.nat tptp.nat))) (= (@ (@ (@ tptp.if_nat_nat_nat true) X4) Y) X4)) (forall ((X4 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o false) X4) Y) Y)) (forall ((X4 tptp.produc6271795597528267376eger_o) (Y tptp.produc6271795597528267376eger_o)) (= (@ (@ (@ tptp.if_Pro5737122678794959658eger_o true) X4) Y) X4)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X4 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger false) X4) Y) Y)) (forall ((X4 tptp.produc8923325533196201883nteger) (Y tptp.produc8923325533196201883nteger)) (= (@ (@ (@ tptp.if_Pro6119634080678213985nteger true) X4) Y) X4)) _let_3 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 106.83/107.24 )
% 106.83/107.24 % SZS output end Proof for ITP221^3
% 106.83/107.24 % cvc5---1.0.5 exiting
% 106.83/107.25 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------